faculty of mathematics handbook, 1977...may i first welcome all those students who arc enrolled, or...

FACULTY OF MATHEMATICS

HANDBOOK 1977

THE UNIVERSITY OF NEWCASTLE

NEW SOUTH WALES 2308

LEGEND BUILDINGS DESIGNATION

ARTS/ADMINISTRATION A LG LOWEH GROUND FLOOR

G = GROUND FLOOIl I = FIRST FLOOf?

ADMINISTRATION LG, G & I CLASSICS LG COMMUNITY PROGRAMMES LG COMPUTING CENTRE G ENGLISH I HERSU I HISTORY LG LINGUISTICS I MODERN lANGUAGES G PHILOSOPHY I UNIVERSITY COUNSELLING SEI1VICE LG

MAIN LECTURE THEATRE 8 GEOLOGY C PHYSICS 0 LECTURE THEATRE E CHEMISTRY G BASOEN THEATRE H 810LOGICAL SCIENCES J AUCHMUTY LIBRARY L METALLURGY M ARCHITECTURE N DRAMA THEATRE P SOCIAL SCIENCES 1',S

GEOGRAPHY R COMMERCE S ECONOMICS S LEGAL STUDIES S

TEMPORARY BUILDINGS T MEOICINE T

MATHEMATICS V DRAMA V

BEHAVIOUHAL SCIENCES W EDUCATION W PSYCHOLOGY W SOCIOLOGY W

ENGINEEHING COMPLEX CHEMICAL ENGINEERING CIVIL ENGINEERING ELECTRICAL ENGINEERING ~lECHANICAL ENGINElIllNG ENGINEERING THEATRE

& CLASSROOMS UNION

CHAPLAINCY SEIMe, HEALTH SERVICE OVERSEAS STUOE~ITS

ADVISER

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NEW( OF AOV

FACULTY MATH

HAN 1

THE UNIVERSITY OF NEWCASTLE NEW SOUTH WALES 2308

ISSN 0313,,0010

Telephone -"' Newcastle 680401

One Dollar

May I first welcome all those students who arc enrolled, or are contemplating enrolling, in the Faculty of Mathematics. I assure you that the staff of the Faculty will always be ready to help with your proposed course and to discuss other academic matters with you.

Your desire to study mathematics is, I am sure, based on the couvio" tion that mathematics will be the most enjoyable of all those disciplines open to you~there can be no better reason. If you enjoy mathematics you will welcome the demands it makes upon you and your studies will be most rewarding. May I commend to you the essay Oll

Mathematics by Professor E. C. Zeeman in the book University Choice (edited by Klaus Boehm) Pl'. 261~270, Penguin 1966.

Although Faculties of Mathematics are not uncommon overseas, the Faculty of Mathematics at the University of Newcastle was the first jn Australia. This lead has now been followed by otller universities in Australia.

In constituting this Faculty the Council of the University recognised the central role of mathematics in most universities, and especially in Newcastle.

The Senate, before recommending the proposal to Council, bad OO!l8

sidered very carefully two crucial questions:

how best can the needs of students requiring studies in matb~, matics, supplementary and complementaxy to their principal subject of study, be met;

(Ii) how best can the needs of students reading mathematics a,s thei.r major discipline be met?

Senate conduded that the broad applicability and servicing aspect'> of mathematics constituted the strongest argument for the location. of mathematics in an independent faculty. Such a faculty would be able to arrange appropriate combined degree courses emphasising these areas of application. The needs of the student specialising in mathematics would also be best met by an independent faculty.

Thi.s handbook details the manner in which the Faculty of Mathematics is implementing the wishes of Council and Senate. The postgraduate course leading to the award of the Diploma in Computer Science, introduced in 1972, has proved particularly successful, and accor&" ingly the Faculty will, in 1977, offer an undergraduate subject, Computer Science II, which will probably lead to a subject, Computer Science HI, in 1978. A major innovation in ] 975 was the provision for concurrent studies leading to the award of two degrees. The first 01 these would be Bachelor of Mathematics; but the other may be Bachelor of Arts, Commerce, Metallurgy or Science.· Full details are given on Pl'. 11 et seq.

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A postgraduate Diploma in Mathematical Studies is now available. This Diploma will be awarded to candidates who have successfully completed one full time year of advanced work. The course is offered especially for those who graduated some years ago and wish to update and broaden their knowledge of modem developments in mathematics. Details of this Diploma appear on page 134.

The application of mathematics to physical problems has, of course, been well established for centuries, but mathematics is now used in a large number of other endeavours, and this number is rapidly increasing. This wide spectrum of applications is reflected in the provision for joint honours degrees and also in the membership of the Faculty Board, on which almost all depaI1ments of the University are represented.

The needs of students who wish to specialise in mathematics are met not only by the provision of topics in the conventional disciplines of pure mathematics, applied mathematics and statistics, but also by the provision of topics in computing science, operations research and other aspects of modem applied mathematics. It is confidently expected that the number of topics offered will increase as the University expands. Summaries of all topics offered in 1977 appear in this handbook.

Finally, may I encourage you to take an active part in other facets of University life. You should find there is time available for these general activities in addition to that required for your studies.

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R. G. KEATS

Dean (1976)

Faculty of Mathematics

CONTENTS

Faculty of Mathematics

The cololl\' balld 011 the spille of this JH[andbool, is the lining colo",' of Ihe 1100d worn by Bachclom of IV/athema!! .. of Ihis University

Page

3 6

7 8

10 11 14 15 16

16

19

20

21

21 25 39 52 71 78 81

111

113

114 115

118 118 123 131

134

135

137

139

140

Preface Faculty Staff

Bachelor of Mathcrnatics -- Requirements General Ordinary Degree Honours Degree Combined Degree Courses .schedule A Schedule B Schedule C

Notes on Combined Degree Courses

Knowlcdge of teachers in specific subjects

Prerequisites for curriculum & Method Subjects offered in the Diploma in Education

Note on subject entrics

Description of Subjects .schedule A ~- Part 1

Part II Part III Part IV

Schedule B - Part I Part II Part III

Schedule C

A Guide to studcnts enrolling in the Facuity of Mathcmatics

Diploma in Computer Science Schedule of Subjects

Requirements

Subjects overlapping in content Description of Subjccts - Group I

Group II Group III

Diploma ill Mathcmatical Studies

Master of Mathematics

Doctor 01 Philosophy .

Doctor 01 Science } '~Requirements

Research in the Department of Mathematics

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ill03n Professor J. A. Campbell

Sub·Dcan Associate Professor W. Brisley

Facuity Secretary Linda S. Harrigan MA'l'HIEMA'lf'J[(C§ Professors J. A. Campbell, MSc(Adelaidc), SM(Massachllsctts Institute of Technology), MA(Cam-

bridge) D.PhiJ(Oxford) R. G. Keats, ESc, PhD(Adelaide), FIMA, FASA R. W. Robinson, MA(Dartmollth), PhD(Cornell) (Head of DepaI'lment)

Associate Professors W. Brisley, BSc(Sydney), MSc(New South Wales), PhD; DipEd(Ncw England) C. A. Croxton, BSc(Lcicester), MA, PhD (Cambridge) J. R. Giles, EA(Sydney), PhD; DipEd(Sydncy) A. J. Guttmann, MSc(Melbourne), PhD (New South Wales) W. D. Wallis, ESc, PhD (Sydney)

Senior Lecturers V. Ficker, l'rom.Mat, CSc, RNDr(Comenius) R. W. Gibberd, ESc. PhD (Adelaide) W. 1'. F. Lau, ME(New South Wales), PhD(Sydncy), MAIAA T. K. Sheng, BA(Marian College), BSc(Malaya & London), PhD (Malaya) E. R. Smith, MSc(Melbourne), PhD(London) P. K. Smrz, PromPhys, CSc, RNDr(Charles)

I,ectmers R. F. Berghout, MSc(Sydney) J. G. Couper, ESc. PhD (New England) R. B. Eggleton, BSc, MA(Melbourne), PhD(Calgary) M. J. Hayes, EA(Cambridge) D. L. S. McElwain, BSc(Queensland), PhD(York (Canada) ) W. Summerfield, ESe(Adelaide), PhD(Flil1ders) R. J. Vaughan, BSe, MEngSc, ME(Ncw South Wales), PhD(Adclaide), FSS W. P. Wood, BSc, PhD(Ncw South Wales)

Senior Tutors C. J. Ashman, BA, LittB(New England) G. W. Southern, BA(New South Wales), DipCompSe

Tutor C. S. Dibley, EMath

Honor,ll'Y Associate I. L. Rose, EE(Sydney), PhD (New South Wales)

Computer Programmers E. R. Cheek, BMath A. Nymcyer, BMath, DipCompSe

Professional Officer Joan A. Cooper, BMath, PhD

Departmental Office Stuii' Judy A. Halliday, ESc, Dip&! Anne M. McKim Joanne L. Duggan Julie H. Latimer Vicki M. Piller Students are invited to discuss theIr interests in a particular branch of matlwmaties with members of the Department who are working in that branch. The appropriate staff members for each branch may be detennined by referellce to the section entitled "Research in the Dcparlnlent of Mathelnatics" p. 140.

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REQUIREMENTS FOR THE DEGREE OF BACHELOR OF MATHEMATICS

SECTION I - GENERAL 1. Definitions

In these Requirements, unless the contrary intention appears, "the Faculty" means the Faculty of Mathematics and "the Faculty Board" means the Faculty Board of the Faculty of Mathematics.

2. Grading of Degree The degree of Bachelor of Mathematics may be conferred either as an ordinary degree or as an honours degree.

3. Approval of First Enrolment A candidate when enrolling in the Faculty for the first time shall report in person to the Dean, or his nominee, to have his enrol~ ment for that year approved.

4. Timetable Requirements No candidate may enrol in any year for any combination of subjects which is incompatible with the requirements of the timetable for that year.

5, Annual Examinations The Annual Examinations shall normally be held at the end of third term and shall be conducted by means of written examinations supplemented by such oral or practical work testing as the ex~ aminers think fit.

6, Special Examinations A candidate may be granted a special examination in accordance with the provisions of By-Law 5.9.3.

7. Examination Grades The results of successful candidates at Annual Examinations and Special Examinations shall be classified: High Distinction, Distinction, Credit, Pass.

8, Withdrawal (a) A candidate may withdraw from a subject only by notifying

the Secretary to the University in writing of his withdrawal within seven days of the date of withdrawal.

(b) A candidate who withdraws after the sixth Monday in second term from a subject in which he has enrolled shall be deemed to have failed in that subject. However, such a candidate may apply to the Dean, who, after consultation with the Head of Department concerned, may allow him to withdraw without penalty.

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9. Subjects Offered (a) A candidate shall select at least five of his subjects from the

Schedules appended to these Requirements and shall comply with the rules relating to the selection of subjects set ont in the Schedule.

(b) Up to four subjects from those offered in other degree courses in the University may, with the permission of the Dean, be counted as qualifying subjects for the degree. When approving a subject, the Dean shall determine whether the subject concerned shall be classified as Part I; Part II; Part III; or Part IV.

10. Relaxing Clause In order to provide for exceptional circumstances arising in par~ ticular cases, the Senate, on the recommendation of the Faculty Board, may relax any requirement.

SECrION II -~- THE ORDINARY DEGREE

11. A Subject (a) To complete a subject qualifying towards the degree, herein·,

after called a subject, a candidate shall attend such lectures, tutorials, seminars, laboratory classes and field work and submit such written work as the Department concerned shall require.

(b) To pass a subject a candidate shall satisfy the requirements of the previous clause and pass such examinations as the Faculty Board concerned shall require.

12. Degree Patterns (a) Except as provided in Section IV of these Requirements,

to qualify for the ordinary degree a candidate shall pass nine subjects provided that: 0) at least five are subjects in Mathematics; Oi) at least two are Part III Mathematics subjects; and

(iii) no more than five are Part I subjects. (b) Notwithstanding the provisions of subsection (a) of this

clause, a candidate may substitute for one Part III Mathematics subject another Part III subject from the Schedule of Subjects with a substantial mathematical content (Schedule B).

13. Prerequisites and Corequisites No candidate may enrol in a subject unless he has satisfied the prerequisites and corequisites for that subject.

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14. Progression (a) Progression in the course is by subject. A full-time student is

required to pass four subjects and a part··time student is required to pass two subjects in the first two years of his course. A parHime student is required to pass four subjects in the first four years of his course.

(b) The following restrictions on yearly course loads shall apply. The Dean may, in individual cases, relax restrictions 0), (ii), (iii), but only if he is satisfied that the academic merit of the candidate warrants such relaxation.

(i) No one academic year is to involve more than four subjects.

(ii) If four subjects are taken in anyone year, at least three of them must be Part I subjects, and none may be a Part HI subject.

(iii) If three subjects are taken in anyone year, not more than two of them may be Part III subjects.

15. Time Requirements Except with the special permission of the Faculty Board, a candidate shaH complete the Requirements for the ordinary der,ree within nine calendar years of the commencement of the degree course. A candidate who has been granted standing in recognition of work completed elsewhere shall be deemed to have commenced his degree course from a date to be determined by the Dean.

16. Standing The Faculty Board may grant standing under the following con· ditions. (a) A candidate may be granted standing in recognition of work

completed in another tertiary institution or faculty, provided that:

(i) the subjects for which credit is given shall have a reasonable correspondence with those offered in the Faculty;

Oi) an undergraduate of another tertiary institution shall not receive credit for more than four subjects;

(iii) a graduate or diplomate of another tertiary institution or faculty shall not receive credit for more than four subjects and if granted credit may not include as a qualifying subject any subject equivalent to one counted towards his previous qualification.

(b) Notwithstanding the provIsIon of section (a) (i) of this clause, a graduate or undergraduate of another tertiary institution may be given credit for subjects not offered for the degrce of Bachelor of Mathematics in the University of Newcastle provided that: (i) the candidate complics with all other conditions of these

Requiremen ts; (ij) the candidate has his proposed pattern of course approved

at the time at which the concession is granted and does not depart from the proposed pattern without the approval of the Dean.

17. Preparation jor Honours (a) A candidate who wishes to enrol in an Honours course must

obtain the approval of the Head of the appropriate Department, or Departments, by the dates specified.

(b) A candidate wishing to enrol in an Honours course will be required to complete extra work concurrently with work for the ordinary degree.

SECTION III -. THE HONOURS DEGREE

18. Honours in Mathematics To qualify for admission to Honours in Mathematics a candidate shall:

(i) have satisfied the requirements for admission to the ordinary degree; the subjects Mathematics IlIA and Mathematics IIlE must be included;

(ii) have completed additional work concurrently with his ordin~ ary degree, as prescribed by the Department of Mathematics;

(iii) pass the subject Mathematics IV.

19. Combined Honours To qualify for admission to combined Honours, a candidate shall:

(i) have satisfied the requirements for admission to the ordinary degree and have included in his course such prerequisite subjects as may be prescribed for admission to the combined Honours subject or subjects;

(ii) have completed such additional work concurrently with his ordinary degree as may be prescribed by the Department of Mathematics and the other Department concerned;

(iii) pass the combined Honours subject or subjects (Schedule C).

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20. Time Requirements (a) Except with the special permIssIon of the Faculty Board, a

candidate for Honours shall complete the requirements within five years from the commencement of his degree course, provided that where it is deemed practical to allow a part-time student to become a candidate for Honours, the corresponding period shall be seven years. A candidate wishing to proceed to Honours who has been given standing in recognition of work completed elsewhere shall be deemed to have commenced his degree course from a date determined by the Dean.

(b) The Dean may permit a part-time candidate for Honours to complete the Honours subject or subjects over two successive years.

21. Classes oj Honours There shall be three classes of Honours, namely Class I, Class n and Class III. Class II shall have two divisions, namely Division (I) and Division (II).

22. Medal In each Honours subject, including combined subjects, the Faculty Board may recommend the award of a University Medal to the most distinguished candidate or candidates of the year.

23. Equivalent Honours (a) On the recommendation of a Head of a Department in the

Faculty and with the permission of the Dean, a graduate who, in the disciplines concerned, has not completed a fOUlth year Honours subject either as a full-time or a part-"time student at this or at any other Australian university, may enrol in fourth year Honours as a full-time or a part-time student.

(b) Such a graduate who has completed all of the requirements of fourth year Honours shall be issued with a statement to this effect by the Secretary; the statement shall indicate the Honours level equivalent to the standard achieved by the student in completing fourth year Honours.

SECfION IV - COMBINED DEGREE COURSES

24. General A candidate may complete the Requirements for the degree of Bachelor of Mathematics in conjunction with another Bachelor's degree by completing a combined course approved by the Faculty Board of the Faculty of Mathematics and the other Faculty Board concerned provided that:

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0) admission to a combined coun;c shall normally be at tbe end of the first year and shall be subject to the approval of the Deans of the two Faculties concerned;

(ii) admission to comhined courses wiII be restricted to students with an average of at least Credit level;

(iii) the Deans of both Faculties shall certify that the work in the combined degree course is no Jess in quantity and quality than if the two courses were taken separately;

(iv) the Requirements for both degrees shall be satisfied except as provided below.

25. Arts/Mathematics (a) A candidate shall comply with all the proVIsIOns of the

Requirements for the degree of Bachelor of Arts other than Clause 12 and all the Requiremcnts for the dcgrec of Bachelor of Mathematics.

(b) To qualify for admission to the ordinary degrecs of Bachelor of Arts and Bachelor of Mathematics, a candidate shall pass fourteen subjects, five of which shall be rvlathematics I, Mathematics JIA, Mathematics HC, Mathematics IlIA and either Mathematics IUB or a Part HI subject chosen from Schedule B of the Schedule of subjects approved for the degree of Bachclor of Mathematics and the remainder of which shall be chosen from the other subjects listed in the Schedule of subjects approved for the degree of Bachelor of Arts, provided that: 0) not more than three subjects from Group II of the

Schedule of subjects approved for the degree of Bachelor of Arts may be counted;

(ii) not more than five Part I subjects out of thc total fourteen may be counted;

(iii) at least three subjects shall be Part HI subjects; (iv) a candidate counting Psychology IIlC shall not count

either Psychology IlIA or Psychology nIB; (v) a candidate counting Economics nIC shall not count

either Economics lIlA or Economics lIIB.

26. Mathematics/Science After completing the first year of study towards either the degree of Bachelor of Mathematics or the degree of Bachelor of Science including a pass at a satisfactory level in the subject Mathematics I, a candidate may enrol in a combined Mathematics/Science course. A candidate who has enrolled in sllch a combined course shall qualify for admission to the ordinary degrees of Bachelor of Mathematics and Bachelor of Science by passing fourteen subjects as follows:

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(a) five subjects, beingiVlathematics 1, Mathematics IIA, Mathematics HC, Mathematics IlIA and either Mathematics nm or a Part HI subject chosen from Schedule B of the Schedule of Subjects approved for the degree of Bachelor of Mathe"" matics and

(b) six subjects chosen from the other subjects listed in the Schedule of Subjccts approved for the degree of Hachelor of Science and

(c) three subjects chosen, with the approval of the Deans of the Faculties of Mathematics and Science, from the subjects approved for any of the degreG courses offered by the University provided that:

(i) the number of Part I subjects shall not exceed six; Oi) the minimum llumber of Part HI subjects shall be

three; (iii) a candidate counting Psychology lIC shall not be

entilled to count either Psychology IIA or Psychology UB;

(iv) a candidate counting Psychology IJIC shall not be entitled to cOllnt either Psychology lIlA or Psychology HIS;

(v) a candidate counting Economics HIC shall not be entitled to count either Economics lIlA or Economics WB.

27" Mathematics/Metallurgy After completing a successful first year of study towards either the degree of Bachelor of Mathematics or the degree of Bachelor of Metallurgy, a candidate may enrol in a Mathematics/ Metallurgy course. A candidate who has enrolled in such a combined course shall qualify for admission to the ordinary degrees of Bachelor of Mathematics and Bachelor of Metallurgy by passing Mathematics I, Mathematics UA, Mathematics HC, Mathematics IlIA and either Mathematics nIB or a Part III subject chosen from Schedule B of the SchedUle of Subjects approved for the degree of Bachelor of Mathematics, and by satisfying all the Requirements for the degree of Bachelor of Metallurg)', except that: (a) Metallurgical Computations shall be replaced by Mathematics

lIB, which may be taken in two parts, each of three terms duration;

(b) Mathematics I shall be replaced by Chemistry I or Geology I or any other subject approved by the Deans;

(c) No Mathematics subjects shall be taken as electives.

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28. Commerce/Mathematics After completing the first year of study towards either the degree of Bachelor of Commerce or the degree of Bachelor of Matherne. atics, including a pass at a satisfactory level in the subject Mathematics I, a candidate may enrol in a combined Commerce/ Mathematics course. A candidate who has enrolled in such a combined course shall qualify for admission to the ordinary degrees of Bachelor of Commerce and Bachelor of Mathematics by passing seventeen subjects, five of which shall. be Mathemati.cs T, Mathematics IIA, Mathematics lIC, Mathematics IlIA and either Mathematics IIlB or a Part III subject chosen from Schedule B of the Schedule of Subjects approved for the degree of Bachelor of Mathematics and the remainder of which shall by themselves satisfy the Requirements for the degree of Bachelor of Commerce.

Subject

PART I

Mathematics I

PART II

Mathematics IIA Mathematics lIB

Mathematics lIC

PART III

Mathematics IlIA

Mathematics lIIB

PART IV

Mathematics IV

SCHEDULE A

MATHEMATICS SUBJECTS

Remarks including Prerequisites and Corequisites

It is assumed that students have studied Higher School Certificate Mathematics at the two-unit level or higher

Prerequisite Mathematics I Prerequisite Mathematics I The Dean may permit a candidate to take this subject in two parts, each of three terms duration Prerequisite Mathematics I Pre- or Corequisite Mathematics IIA

Prerequisites Mathematics HA & Mathematics HC

Pre- or Corequisite Mathematics IlIA

Prerequisites Mathematics nlA & Mathematics nIB

COMPUTER SCIENCE SUBJECT PAR1'l!I

Computer Science II Prerequisite Mathematics I

SCHEDUl.E B

SUBJECTS WITH A SUBSTANTIAL MATHEMATICAL CONTENT

Subject

PART I

Civil Engineering 1M

Materials Science I

PART n Civil Engineering lIM

Psychology lIC

PART III

Accounting IIIC

Biology IIlB


It is assumed that students have studied Higher School Certificate Mathematics at the two.,lInit level or higher together with either MlIltistrand Science at the four-unit level or Physics at the two-unit level and Chemistry at the two-unit level It is assumed that students have studied a Higher School Certificate Science subject at two-unit level or higher Corequisites Mathematics I, Physics IA

Prerequisites Civil Engineering IM & Mathematics I

Prerequisites Mathematics I, Psychology 1. A candidate counting Psychology IlC shall not be entitled to count Psychology ITA or Psychology lIB

Prerequisites Mathematics IIA & Mathematics HC & either Accounting IIA or Accounting lIB

Prerequisites Mathematics IIA & Mathematics lIC & either Biology IIA or Biology IIB

Chemical Engineering HIC Prerequisites Chemical Engineering J1, Mathematics IIA & Mathematics lIC

Civil Engineering HIM

Communications & Automatic Control

(including Topics E & F) Prerequisites Civil Engineering HM, - Mathematics IIA & Mathematics lIC

(including Topic E) Prerequisites Mathematics IIA &

Mathematics lIC (including Topics C, D & E)

1 A candidate with better than pass level in Physics I and Chemistry I and the ability to write real situations in mathematical (erms and to read around his subject, could complete the components of Chemical Engineering lIIC without Chemical Engineering I. and may. after interview, be granted exemption by the Head of the Department of Chen1ical Engineering.

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Subject

Digital Computers & Automatic Control

Economics nrc

Geology mc

Industrial Engineering I

Mechanical Engineering IIIC

Physics IlIA

Psychology IIIC


Prereqllisites Mathematics IIA & Mathematics HC (including Topics C, D & E)

Prerequisites Economics IIA, Mathematics IIA & Mathematics IIC

Prerequisites Physics lA, Mathematics HA, Mathematics lIC & Geology IIA

Prerequisites Mathematics IIA & Mathematics lIC

Prerequisites JV! athematics IIA & Mathematics lIC (including Topics E, F & H)

Prerequisites Physics II, Mathematics IIA & Mathematics IIC

Prerequisites 1977-Mathematics IIA, Mathematics lIC and one of Psychology lIA or Psychology lIB. 1978·-·Mathematics lIA, Mathematics lIC and either Psychology lIA and Psychology IIB 01' Psychology ne.

SCHEDULE C

COMBINED HONOURS SUBJECTS

Mathematics!Physics IV

Mathematics! Psychology IV

Prerequisites Mathematics IlIA & Physics IlIA

Prerequisites Mathematics IlIA & Psychology HIC

NOTES ON COMBINED DEGREE COURSES

ARTS! MATHEMATICS

The details for the combined course follow simply from the Requirements for each degree. Each degree requires nine subjects so the combined degree requires 18 subjects less four subjects for which standing may be given, thus the combined degree should contain 14 subjects. The Bachelor of Mathematics requires Mathematics I, Mathematics lIA, Mathematics nc, Mathematics IlIA and either Mathematics HIB or a Part III subject from Schcdule 13 of the Requirements. This leaves nine subjects which must clearly satisfy the Requirements for the Arts degree.

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The course could be pursued in the following manner:

Mathematics I and thrcc other Part I subjects,

Y@1'I]' If]! three Part n subjects including Mathematics HA and Mathematics He and another subject which should be a Part I or Part n subject approved for the degree of Bachelor of Alis,

Y~,' ill Mathematics IlIA plus two other subjects which must in" c1ude at least one Part HI subject,

Y(,):i1,g JrV either Mathematics nm or a Schedule B subject from the Requirements for Bachelor of Mathematics plus two other subjects which will complete the Requirements for the Arts degree.

Commerce! Mathematics

The details of the combined course in Commerce and lVlathematics follow from the Requirements for each degree. The combined course should contain Mathematics I, Mathematics JIA, Mathematics HC, Mathematics lIlA and either Mathematics Hm or a Part III subject from schedule B of the Schedule of Subjects approved for the degree of Bachelor of Mathematics. This leaves twelve subjects which must clearly satisfy the Requirements for the Commerce degree, The course could be pursued in the following manner:

Mathematics I IIntroductory Quantitative Methods Economics I Accounting I

YC17f II Mathematics IIA Mathematics lIC Economies & Commerce Group A or B

Year U][ Mathematics IlIA Economics & Commerce Group A or B Economics & Commercc Group B Economics & Commerec Group 13

Yeaf IV Mathematics BIB or a Part III Schedule B subject from the Requirements for the B.Math.

Economics & Commerce Group B Economics & Commerce Group B

Year V Economics & Commerce Group C Economics & Commerce Group C Economics & Commerce Group C

!Introductory Quantitative Methods is no! a compulsory subject for students who have successfully completed Mathematics lID Topic H and who proceed directly to Economic Statistics II. Statistical Analysis, Quantitative Business Analysis or Com~ mercial Electronic Data Processing.

MATHEMA TICS/ SCIENCE

The details for the combined course follow simply from the Requirements for each degree. Each degree requires nine subjects so the combined degree requires 18 subjects less four subjects for which standing may be given, thus the combined degree should contain 14 subjects. The Bachelor of Mathematics requires Mathematics I, Mathematics IIA, Mathematics nc, Mathematics IlIA and cither l\1athem· atics JIIB, or a Part III subject from Schedulc B of the Requirements. This leaves nine subjects which must clearly satisfy the Rcquirements for the Science degree.

The course could bc pursued in the following manner: Yellr I Mathematics 1 and three other Part 1 subjects. Yelll' III three Part II subjects including Mathematics IIA and

Mathematics He and another Part I subject, Year m Mathematics IlIA plus two other subjects which must in"

clude at least one Part III subject, Year IV either Mathematics JIm or a Schedule B subject from the

Requirements for Bachelor of Mathematics, plus two other subjects which will complete the Requirements for the Science degree.

MA THEMA TICS/ METALLURGY

The details of the combined course in Mathematics and MetaJlurgy follow simply from the Requirements for each degree. The combined degree course should contain Mathcmatics I, Mathematics HA, Mathematics HC, Mathematics IlIA and either Mathematics lIIB or a Part III subject from Schedule B of the Schedule of Subjects approved for the degree of Bachelor of Mathematics, and all the subjects satisfying the Requirements for the dcgree of Bachelor of Metallurgy, except that:

(a) Metallurgical Computations shall be replaced by Mathematics HB, which may be taken in two parts, each of three terms duration;

(b) Mathematics I shall be replaced by Chemistry I or Geology I or any other subject approved by the Deans;

(c) No Mathematics subjects may be taken as electives.

The course could be pursued in the following manner: Ycm' l! Mathematics I, Physics lA, MEI2I, ChEIO!, Met141,

Met151, Met181, Metl82, Metlll, and two of MEl31, MEl 11 and ME1l2

YI).IIl!' n Mathematics HAl, Mathematics HB Part II, Met22l, Met212, Met213, Met231, Met2.52, Met241, Met261, Met271 and one of Chcmistry I, Geology I or any other subject approved by the Deans

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Year Ul Mathematics no, Mathematics HB Part Ill, Met301, Met361, ChE331, 6 of Met 300 subjects, Elective P and 2 units of Elective 112

Year XV Mathematics IlIA and either Mathematics nm, or a Schedule B Part III subject from the Requirements for the degree of Bachelor of Mathematics and 4 units of Elective 112

Year V Met401, Met407" and 2 units of Elective III

1 Mathematics IIA -- Topics A. C, D, B, Mathematics lIB, Part I - Topics F, G. Mathematics lIB, Par! II _. Topics n, J. Mathematics lIe - Topics H, I, K, L.

2 No Mathematics subject may be taken as an elective.

KNOWLEDGE OF TEACHERS IN SPECIFIC SUBJECTS

In 1975 the Senate of the University established a number of committees to advise on the level of University studies required to maintain an informed competence in particular disciplines. These enquiries were particularly directed towards secondary school teaching but their application is, in most cases, quite general. The advice tendered by the committees was accepted by Senate and is reproduced below.

Discipline

Classics

Commerce & Eoonomics

EngIish

Geography

MruthematiC'J

Modern I~1;nguages

Scicnoe

Level of Study Recommended

A major in Latin or Greek with some studies in both

Two years (preferably rhree) of Economics including Microeconomics and Macroeconomics; Accounting I and Legal Studies I

A major in English, together with one additional subject chosen from English, Drama or Linguistics

Geography UA, Geography lIB, Geography IlIA. An Honours Degree in Geography would be of considerable benefit

At least two, and preferably thr<:<;, courses in History

l\bthenmtics IlTA as a minimum Ideally an Honours Degree in the foreign language

proposed, together with a period of residenoe in the appropri3Jte foreign coun~ry

A Part III subject in the relevaJ1lt science, together with some breadth ill scientific disciplines

19

Prerequisites fm· Curriculum ami Method Subjects Offered in the Diploma in Education

Students in the Faculty of Mathematics who a.re intending to study for the postgraduate Diploma in Educ:ation' may be interested in the following prerequisite subjects for that Diploma. r.t will be noted that any graduate holding the degree of Bachelor of Mathematics possesses ,the prerequisites required for the Diploma in Education and the prerequisites for at least one curriculum and method subject, namely Mathematics.

These prerequisites are stated in terms of subjects of the University of Newcas,tle. Applicants with qualifications from other universities, whose courses of study have included subjects which are deemed for this purpose to provide an equivalent foundation, may be admitted by the Dean of the Pacul1y of Education on the recommendation of the Head of the Depart-· ment of Education.

Subjects

(a) English

(b) History

(c) Modern Languages

(d) Classics

(e) Geography

(f) Commerce/ Economics

(g) Social Science/ Studies

(h) Mathematics

Prerequisites

(i) A Part I and a Part II subject in English:

and (ii) one additional subject from English, Linguistics

or Drama

A Papt II subject in History

A Part III subject in French or German

A Part III subjeot in Greek or Latin

A Part II subject in Geography

B.A. including Economics IIA or B. Com. including Microeconomics and Macro

economics

Out of Economics, Geography, History, Psychology, Sociology, Legal Studies and Economic History

one subject at Part II level

and

two other subjects a.t Part I level

(i) A,t least four subjects in Mathematics for the degree of B.A., B.Math., or B.Sc.

or

(ii) A degree in a field of applied science, with experience in the application of mathematics

20

Subjects

(i) Science

Prerequisites

(i) Three subjects from the disciplines of Biology, Chemistry, Geology and Physics, or related fields of applied science, such subjects 10 be drawn from at least two of the disciplines of Biology, Chemistry, Geology and Phys>ics

and (ii) at least one 01he1 subject drawn from any of the

above or from Mathematics, Geography, or Psychology

(j) Primary No specific prerequisites.

Note A Part n subject assumes as a prerequisite a pass in a PUTt I subject in the same discipline. A Part III ,;ubject assumes a pass in a Part I subject and a Part II subject in the same discipline.

NOTE ON SUJU-ECT EN'll'R1E§

Subject outlines and reading lists are set out in a standard format to facilitate easy reference. An explanation is given below of some of the technical terms used in this Handbook.

(a) Prerequisites are subjects which must be passed before a candidate enrols in a particular subject. The only prerequisites noted for topics are any topics or subjects which must be taken before enrolling in the particular topic. To enrol in any subject which the topic may be part of, the prerequisites for that subject must still be satisfied.

Where a prerequisitc is marked "(advisory)", lectures will be given on the assumption that the subject or topic has been completed as indicated.

(b) Corequisites for suhjects are those which the candidate must pass before enrolment, or be taking concurrently. Corequisites for topics are thosc which the candidate must take before enrolment, or be taking concurrently.

(c) Examination - see note on progressive assessment below.

(d) Texts are essential books recommendcd for purchase.

(e) References are books relevant to the subject or topic which, however, need not be purchased.

SCHEDULE A

Preliminary Notes The Department of Ma.thcrn<ttics offers and examines subjects. Each subject is compos~d of topics, each topic consisting of about 27 lectures and 13 ·tutorials throughout the year. Each of the Part I, Papt II, and Part III Mathematics subjects consists of four topics. For Mathematics I, there

21

IS no choice of topics; for Mathematics llA, un, He there is some choice a,vailable to SItudents; for Mathematics IlIA and urn there is a wider ch{)ice. No topic may be c{)uJ]ted twice in making up distinct subjects. (Students who passed S'Ome mathematics subjects bef{)re this arrangemcIJlt of subjects was introduced should consult the "transHion arrangements" set out on p.155 of the 1970 Faculty of Arts' handbook, and p.76 of the 1973 Faculty {)f Ma.(hema,tics ha.ndbook. Note that the "code letters" for the, topics may vary slightly from year to year.) The PaDt II subject Computer Science II is taught and examined jointly by the Department of Electrical Engineering and the Depaptment of Mathematics. In Computer Science II, there is no choice of topics.

Progressive Assessment From time to time during the year students will be given assign·· ments, tests, etc, Tho student's performance in this work will be taken into account in the following manner. (a) For the implementation of By-law 5.4.1.1 which deals with

unsatisfactory progress. A copy of this By-law appears in the General Supplement supplied with this Handbook.

(0) Where a student's performance during the year has been better than his performance in the final examination, then the former will be taken into account in determining his final result. On the other hand, when a student's performance during the year has been worse than his performance in the final examination, then his performance during the year will be ignored in determining his final result.

PAIU l! SUBJECT

Prerequisites Nil

Hours 4 lecture hours ancI 2 tutorial hours per week

Examination Two 3~hour papers

Content Topics AN - Real Analysis

AL-Algebra CA ._- Calculus

NM - Numerical Mathematics

PART I TOPICS

Topic AN --" Real Analysis ~~ M. J. Hayes

Prerequisites

Hours

Nil

1 lecture hour per week and 1 tutorial hour per fortnight

Content Real Numbers. Sequences and series. FUIlctions of one real variable, continuity, differentiability, integrability. Power series, Taylor Series.

Text

R.eferences Apostol, T. Spivak, M.

Nil

Calculus Vol. 1 2nd edn (Blaisdell 1967) Calculus (Benjamin 1967)

Topic AL ~~~ Algebra R. B. Eggleton

Prerequisites

Hours

Content

Nil


Introduction to basic algebraic objects and ideas. Matrices, permutations, complex numbers. Linear Algebra: vectorspaces, homomorphisms, matrices, determinants; algorithms for solution of equations; rank, nullity: eigenvectors and eigenvalues; applications various.

Text Brisley, W.

R.eferences Liebeck, H.

Lipschutz, S. McCoy, N.

Troppcr, M. A.

A Basis for Linear A 1gebra (Wiley 1973)

Algebra for Scientists and Engineers (Wiley 1971)

Linear Algebra (Schaum 1968) Introduction to Modern Algebra (Allyn &

Bacon 1968) Linear Algebra (Nelson 1973)

Topic CA -~~ Calculus ~ R. F. Berghout

Prerequisites

Hours

Content

Nil


Vector geometry in three dimensions. Revision of differentiation and integration of polynomials and trigonometric functions. Differentiation of rational functions and of implicit and parametrically defined functions. Definition and properties of logarithmic, exponential and hyperbolic functions. Integration by parts and by substitution tech~ niques. Integration of rational functions. First 'OHler separable and

23

linear differential equations. Second order linear differential equations with constant coefficients. Conic sections 'and simple three-dimensional geometry of curvcs and surfaces. Partial differentiation. Tangency.

Text

References Apostol, T. Ayres, F.

Greenspan, H. D. & Benney, D. J.

Hille, E. & Salas, S.

Kaplan, W. & Lewis, D. J.

Nil

Calculus Vol. 1 2nd edn (Blaisdell 1967) Calculus (Schaum Outline Series, McGraw

Hill) Calculus--an Introduction to Applied l\IJathe

mafics (McGraw-Hill 1973) First Year Calculus Internat. Textbook Series

(Blaisdell 1968) Calculus and Linear Algebra Vol. I

(Wiley 1970)

Topic NM~· Numerical Mathematics -- R. J. Vaughan

Prerequisites

Hours

Content

Nil


Introduction to computers, flowcharts and Fortran coding. Elementary data analysis: calculations of sample moments of discrete distributions and programming of these operations. Introduction to statistical analysis and numerical analysis with computer illustrations. The wdting of successful computer programs is a required part of this topic.

Texts Blatt, J. M.

or

Bellamy, C. J. & Whitehouse, L. G.

and Hoel, P. G.

References Greenspan, H. D.

& Benney, D, J. Ralston, A.

Wilkes, M. V.

Basic Fortran IV Programming; Version MIDITRAN (Computer Systems of Australia Pty Ltd 1969)

An Introduction to Computer Programming in Fortran (monrcs Fortran) (Monash Univ. Computer Centre 1976)

Introduction to Mathematical Statistics 4th cdn (Wiley 1971)

Calculus-an Introduction to Applied i1.1athematics (McGraw-HilI 1973)

A First Course in Numerical Analysis (McGraw-Hill 1965)

A Short Introduction to Numerical Analysis (Cambridge U.P. 1971)

PART IIi §UlfUEC'f§

The Department of Mathematics offers three Pm't II Mathematics subjects, Students whose course restriots them to one subject must study Mathe" mancs lilA or Matbematics liB. The subject Mathematics HA is a pre·· or corequisite for Mathematics nc, and UA and IIC together a prerequisite for any Pad In subject, so students wishing to take two Part II subjects would normally choose Mathematics HA and nco Students taking 'all three of the Part n subjects would study all twelve of the topics listed below,

Summaries and booklisls for these topics arc given on page 27 et seq, of this handbook. The Department of Mathematics also offers jointly with the Department of Electrical Engineering, the subjeot Computer Science II. No student taking this subject may choose the Mathematics Topic F as a component of another Part II subjeot. A description and course outline of Computer Science II will be found on page 36 e.t seq.

List oj Topics for Pari Jl Mathematics subjects Topic

A Mathematical Models B C

Complex Analysis Calculus and Vector Calculus

D Linear Algebra B

F G

H I

J

Differential Equations and Integral Transforms

Numerical Analysis and Computing Fourier series, Partial Differential

Equations and Special Functions Probability and Statistics Topic in Statistics e,g. Applications of Statistics Topic in Applied Mathematics e.g. Mechanics

K Topic in Pure Mathematics e.g. Group Theory

L Analysis of Metric Spaces

Corequisite or Prerequisite Topic

C C

C

C C

H

C,E

The selection rules and definitions of the Pllrt n subjects follow.

662100 MathemajJics lilA

Prerequisite

Hours

Mathematics I

4 lecture hours and 2 tutorial hours per week

25

Examination Each topic is examined separately

Content

Topics B, C, D, and E. In exceptional circumstances and with the consent of the Head of the Department, one topic from A, F, G, or H may be substituted for B. Additional substitutions may be allowed in the case of candidatcs who have passed the subjects Mathematics lIB.

662200 Mathematics Im

Prerequisite

Hours

Examination

Content

Mathematics I


Each topic is examined separately

Four topics chosen from A to H and approved by the Head of the Department. In exceptional circumstances and with the consent of the He~d of the Departme~t one or more of thc topics, I, J, K or L may be mcluded. Students 111 the Faculty of Mathcmatics may, with the consent of the Dean, take Mathematics lIB in two parts each con" sisting of two topics. . ,

662300 Mathematics lIe

Prerequisite

Pre- or Corequisite

Hours

Examination

Content

Mathematics I

Mathematics IIA

4 lecture hours and 2 tutorial hours per wcek


Either topics G, J, K and L or topics H, I, K and L. Subject to the cons~nt of the Head of the Department one topic from A to J may be substituted for one of the topics I or 1.

Notes 1. Stud~r;ts. v.:hose cour~c. includes ~ Schedule B subject may have their choice of topics

rcstnclcd iurther than 1S set out In the rules above.

2. ~tude~~ts whose cOl~rse~ in.c1uc1e yhy~ic:. III!: arc a[]vi5c.d to include t~)pics C, E, G, H Hl thcir MathematIcs 1 aIt II subject::.. thIS may reqllIre the ll:iC of the substitution rules.

3. StudCI:ts who passed a Part II Mathematics subject prior to 1974 and \vl1o wish to tnke further Part II Iviathcmatics subjects should note that the tt'pic coded "i," in 1974, 1975, 1976 and 1977 corresponds to. the topic coded "A" in previous years. SuCh, students may reqUIre specwJ permISSIOn for their selection of Part Ii topics and should consult with the Head of the Dellartment. '

26

PART n TOPICS

662101 Topic A -~~ Mathematical Model§ ~"' D. L. S. McElwain

Prerequisite or Corequisite

flours

Examination

Content

Topic C

1 lecturc hour pcr week and 1 tutorial hour per fortnight

One 2-hour paper

This topic is designed to introduce students to the idea of a mathematical model. Four or five realistic situations will be treated beginning with an analysis of the non-mathematical origin of the problem, the formulation of the mathematical model, solution of the mathematical problem and interpretation of the theoretical results. For example, models involving applications of operations research, probability and differential equations will be developed.

Text

R.eferences Kemeny, J. G. &

Snell, J. L. Noble, B.

Rapoport, A. & Chammah, A. M.

Taha, H. A.

Wagner, H. M.

Nil

Mathematical Models in Social Sciences (Blaisdell 1963)

Applications oj Undergraduate Mathematics in Engineering (M.A.A.!Collier .. MacmilIan 1967)

Prisoner's Dilemma (Michigan U.P. 1965)

Operations Research - an Introduction (Macmillan 1971)

Principles of Operations Research (Prentice-Hall 1969)

662102 Topic n ,~- Complex Analysis ~ R. B. Em;lelon

Prerequisite or Corcquisite

Hours

Examination

Content

Topic _C

1 lecture hour pCI' weck and 1 tutorial hour per fortnight

One 2-hour paper

Complex Numbers -- polar, cxponcntial forms. Functions of a complex variable-limit, continuity, derivative. Analytic Functions-

27

Cauchy"Riemann equations, HarmOjlic functions. Elemcl1(Rry Functions "-' exponential, trigonometric, hyperbolic, logarithmic, generalised power. Integration·- Cauchy integral theorem Rnd formulae; multiplyconnected domains. Sequences and Series - power, Taylor and Laurent series. Calculus of Residues _._. singUlarities, residues, zeros and poles of Meromorphic Functions, real integrals. Conformal Rcpresen·· tat ion -·linear and bilinear transformations. Application of analytic functions to the theory of flows.

Text Spiegel, M. R.

R.eferences Grove, E. A. &

Ladas, G. Paliouras, J. D.

Polya, G. & Latta, G. E.

Theory and Problems of Complex Variables (McGraw-HilI 1964)

Introduction to Complex Variables (Houghton Mifflin 1974)

Complex Variables for Scientists and Engineers (Macmillan 1975)

Complex Variables (Wiley 1974)

662103 Topic C··~Cakuhm lIud Vector Cllkulus~E. R. Smith

Prerequisites

Hours

Examination

Content

Nil


One 2 .. hour paper

Functions of several variables: graphical representation; domain and range; limits and continuity. Differential calculus of functions of several variablcs including: partial derivatives; total differentials and the tangent plane, directional derivatives and grad; chain rules, implicit functions, transformations and Jacobians; Taylor's theorem; optimiz~ ation of functions of two variables and Lagrange multipliers. Integral calculus of functions of several variables: the iterated integral; change of variable. Line and surface integrals: Green's, Gauss' and Stokes' theorems. Vector functions of vectors: vector fields; the gradient field, conservative vector fields; div. Gauss' Theorem in vector form; curl. Stokes' Theorem in vector form; the operator 'Del'.

Text Greenspan, H. D. &

Benney, D. J. or Marder, L.

Calculus - an Introduction to Applied Mathematics (McGraw-Hill 1973)

Calculus of Several Variables (Allen Unwin 1972)

28

Marder, L. or Spiegel, M. R.

R.eferences Courant, R.

Kaplan, W. Keane, A. &

Senior, S. A. Kreyzig, E.

O'Neill, P. V.

Vector Fields (Allen Unwin 1972.)

Theory and Problems of Advanced Calculus (Schaum Outline Series, McGraw-Hill 1963)

DifJerential and Integral Calculus Vols I & II (Blackie 1949)

Advanced Calculus (Addison~Wesley 1952) Mathematical Methods (Science Press 1961)

Advanced Engineering Mathematics (Wiley 1962)

Advanced Calculus (Collier«MacrnilIan 1975)

662104 Topic D Linear Algebra "~~ W. Brisley

Prerequisites Nil

Hours

Examination

Content

1 lecture hour per wcek and 1 tutorial hour per fortnight

One 2~hour paper

Review, extension and application of some material in Topic AL. Inner product spaces, orthogonality, and applications. "Canonical forms" for matrices (and linear maps and operators). Eigenvalues, eigenspace;; and spectral theory. Duality. Various applications and algorithms. "Linear programming". Functions of matrices, and matrix manipulations. Applications of linear algebra and of matrix represen .. tations.

Text

Lipschutz, S.

References Ayres, F. Brisley, W. Lange, L. H. Nering, E. D.

Pipes, L. A.

Trapper, Mary A.

Lineal' Algebra (Schaum 1968)

Matrices (Schaum 1962) A Ba:iis for Linear Algebra (Wiley 1973) Elementary Linear Algebra (Wiley 1968) Lineal' Algebra and Matrix Theory (Wiley

1964) Matrix Methods for Engineering

(Prentice-Hall 1964) Linear Algebra (Nelson 1969)

29

662201 Topic E ~~". Differential Equatiolls llnd Integral Transforms W. Summerfield

Prerequisite 01' Corequisite

Hours

Examination

Content

Topic C

1 lecture hour per week and 1 tutorial hOllr per fortnight

One 2-hour paper

First order linear equations. Second order linear equations with constant coefficients. General solution for second order linear homogeneous and nonhomogeneous equations, initial value problems. Laplace transform and initial value problems for second order linear equations. Series solutions for Legendre's equation and Bessel's equation of integral order. Systems of linear equations with constant coefficients; general solution, matrix exponential. Higher order linear equations. Introduction to nonlinear equations. Some of the examples and exercises will be set up by modelling physical problems; the dimensional homogeneity of the derived equations will be emphasised. Particular attention wiil be paid to the interpretation of solutions of such equations.

Text Boyce, W. E. &

DiPrima, K C. Elementary Differential Equations and

Boundary Value Problems (Wiley 1969)

662202 Topic F ~ Numerkal Analysis amI Computing~D. L. S. McElwain

Prerequisites

Hours

Examination

Content

Nil


One 2-hour paper

Revision and extension of Fortran programming. Sources of error in computation. Solution of a single nonlinear equation. Interpolation and the Lagrange interpolating polynomial. Finite differences and applications to interpolation. Numerical differentiation and integration including the trapezoidal rule, Simpson's rule and Gaussian integration formulae. Numerical solution of ordinary differential equationsRunge-Kutta and predictor-corrector methods. Numerical solution of linear systems of algebraic equations. Applications of numerical methods to applied mathematics, engineering and the sciences will be made throughout the course.

30

Text

References Balfour, A. &

Beveridge, W. T. Carnahan, B. et a!. Contc, S. D. &

de Boor, C. Kreitzberg, C. B. &

Shneiderman, B.

Ralston, A.

Nil

Basic Nllmerical Analysis with Fortran (Hcinenlann 1973)

Applied Numerical Methods (Wiley 1969) Elementary Numerical Analysis (MeGraw

Hill 1972) Thc Elemcnts of Fortran Style (Harcourt,

Brace & Jovanovich 1972) A First Course in Numerical Analysis

(McGraw-Hill 1965)

662203 Topic G ~- FOluier Series, Pllrtial Differential Equations lImi Special FlmclioJ[1§ R. J. Vaughan


Hours

Examination

Content

Topic C

1 lecitll'e hour per week and 1 tutorial hour per fortnight

One 2-hour paper

Outline of derivations of partial differential equations; inadequacy of equations alone to specify solutions; boundary conditions; classification. Solutions using characteristics, solution by separation of variables. Fourier series, computation of cosine and sine series, convergence properties of Fourier series, representation of functions by Fourier series, diiIerentiation ,:nd integration of Fourier series. Solution of partial diiIerential equations using Fourier series. Solution of partial differential equations with two-dimensional space co-ordinates, separation of variables in polar and rectangular co-ordinates. The Bessel equation and Bessel functions. Gamma and Beta functions. Solution of partial differential equations with three dimensional space coordinates, separation of variables in spherical co-ordinates and other co-ordinate systems, spberical harmonics, Legendre equations and Legendre polynomials.

Texts Boyce, W. E. &

DiPrima, R. C. and Sneddon,I.N.

Elementary DifJerential Equations and Boundary Value Problems (Wiley 1969)

FOllrier Series (Routledge 1961)

31

Referenc.es Berg, P. W. &

McGregor, J. L. Churchill, R. V.

K.aplan, W. Keane, A. &

Senior, S. A. Piaggio, H. T. H.

Sneddon,!. N.

Sneddon, 1. N.

Stephenson, G.

Weinberger, H. F.


Hours

Ex .. mination

Content

Elementary Partial Differential Equations (Holden-Day 1966)

Fourier Series and Boundary Value Problems 2nd edn (McGraw-Hill 1963)

Advanced Calculus (Addison-Wesley 1965) Mathematical Methods (Science Press 1961)

An Elementary Treatise on Differential Equations and their Applications (Bell 1971)

Elements of Partial Differential Equations (McGraw-Hill 1957)

Special Functions oj Mathematical Physics and Chemistry 2nd edn (Oliver & Boyd 1961)

An Introduction to Partial Differential E'quations jor Science Students 2nd edn (Longman 1970)

A First Course in Partial Differential Equations (Blaisdell 1965)

R. G. Keats

Topic C


One 2-hour paper

This topic is an introduction to the theory of probability and statistics. No previous knowledge of probability or statistics will be assumed. The lectures will include a discussion of the following. Finite probability space, simple random variable, expectation, mean, variance, covariance, correlation, independence, frequency function, distribution function, joint frequency function, moments and binomial variates. Error propagation. Tchebichev inequality and the weak law of large numbers. Elementary random variables, Poisson's theorem; conditional probability; Bayes' theorem, tree dia&'Tams. Continuous random variables, frequency function, expectation, joint frequency function, moments. Normal variates. Classification of experimental data, histo~ grams, empirical moments, measures of location and scatter. Statistical :inference, hypothesis testing, types of error, power function, sampling theory, maximum likelihood estimation; frequency functions of the mean (X), difference of two means CX~y), and the statistics X2, S2, T and F with applications.

32

Text Freund, J. E. or Boel, P. G.

References Allendoerfer, C. B. &

Oakley, C. O. Feller, W.

Gnedenko, B. V.

Bine, J. & Wetherill, G. B.

Kolmogorov, A. N.

Lipschutz, S.

Loeve, M.

Mendenhall, W. & Scheaffer, R. L.

Moran, P. A. P.

Mathematical Statistics 2nd edn (Prentice~Hall 1971)

Introduction to Mathematical Statistics 4th edn (Wiley 1971)

Principles of Mathematics Chapter 12 (McGraw-Hill 1955)

An Introduction to Probability Theory and its Applications Vol. I 3rd edn (Wiley 1968)

The Theory of Probability Chapters I & II (Chelsea 1962)

A Programmed Text in Statistics Vols. 1, 2, 3, 4 (Chapman & Hall 1975)

Foundations oj the Theory of Probability (Chelsea 1950)

Theory and Problems 0/ Probability (Schaum 1968)

Probability Theory pp.l-18 (Van Nostrand 1960)

Mathematical Statistics with Applications (Duxbury Press 1973)

An Introduction to Probability Theory (Oxford u.P. 1968)

662301 Topic l! ~ Topic in Statistics c.g. Applications of Sfatisticrr-R. W. Gibberd


Hours

Examination

Content

Topic H


One 2-hour paper

This topic is an introduction to some methods of statistics and its app!ic.ations. The l~ctuTes will include the following topics-descriptive statIstICS, standarchzation of data, linear regression and correlation, introductory multiple linear regression, markov chains, analysis of categorized data, rank statistics, goodness of fit tcsts and nOIl~ parametric statistics.

Text Nil

33

References Draper, N. R. &

Smith, H. Kemeny, .T. G. &

Snell, .T. L. Noether, G. E.

A pplied Regression A nalysis (Wiley 1966)

Finite Markov Chains (van Nostrand 1967)

Introduction to Statistics: A Nonparametric Approach 2nd edn (Houghton/Mifflin 1976)

662302 Topic J .~~~ Topic in Applied Mathematic/; e.g. Mecbanics ~ C. A. Croxton

Prerequisites or Corequisites

Hours

Examination

Content

Topics C and E

1 lecture hom per week and 1 tutorial hom per fortnight

One 2-hour paper

Mass and momentum - Newton's First Law, Force, Newton's Second Law, Conservation of Energy, rotating frames of reference transformation from one reference frame to another. Centrifugal' forces. Rigid bodies, centres of mass, angular momentum, moments of i~ertia, conservation of angular momentum, gyroscopes. Principle of ~lrtual wor~ and d'Alembert's principle, Hamilton's principle, general~ lzed co-ordll1ates, Lagrange's equation.

Text Nil

References

Feynman, R. F. et aJ. The Feynman Lectures in Physics Vol. I (Addison-Wesley 1971)

Sommerfeld, A.

Spiegel, M. R.

Mechanics - Lectures in Theoretical Physics Vol. 1 (Academic Press 1965)

Theory and Prohlems of Theoretical Mechanics (Schaum 1967)

662303 Topic K ~. Topic in Pure Matliel!Uatirn e.g. GrollI' Theory ~ R. F. Berghout

Prerequisites

Hours

Examination

Nil


One 2-hour paper

34

Content Groups, subgroups, isomorphism, direct product. Permutation groups, groups of linear transformations and matrices, isometries, symmetry groups of regular polygons and polyhedra. Cosets, Lagrange's theorem, normal subgroups, isomorphism theorems, correspondence theorem. Orbits, stabilisers, and their applications to the Burnside-Polya counting procedure and classification of finite groups of isometrics in R2 or R3.

Text

References Baumslag, B. &

Chandler, B. Budden, F. J.

Coxeter, H. S. M. Rotman, J. J.

WeyJ,H.

Nil

Group Theory (Schaum 1968)

The Fascination of Groups (Cambridge UP. 1972)

Introduction to Geometry (Wiley 1961) The Theory of Groups: an Introduction

(Allyn & Bacon 1966) Symmetry (Princeton V.P. 1952)

6623414 Topic L - Anmysis @f Meta'le Splices ~~, M. J. Hayes

Prerequisites

Hours

Examination

Content

Nil

1 lecture hom per week and 1 tutorial hour per fortnight

One 2-hour paper

Metric spaces and their topology. Convergence, completeness. Continuity. Compactness. Function spaces, uniform convergence, differentiation and integration of sequences and series of functions; approximation of continuous functions by polynomials. Connectedness.

Text

References Goldberg, R. R. Simmons, G. F.

White, A. .T.

Nil

Methods oj Real Analysis (Blaisdell 1964) Introduction to Topology and Modern Analysis

(McGraW-Hill 1963) Real Analysis (Addison-Wesley 1968)

35

66240() Computer Science IJ[

Prerequisite

Hours

Examination

Content Topics

Mathematics I

168 hours of lectures, tutorials and practical work as listed below

See components descriptions below

SI-Introduction to Structuring of Information SP-Systematic Programming

ML-Computer Structure: Machine and Assembly Languages F-Numerical Analysis and Computing

Topic Sl~· Intmdlldioll to Structuring of Infommtioll ~ J. A. Campbell and P. J. Moylan

Prerequisite

Corequisite

Hours

Examination

Content

Mathematics I

Topic SP

1 lecture hour per week and 1 tutorial hen per fortnight

One 2-hour paper

Influence of structuring of information on design of programming languages. Data structures: lists, trees, queues, deques and stacks. Examples of and methods for implementing these structures. Storage allocation for complex data items. Scatter storage and hash addressing. Elementary string processing, and list processing. Searching and sorting. A description of several sorting algorithms and comparison of their efficiencies.

Text Elson, M.

References Dahl, D. J. et al. Horowitz, E &

Salmi, S. Katzan, H. Jr

Data Structures (Science Research Associates 1975)

Structured Programming (Academic J 972) Fundamentals oj Data Structures (Computer

Science Press 1976) Introduction to Computer Science (Petrocellic.

Charter 1975)

36

Knuth, D. E.

Wirth, N.

The Art oj Computer Programming Vols. I - Fundamental Algorithms, II - Semi-numerical Algorithms,

III - Sorting and Searching (Addison·Wesley 1968, 1969, 1973)

Algorithms + Data Structures = Programs (Prentic<!-Hall 1976)

Topic SP .~~ Systematic Pmgramming J. A. Campbell and P. J. Moyl~.Il

Prerequisite

Hours

Examination

Content

Mathematics I

1 lecture hour and t tutorial or practical work hour per week

One 2-hour paper

The case for high level programming languages. The formal definition of the syntax of high level languages. An overview and comparison of several high level languages, including FORTRAN, ALGOL 60, PL/ I and COBOL. Comparison of compiler languages and interpretive languages. A brief introduction to list processing languages and macrogenerators. Structured programming: its objectives and the techniques used to achieve them. Modular design, top-down programming, good coding style. The role of 'goto' constructs, conditional statements, looping, 'case' statements. The virtues and faults of existing programming languages. Procedures, co-routines, re-entrancy. Recursive programming. Approp~ riate and inappropriate uses of recursion.

Text Elson, M.

Rejerences Bates, F. &

Douglas, M. L. Dahl, O. J. et al. Guttmann, A. J.

International Computers Ltd


Katzan, H. 11'

Concepts oj Programming Languages (Science Research Associates 1973)

Programming Language! One 3rd edn (Prentice~Hall 1975)

Structured Programming (Academic 1972) Programming and Algorithms (Heinemann

1977) ALGOL Programming Manual

1900 series COBOL Manual

Introduction to Computer Science (Petrocelli·· Charter 1975)

37

Kernighan, B. W. & Plauger, P. J.

Kreitzberg, C. B. & Shneiderman, B.

Wirth, N. Yourdan, E. J.

Software Tools (Addison-Wesley 1976)

The Elements of FORTRAN Style (Harcourt, Brace, Jovanovich 1972)

Systematic Programming (Prentice-Hall 1973) Techniques of Program Structure and Design

(Prentice .. Hall 1975)

Topic IVIL ~ Computer Stmcture: Machine and Assembly Lauguages K. K Saluda

Prerequisite

Hours

Examination

Content

Mathematics I

H lecture and practical work hours per week

Progressive assessment and final examination

Basic computer elements and peripherals, representation and organiza~ tion of information, number systems and arithmetic, logical operations. Hardware components, processor structure, addressing modes and instruction set, machine-language programming, subroutines, usc of the stack. Assembly: pseudo··ops, macros, recursion and re-entrancy, relocation, linking and loading. System software: assemblers, linkers, loaders, dumpers, interpreters, simulators, compilers. Lectures will be supplemented with practical assignments using the PDP~11 computer.

Texts Eckhouse, R. H. Jr

References Chu, Y. H.

Donovan, J. J. Stone, H. S.

Minicomputer Systems Organisation and Prowamming (PDP-II) (Prentice-Hall 1975)

Processor Handbook PDP-Il /20

Computer Organization and Micro Programming (Prentice-Hall 1972)

Systems Programming (McGraw-Hill 1972) Introduction to Computer Organization and

Data Structures (McGraw-Hill 1972)

Topic F~· Numerical Analysis and Computing ~ D. L. S. McElwain

Prerequisite Mathematics I

Hours

Examination

Content


One 2-hour paper

Revision and extension of Fortran programming. Sources of error in computation. Solution of a single nonlinear equation. Interpolation and the Lagrange interpolating polynomial. Finite differences and applications to interpolation. Numerical differentiation and integration including the trapezoidal rule, Simpson's rule and Gaussian integration formulae. Numerical solution of ordinary differential equations-Runge-Kutta and predictor-corrector methods. Numerical solution of linear systems of algebraic equations. Applications of numerical methods to applied mathematics, engineering and the sciences will be made throughout the course.

Text

References Balfour, A. &

Beveridge, W. T. Carnahan, B. et al. Conte, S. D. &

de Boor, C. Kreitzberg, C. B. &

Shneiderman, B. Ralston, A.

Nil

Basic Numcrical Analysis with Fortran (Heinemann 1973)

Applied Numerical Methods (Wiley 1969) Elementary Numerical Analysis (McGraw~

Hill 1972) The Elemcnts of FORTRAN Style (Harcourt,

Brace & Jovanovich 1972) A First Course in Numerical AnalYsis

(McGraw-Hill 1965)

P ART HI SUBJECTS

The Mathematics Depaltment offers two Part rn subjects, ea.ch comprising four topics chosen: from the list below. Students wishing to proceed to Honours in Mathematics are required to take both these subjects. Students wishing to proceed to Combined Honours are required to take Mathematics IlIA together with the appropriate subject from Schedule B. Students proceeding to Honours will also be required to study additional topics as prescribed by the Heads of the Departments concerned. Passes in both Mathematics IlIA and IIIC are prerequisite for entry to Mathematics rnA, and Mathematics rnA is pre- or corequisite for Mathematics IllS. It will be assumed that students taking a third-year subject in 1977 have already studied topics C, D, E, K, L in their PaIt II subjects. Students from other faculties who wish 10 enrol in particular Part rn topics, according to the course schedules of those Faculties, should consult the particulars of the list below, and should consult the lecturer concerned. In particular, the prerequisites for subjects may not all apply to isolated topics.

39

Summaries of these topics, together with texts and references, appear on page 41 et seq. of this handbook.

List of Topics for Pari III Mathematics

Topic General Tensors Variational Methods Mathematical Logic Differential and Integral Equations Partial Differential Equations Fluid Dynamics Probability and Statistics Geometry Group Theory

Prerequisite Corequisite C

C, E

K,L E E

B, C, E H C

D, K C, F

D

M N o P PD

Q R

S T TC U V W X Y

Theory of Computing Operations Research Measure Theory and Analysis of Normed Rings and Fields

Integration Linear Spaces

L L

D,K

z

Topic in Applied Probability e.g. Information Theory

Mathematical Principles of Numerical Analysis

C,D,H

C, D, E

The selection rules and definitions of the Part m subjects follow.

663100 Matbcmaticll InA

Prerequisites

Hours

Examination

Content

Mathematics IIA & lIe



A subject comprising four topics, which must include 0, and at least one of P, PD, Q, R, U or Y. In addition, students taking this subject will be required to complete an essay on a topic chosen from the history or philosophy of Mathematics.

663200 Mathematics um

Prerequisite Mathematics lIlA or Corequisite

Hours 4 lecture hours and 2 tutorial hours per week

40

Examination Each topic is examined scparately

Content A subject comprising four topics chosen from thc sixteen listed above.

Notes 1. In order to take both Mathematics IlIA and Mathematics IUB, a student must study

eight topics from M to Z above with the restriction that Topic 0, and at least one of P, PD, Q, R, U or Y must bc included iu these eight topics.

),' Students whose course includes a subject from Schedule B may have their choice of topics further restricted.

3. Students aiming to take Mathematics IV may be required to undertake study of more topics than the eight comprising the two Part HI subjects,

PART HI TOPICS

663101 Topic M ~~~ General Tensors ~ W. T. F. Lan

Prerequisite

llours

Examination

Content

Topic C

1 lecture hour per week and 1 tutorial hour pel' fortnight

One 2··hour paper

Vector spaces: oasis, change of oasis; dual spaces; dual basis; contravariant and covariant components. Point spaces. Tensor algebra. Tensor calculus: derivatives and differentials; Christoffel symbols; differcntial operators in curvilinear coordinates. Riemannian spaces: tangential and osculating Euclidean mctrics; Geodesics; curvature tensor; Riemann-Christoffel tcnsor, Applications: dynamics; continuum mechanics.

Text

References Lichnerowicz, A. Sokolnikoff, I. S.

WeIls, D. A.

Willmore, T. J.

Nil

Elements of Tensor Calculus (Methuen 1962) Tensor Analysis--Theory and Applications to

Geometry alld Mechanics of Continua (Wiley 1964)

Theory and Problems of Lagrangian Dynamics (McGraw-Hill 1967)

An Introduction to Differential Geometry (Oxford 1972)

663102 Topic N .o~~. Vadational Method§ ~ W. P. Wood

Prerequisites

Hours

Topics C & E


41

Examination One 2-hour paper

Content Introduction - statement and formulation of relevant problemsfunctionals. Euler-Lagrange equation - fixed boundaries - weak variations - corner conditions -- the second variation --- functionaIs involving derivatives of higher order --- several indcpendent variables "- parametric representation. Moveable boundaries ..... transversality conditions .-. Hilbert's integral. Strong variations. Isoperimetric problems. Direct methods of solving variational problems - numerical solutions in the simplest problem _.- Rayleigh-Ritz method·- Galerkin method. Applications - dynamics of particles -- vibrating string·Sturm-Liouville eigenvalue-eigenfunction problems - vibrating membrane - groundstate of the helium atom - nonlinear problems-growth models in economics.

Text Elsgolc, L. E.

References Arthurs, A. M.

Hadley, G. & Kemp, M. C.

Mikhlin, S. G.

Weinstoek, R.

Calculus of Variations (Pergamon 1963)

Complementary Variational Principles (Pergamon 1964)

Variational Methods in Economics (North-Holland 1971)

Variational Methods in Mathematical Physics (Pergamon 1964)

Calculus of Variations (MeGraw-Hill 1952)

663103 Topic 0 ~ Mathematical Logic ~-~ R. W. Robinson

Prerequisites

Hours

Examination

Content

Topics K & L


One 2-hour paper

Introduction: inferenee rules as a formalisation of deduetive proeesses; sets; axiomatic theories; predicates. The sentential calculus, predicate calculus and predicate calculus with equality. First order theories; consistency, independence and completeness. Examples will be taken from the usual axiomatically defined Mathematical systems, and GadeI's undecidability theorem will be diseusscd.

Text

Enderton, H. B. A Mathematical Introduction to Logic (Academic 1972)

42

References Crossley, J. et a!. Hayden, G. E.

& Kennison, J. F. Kleene, S. C. Mendelson, E.

What is Mathematical Logic? (Oxford 1972) Zermelo-Fraenkel Set Theory (Merrill 1968)

Mathematical Logic (Wiley 1967) Introduction to Mathematical Logic (Van

Nostrand 1964)

663'104 Topic P~Diffcrcntial and Integral Equations·~~J. G. Couper/ W. T. F. Lau

Prerequisite

Hours

Examination

Content

Topic E

1 lceture hour per week and 1 tutorial hour per fortnight

One 2-hour paper

Differential equations: Stability for linear systems with eonstant coefficients. Existenee of solutions of non-linear systems, uniqueness and properties of solutions. Stability for non-linear systems. Integral equations: existence and uniqueness theorems. Fredholm '8 equation and its solutions. Hilbert-Schmidt theory.

Text Sanehez, D. A.

References Cochran, J. A.

Courant, R & Hilbert, D.

Kanwal, R. P.

Lovitt, W. V.

Ordinary Differential Equations and Stability Theory: an Introduction (Freeman 1968)

The Analysis of Linear Integral Equations (McGraw~Hill 1972)

Methods of Mathematical Physics Vol. I (Interscienee 1953)

Linear Integral Equations: Theory and Techniques (Academic 1971)

Linear Integral Equations (Dover 1950)

663108 Topic PH ~ Partial Differential Equations ~ W. T. F. Lau

Prerequisite

Hours

Examination

Topic E

1 lceture hour per week and 1 tutorial hour per fortnight

One 2-hour paper

43

Content First order equations and second order equations. The Laplace equa" don, the wave equation and the diffusion equation. Integral transforms, Green's function and other mcthods. Applications on fluid mechanics, heat flow, potential theory, etc.

Text

References Carroll, R. W.

Courant, R. & I-Iilbert, D.

Croxton, C. A Epstein, B.

Friedman, A.

Kellogg, O. D. Licberstein, H. M.

Weinberg{:r, H. F.

Nil

Abstract Methods in Partial Di,Oerential Equations (Harper & Row 1969)

Methods of lv1athematical Physics Vol. n Partial Differential Equations (Interscience 1966)

Introductory Eigenphysics (Wiley 1974) Partial Differential Eqll(/tio/1s·~··(/n Introduction

(McGraw-Hill 1962) Generalised FUllctiolls alld Partial DiOerential

Equations (Prenlice-l-}all 1963) Foundations of Potential Theory (Dover 1953) Theory oj Partial DiOerential Equations

(Academic 1972) A First Course in Partial DWerential Equatiol1s

with Complex Variables and Transjorm Methods (Blaisdell 1965)

663105 Topic Q ~ Fluid Dynamics ~ W. Summerfield

Prerequisites

Hours

Examination

Content

Topic B, C & E

1 lecture hour per \-veck: anel 1 tutorial hour per fortnight

One 2-hour paper

Basic concepts: continuum, density, pressure, viscosity. Derivation of governing equations for the motion of an ideal (non .. viscous) fluid. Investigation of simple flows; particularisation to cases where motion irrotational, and further, to instances where the flow can also be considered two dimensional (e.g., surface wave motion). Introduction to the powerful complex variable method of solution for the latter type of motion. Comparison between ideal and real fluid flows; boundary layers.

Text Nil

44

References Batchelor, G. K.

Coulson, C. A. Curle, N. &

Davies, H. J. Milne-Thompson,

L. M. Rutherford, D. E.

663106 Topk n

Prerequisite

Hours

Examination

Content

All Introduction to Fluid Dynamics (Cambridge U.P. 1967)

Waves (Oliver & Boyd 1958) Modern Fluid Dynamics Vol. 1 (Van Nostrand

1968) Theoretical Hydrodynamics (Macmillan

1962) Fluid Dynamics (Oliver & Boyd 1959)

Topic H


One 2-hour paper

This topic consolidates and extends the study of probability and statistics made in Topic H. Itcms studied include random vectors, generating functions of random vectors. Multinomial and multivariate normal random vectors. Sampling theory, the T and F distributions. Point and interval estimation. Decision theory, Bayes decision rules. Hypothesis-testing, Neyman-Pearson Lemma, likelihood ratio. Cochran's theorem. Linear statistical estimation. Linear regression analysis, normal regression theory. Analysis of variance. The complete two and three-factor experimental designs and the latin square experimental design. If time permits basic results in factor analysis will be discussed.

Text Zelma, P. W.

References Johnson, N. L. &

Leone, F. C.

Kendall, M. G. & Stuart, A.

Lindgren, B. W.

Sveshnikov, A. A. ( cd.)

Wilks, S. S.

Probability Distributions and Statistics (Allyn & Bacon 1970)

Statistics and Experimental Design in Engineering and the Physical Sciences (2 Vols) (Wiley 1964)

The Advanced Theory oj Statistics (3 Vols) (Griffin 1958-1966)

Statistical Theory 2nd edn (Collier-Macmillan 1968)

Problems in Probability Theory, Mathematical Statistics and Theory oj Random Functions (Saunders 1968)

Mathematical Statistics 2nd edn (Wiley 1962)

45

663107 Topic S ~~, Geometry ~~~ T. K. Sheng

Prerequisite

Hours

Examination

Content

Topic C

1 lecture hour per week and 1 tutorial hour pel' fortnight

One 2-hour paper

Euclidean geometry: axiomatic and analytic approach, transformations, isometries, decomposition into plane reflections, inversions, quadratic geometry. Geometry of incidence: the real projective plane, invariance, projective transformation, conics, finite projective planes, field planes.

Text

References Albert, A. A. &.

Sandler, R. Ayres, F. Dorwart, H. L.

Fishback, W. T.

Gaus, D.

Moise, E. E.

663201 Topic T

Prerequisites

Hours

Examination

Content

Nil

An Introduction to Finite Projective Planes (Holt, Rinehart & Winston 1968)

Projective Geometry (Schaum 1967) The Geometry of Incidence (Prentice-Hall

1966) Projective and Euclidean Geometry (Wiley

1962) Transformations and Geometries (Appleton

Century Crofts 1969) Elementary Geometry from an Advanced

Standpoint (Addison~Wesley 1963)

Group Theory.~ W. Brisley

Topics D & K


One 2-hour paper

Structure of groups: Sylow theorems for finite groups; Series decomposition of groups; soluble groups; nilpotent groups. Finite and infinite abelian groups. Free groups, and presentation of groups in terms of generators and relations.

46

Text Baumslag, B. &.

Chandler, B. OR Macdonald, I. D.

Reference Rotman, J. J~

Group Theory (Schaum 1968)

The Theory oj Groups (Oxford V.P. 1968)

The Theory oj Groups (Allyn & Bacon 1966)

663209 Topic 'irC ~ Theory of Computing -~ A. J. Guttmann

Prerequisites

Hours

Exmninatioll

Content

Topics C & F


One 2-hour paper and assignments throughout the year

This course will interest science, mathematics and engincering students who are interested in the theoretical foundations of computer science. Mathematical Models of Computers: Finite Automata are introduced as a first approximation to a model of a compuler and some of its properties arc studied. Three equivalent models of computation are then introduced and compared. These models are Turing machines, computer machines, and recun:ive functions. Some of the limits of models of computation (ul1solvabilily) are also discussed. Algorithmic Aspects of Computation: How "good" an algorithm do we have for performing some computation? Is there any way in which we can say that some algorithm is the "best" for accomplishing some task? Program Correctness: Methods of program verification are introduced and discussed. Formal Languages and Parsing: Methods of systematically and formally specifying the syntax of programming languages are dis~ cussed. Some parsing mcthods are introduced.

Text

References Aho, A. V., Hopcroft,

1. E. & Ullman, J. D.

Hopcroft, J. E. & Ullman, J. D.

Wirth, N.

Nil

The Design and Analysis oj Computer Algorithms (Addison-Wesley 1974)

Formal Languages and Their Relation to Automata (Addison-Wesley 1969)

A 19oritlzms + Data Structures = Programs (Prentice-Hall 1976)

47

663202 Topic U ~.~ Operations 'Research c_·, W, D, Wallis

Prerequisites

Hours

Examination

Content

Topic D

1 lecture hour per week and 1 tutorial hour per fortni~ht

One 2-hour paper

Topics covered will be chosen from ~ames theory; linear programming; integer programmillg; dynamic programming; networks and flows; activity analysis; inventory theory.

Text

References Bellman, R. E. &

Dreyfus, S. E. Dantzig, G. B.

Ford, L. & Fulkerson, D.

HaIl, M. Jr Hillier, F. S. &

Lieberman, G. J. Luce, R. D. &

Raifia, H. Taha, H. A.

Vajda, S.

NiL Duplicated notes will be distributed.

Applied Dynamic Programming (Princeton U.P. 1962)

Linear Programming and Extensions (Princeton U.P. 1963)

Flows in Networks (Princeton u.P. 1962)

Combinatorial Theory (Blaisdell 1967) Introduction to Operations Research (Holden~

Day 1967) Games and Decisions (Wiley 1957)

Operations Research - An Introduction (Macmillan 1971)

Mathematical Programming (Addison-Wesley 1961)

663203 Topic V ~-- Measure Theory and Integration ~ V. Ficker

Prerequisite

Hours

Examination

Content

Topic L - Analysis of Metric Spaces


One 2-hour paper

S.ets and classes of sets: riugs, algebras, a-rings, a-algcbras, generated nngs and uoorings. Measures and outer measures: extension of measures, Lebesgue measure, measurable functions, combinations of measurable functions .. Integration, integrable simple fUnctions, integrable fUllctions, Lebesque lI1tegral, convergence theorems. Lp spaces, Fubini's theorem.

48

Text

References Bartle, R. G. Burkill, J, C. de Barra, G.

Halmos, P. R. Kolmogorov, A. N. &

Fomin, S. V.

Nil

The Elements of Integratioll (Wiley 1966) The Lebesglle Integral (Cambridge U.P. 1961) Introduction to !>feasure Theory (Van

Nostrand 1974) Measure Theory (Van Nostrand 1950) Introductory Real Analysis (Prentice-Hall 1970)

663204 Topic W ."~" Analysis of Normed Linear Spaces " .•. T. K. Sheng

Prerequisite

Hours

Examination

Content

Topic L -~ Analysis of Metric Spaces

1 lecture hour per wcck and 1 tutorial hour per fortnight

One 2-hour paper

Topology, basic conccpts, bases of neighbourhood, countability axioms, complete metric spaces. Contraction mappings, fixed point theorem. Baire's theorem. Supremum-norm spaces, inncr product spaces, Banach spaces. Linear mappings, isomorphisms, opcn mappings. Dense linear subspaces. Sequences of lincar mappings. Uniform bounded ness theorem. Linear functionals. Finite dimcnsional spaces. Convexity. Convex series. Closed graph theorems. Extension and separation theorcms. Hahn-Banach theorcm. Dual spaces, conjugate mappings. Hilbert space, orthonormal sets.

Text

References Banach, S.

Brown, A. L. & Page, A.

Giles, J. R.

Giles, J. R.

Kolmogorov, A. N. & Fomin, S. V.

Liustemik, L. A. & Sobolev, U. J.

Nil

Theories des Operations Lineaires 2nd edn (Chc1sea)

Elements of FUllctional Analysis (Van Nostrand 1969)

Analysis of Metric Spac.es (University of Newcastle)

Analysis of Normal Linear Spaces (University of Newcastle)

·Elemellts oj the Theory of FUllctions and Functional Analysis Vol. I (Grayloch 1957)

l','lements of Functional Analysis (Frederick Unger 1961)

49

Simmons, G. F.

Taylor, A. E.

Wilansky, A.

Introduction to Topology and Modern Analysis (McGraw-Hill 1963)

Introduction to Functional Analysis (Wiley 1958)

Functional Analysis (Blaisdell 1964)

663205 Topic X ~,~ Rings and Fields ~~ M. J. Hayes

Prerequisites

Hours

Examination

Content

Topics D & K


One 2-hour paper

Rings and fields, ideals. Euclidean rings, unique factorisation domains, factorisation of polynomials. Extension fields. Algebraic and transcendental numbers. Trisection of angle, duplication of cube, squaring of circle. Finite fields. Galois theory, solvability by radicals, insolvability of general quintic by radicals.

Text

References Birkhoff, G. D. &

MacLane, S. Herstein, I. N. Kaplansky,1. Stewart, 1.

Nil

A Survey of Modern Algebra (Macmillan 1953)

Topics in Algebra (Wiley 1975) Fields and Rings (Chicago U.P. 1969) Galois Theory (Chapman & Hall 1973)

663206 Topic Y ~ Topic in Applied Probability e.g. Information Theory ~ W. P. Wood

Prerequisites

Hours

Examination

Content

Topics C, D & H


Oue 2-hour paper

An introduction to that theory of information which originated in the work of C.E. Shannon in 1948. The uniqueness theorem for the information content H will be proved followed by proof of several inequalities involving this function. The concept of a channel and its capacity will be introduced and Shannon's fundamental theorem for discrete channels without memory will be proved.

50

If time permits some other aspects of information theory, e.g., Wiener prediction and filtering, will be discussed.

Text

References Ash,R. Brillouin, L.

Feinstein, A.

Gallagher, R. G.

Khinchin, A. 1.

Kotz, S.

Reza, F. M.

Nil

Information Theory (Wiley 1965) Science and Information Theory (Academic

1962) Foundations of Information Theory (McGraw

Hill 1958) Information Theory and Reliable

Communications (Wiley 1968) li1athematical Foundations of Information

Theory (Dover 1957) Recent Results in Information TheOlY

Methuen 1966) An Introduction to In/ormation Theory

(McGraw-Hill 1961)

663207 Topic Z Mathematical Principles of Numerical Analysis ~.~ W. Summerfield

Prerequisites

Hours

Examination

Content

Topics C, D & E


One 2-hour paper

Solution of linear systems of algebraic equations by direct and linear iterative methods; particular attention will be given to the influence of various types of errors on the numerical result, to the general theory of convergence of the latter class of methods and to the con .. cept of "condition" of a system. Solution by both one step and multistep methods of initial value problems involving ordinary differential equations. Investigation of stability of linear marching schemes. Boundary value problems. Finite-difference and finite-element methods of solution of partial differential equations. Some analysis background and some experience in programming computers is assumed but no prerequisites of numerical analysis courses will be expected.

Text Nil

References Cohen, A. M. et al. Numerical Analysis (McGraw-Hill 1973)

51

Daniel, 1. W. & Moore, R. E.

Desai, C. & Abel, 1.

Isaacson, E. & Keller, H. M.

Lambert, 1. D.

Mitchell, A. R.

Ortega, J. M.

Phillips, G. M. & Taylor, P. J.

Smith, G. D.

Strang, G. & Fix, G. J.

Computation (llld Theory in Ordinary Di/lerential Equations (Freeman 1970)

Introduction to the Finite Element Method (Van Nostrand 1972)

Analysis of Numerical Methods (Wiley 1966)

Computational Methods in Ordinary Differential Equations (Wiley 1973)

Computational l1;!ethods in Partial Di/lerential Equations (Wiley 1969)

Numerical Analysis -- A Second Course (Academic 1972)

Theory and Applications of Numerical Analysis (Academic 1973)

Numerical Solution of Partial Differential Equations (Oxford UP. 1965)

An Analysis of the Finite Element Method (Prentice-Hall 1973)

PART IV SUBJECT

664100 Mathematics IV

Prerequisites

Hours

Examination

Mathematics lIlA & lIIB, and additional work as prescribed by the Head of the Department of Mathematics. A student desiring admission to this subject must apply in writing to the Head of Department before 7th December of the preceding year.

At least 8 lecture hours per week over one full-time year of 4 lecture hours pCI' week over two part-time years.

At least cight 2-hour final papers. A thesis; i.e., a study under direction of a special topic using relevant published material and presented in written form. The topics offered may be from any branch of Mathematics including Pure Mathematics, Applied Mathematics, Statistics, Computing Science and Operations Research as exemplified in the publication Mathematical Reviews.

52

Content A selection of topics, each of about 27 lectures, will be offered. Summaries of topics which may be offered in 1977 follow.

PART IV TOPICS

664137 Introiluction to Category Theory c-~R. F. Berghout

Prerequisite Topic T

Hours About 27 lecture hours


Content This course is geared to an examination of the concept of "naturality" in mathematics. Categories and functors will be introduccd as unifying concepts underlying much of mathematics. Adjoint functors will be discussed in some depth and illustrated by applications (0 various branches of mathematics, particularly group theory. The existence of adjoint functors under certain conditions and a monadic approach to universal algebra will end the course.

Text lVlacLane, S.

References Arbib, M. et al. Dickson, S.

Categories for the Working Mathematician (Springer 1971)

The Categorical Imperative An Introduction to Categorical Algebra

(Obtainable from Mathematics Departmcnt)

664133 COllcrete Group Theory W. Brisky

Prerequisite

Hours

Examination

Content

Topic K

About 27 lecture hours

One 2-hour paper

A course on some aspects of group construction, which will include discussion of: presentation of a group by generators and relations; presentation of a group as a group of permutations, and as a symmetry group or structure-preserving group; relations between groups and some geometrical objects; representation of a group as a group of matrices; construction of groups in various ways from known groups; constructions preserving varietal and categorical properties; construction of "generating" groups for certain c1asscs.

53

Text

References Burrow, M.

Coxeter, H. S. M. & Moser, W. O. J.

Feit, W. J.

Hall, M. Jr Kurosh, A. G.

Magnus, W. et a!.

Scott, W. R.

Nil

Representation Theory of Finite Groups (Academic 1965)

Generators and Relations for Discrete Groups (Springer 1957)

Characters of Finite Groups (Benjamin 1969) The Theory of Groups (Macmillan 1962) The Theory of Groups Vois. I & II (Chelsea

1960 (tr. & ed. K. A. Hirsch) Combinatorial Group Theory (Interscience

1966)

Group Theory (Prentice-Hall 1964) and other articles and books mentioned during the course.

664138 Programmillg Languages and Advanced Applications in Computing J. A. Campbell

Prerequisites

Hours

Examination

Content

Topic 0, and at least one of Topics F, U and Z


One 2-houf paper

Classification of the principal types of programming languages, with detailed comparisons of the properties of representative languages of each type. Review of the mutual influences bctween the design of languages and the nature of the applications for which the languages have originally been intended. Presentation of the current state of mathematical and computational work in selected advanced topics, e.g., artificial intelligence, information retrieval and handling of large data bases, computation with symbolic expressions.

Text

References Aho, A. V. et al.

Griswald, R. E. ct a!.

Hunt, E. B. .Tensen, K. &

Wirth, N. McCarthy, .T.

Nil

The Design and Analysis of Computer Algorithms (Addison-Wesley 1974)

The SNOBOL4 Programming Language (Prentice .. Hall 1968)

Artificial Intelligence (Academic 1975) P ASCAL .. Vser Manual and Report

(Springer-Verlag 1974) LISP 1.5 Programmer's Manual (MIT 1965)

54

van Rijsbergen, C. J. Sammet, J. E.

Siklossy, L.

Information Retrieval (Methuen 1975) Programming Languages: History and Funda··

mentals (Prcntice··I-lall 1969) Let's Talk LISP (Prentice··Hall 1975)

664139 Mathematics for Classification am!. Numerical Taxonomy ~ J. A. Campbell

Prerequisite

Hours

Examination

Content

Topic I


One 2-hour paper

The course will deal with the mathematical techniques presently in use for classification or ranking of objects in terms of their attributes. Topics covered will include measures of similarity and dis.similarit~, correlation and weighting of attributes, cluster analysIs, multidimensional scaling, and mathematical models for the process of simplification of data concerning attributes. Fields in which applications will be considered include archaeology, pattern recognition, biology and information retrieval.

Text Sneath, P. H. A. &

SokaI, R. R.

References Jordine, N. &

Sibsol1, R. Kullbaek, S.

Principles of Numerical Taxonomy 2nd edn (Freeman 1973)

Numerical Taxonomy (Wiley 1971)

Information Theory and Statistics (Wiley 1959)

van Rijsbergen, C . .T. Information Retrieval (Butterworth 1975) Taylor, .T. C. Gauge Theories of Weak Interactions

(Cambridge U.P. 1975)

664111 Fluid Statistical Mechanics ~ C. A. Croxton

Prerequisites

Hours

Examination

Nil


One 2-hour paper

55

Content Cluster-diagrammatic expansions -~-low density solutions: integrodifferential equations (BGY, HNC, PY) - high density solutions: quantum liquids - Wu-Fcenburg fermion extension: numerical solution of integral equations: phase transitions--diagrammiitic approach: critical phenomena: the liqnid surface: liquid metals: liquid crystals: molecular dynamics and Monte Carlo computer simulation: irreversibility: transport phenomena.

Text Croxton, C. A.

Reference Croxton, C. A.

Introduction to Liquid State Physics (Wiley 1975)

Liquid State Physics--A Statistical Mechanical Introduction (Cambridge V.P. 1974)

664120 Quantum Mechanics C. A. Croxton

Prerequisite

Hours

Examination

Content

Topic G


One 2-hour paper

Operators: Schrodinger equation: one dimensional motion; parity: harmonic oscillator: angular momentum: central potential: eigenfunctions: spin and statistics: Rutherford scattering: scattering theory: phase shift analysis: nucleon-nucleon interaction: spin-dependent interaction: operators and state vectors: Schrodinger equations of motion: Heisenberg equation of motion. Quantum molecular orbitals: hybridization: LCAO theory: MO theory.

Texts Croxton, C. A. Matthews, P. T.

Introductory Eigenphysics (Wiley 1974) Introduction to Quantum Mechanics (McGraw

Hill 1968)

664140 Dynamical Systems ~ J. G. Couper

Prerequisites

Hours

Examination

Content

Topics Land P


One 2-hour paper

This course will be concerned with the orbit structure of differential equations and diffeomorphisms, with an orientation towards their stable and generic properties.

56

Text

References Hirsch, M. W. &

Smale, S. Hurewicz, W.

Nitecki, Z.

Nil

DifJcrcl1tial Equations, Dynamical Systems and Unear Algebra (Academic 1974)

Lectures on Ordinary DifJerential Equations (M.LT. 1958)

Ditlerentiable Dynarnics (M.I.T. 1971)

664141 Introduction to Nllmber Theory ~ R. B. Eggleton

Prerequisite

Hours

Examination

Content

Topic C


One 2-hour paper

Several areas of elementalY number thcory will first be examined at an introductory level. These will include thc Euclidean algorithm, Farey fractions, Diophantine equations, linear congr~ences and Gaus~'s theorem. A rather detailed study of several major theorems WI,u follow: these will be the Primc Number Theorem, the QuadratIC Reciprocity Theorem, and Dirichlet's Theorem on primes in arithmetic progressions.

Text

References Apostol, T. M.

Davenport, H.

Hardy, G. & Wright, E. M.

Nagell, T.

Rademacher, H.

Nil

Introduction to Number Theory (Springer 1976)

The Higher Arithmetic 3rd edn (Hillary 1968)

Introduction to Number Theory 4th cdn (Oxford U.P. 1960)

Introduction to Number Theory 2nd edn (Chelsea 1964)

Lectures on Elementary Number Theory (Blaisdell 1964)

664142 Topological Graph Theory ~~" R. B. Eggleton

Prerequisite

Hours

Examination

Topic C


One 2-hou!" paper

57

Content This topic deals with drawings of graphs on various surfaces. It will begin with a brief introduction to the theory of graphs, to be followed by a fairly detailed introduction to the topology of surfaces, with particular attention to the classification of surfaces. The main areas to be treated are: Kuratowski's Theorem character~ ising graphs which can be embedded in the plane; genus, thickness, coarseness and crossing numbers of graphs; chromatic number of a surface and the recent proof of the Four Colour Theorem by Appel and Hakin.

Text

References Blackett, D. W.

Harary, F. Ore, O. Ringel, G. Wilson, R. J.

Nil

Elementary Topology: Combinatorial and Algebraic Approach (Academic 1967)

Graph Theory (Addison-Wesley 1969) The Foul' Colour Problem (Academic 1967) Map Colour Theorem (Springer 1974) Introduction to Graph Theory (Oliver &

Boyd 1972)

664143 Families of Sets ~ V. Ficker

Prerequisite

Hours

Examination

Content

Topic V


One 2-hour paper

Properties and sets of properties of families of sets. The intersection and th~ union of a collection of families. The minimal family. Gen.e~atlllg se~ucnces for minimal families. Properties of minimal famIlIes. RelatIOns between the sets of properties. Particular cases of families. Borel families. Subfamilies of sets. The countable chain condition. Families of null sets and their properties. Families of small sets.

Text

References Dinculeanu, N. Halmos, P. R.

Nil

Vector Measures (Pergamon 1967) Measure Theory (Van Nostrand 1950)

58

664119 Population Dynamics ~.~ R. W. Gibberd

Prerequisites

Houi's

Examination

Content

Topics Band H


One 2"hour paper

This topic will cover the models and techniques used by demographers and biologists for predicting and studying population growth and mobility. The initial emphasis will be on human populations and various 'computer experiments' will be carried out to determine the effects of varying age-specific fertility, mortality and migration rates on the future population structure in different countries and cities; then models dealing with the problem of several interacting species will be discussed.

Text

References Batholomew, D. J.

Keyfitz, N.

Keyfitz, N. & Flieger, W.

]\IfontroII, E. W.

Pollard, J. H.

Rogers, A.

Nil

Stochastic Models for Social Processes 2nd edn (Wiley 1973)

United Nations Demographic Yea/·book (UN published annually)

Introduction to the Mathematics of Population (Addison-Wesley 1968)

Population, Facts and Methods of Demography (Freeman 1972)

Some Mathematical Problems in Biology Vol. IV (Amer. Math. Soc. 1972)

Mathematical Models for the Growth of Human Populations (Cambridge 1973)

Matrix Methods in Urban and Regional Analysis (Holden~Day 1971)

664144 High I,cvcl Software Development _. A. J. Guttmann

Prerequisite

Hours

Examination

Content

Programming experience in a high-level language is assumed

A bout 27 lecture hours

One 2~hour paper

This course covers the writing of medium to large scale software projects by developing realistic programs that actually work and solve realistic problems. Emphasis is placed on top-down design, structured

5')

programs, program portability and other aspects of :iOftwarc enr,in·, cering. The writing of successful programs will be an integral part of the course.

Text Kerninghan, B. W. & Software Tools (Addison-Wesley 1976)

Plauger, P. J.

References To be advised

664116 Mathematical Models of Phase 'frarl§itiolls ~ A. J. Guttmann

Prerequisite

Hours

Examination

Content

Topic P


One 2-hour paper

Review of thermodynamics and statistical mechanics. Some rig0l'Om results in statistical mechanics. Survey of critical phenomena and analogies. Classical theories of phase transitions. Ex;)ct solution of two dimensional Ising model. Approximate resulto, in three climcn~i()'1<';. Generation and analysis of exact series expansions. Anisotropic Heisenberg model and symmetry of ground state. Critical exponent ineQualities and scaling laws. Asymptotic degeneracy as a m('chani,;n; cf phase transitions. Kac models in one dimension. Heisenberg and Planar Classical Heisenberg model. Phase transitions for some modrh of biological systems.

Text

Thompson, C. J. Mathematical Statistical Mechanics (Macmillan

References

Brout, R. H. Chretien, M. et a1.

Domb, C.

Domb,C.& Green, M. S. (eds)

Fisher, M. I.

Huang, K.

1971)

Phase Transitions (Acadcmic 1972) Statistical Physics, Phase Transitions and

Superf!uidity (Brandeis Summer Institute 1966)

On the Theory oj Co,operative Phenomel1a in Crystals (Advances in Physics 9 (149) 1960)

Phase Transitions and Critical Phenomena Vok I-V (Acadcmic 1972, 1973, 1974, 1976, 1977)

The Theory oj Equilibrium Critical Phenomena (Rep. Prog. Phys. 30 (6]5) 1967)

Statistical Mechanics (Wiley 1963)

60

Stanley, H. E.

Uhlenbeck, G. E. & Ford, G. W.

Introduction to Phase Transitions and Critical Phenomena (Oxford U.P. 1971)

Lectures ill Statistical 1\/1 echanics (Amer. Math. Soc. 1963)

66412'1 Topology M. 1. Hayes

Prerequisite Topic L

Hours About 27 lecture hours


Content Topological. spaces are sets with enough cohesive properties to allow continuity to be defined. These lectures will concentrate on the geometric aspects of these spaces, and will include the following topics: Metric and topological spaces, homeomorphism. Bases, countable bases, separation. Connected spaces, compact spaces. Product spaces, homotopy and the fundamental group. Simplicial complexes, chains and homology. Orientation. Fixed points.

Text

References Cairns, S. S. Lefschetz, S. Patterson, E. M. Simmons, G. F.

Wallace, A .. H.

Nil

Introductory Topology (Ronald 1961) Introduction to Topology (Princeton 1949) Topology 2nd edn (Oliver & Boyd 1959) Introduction to Topology and Modem Analysis

(McGrawoHill 1963) An Introduction to Algebraic Topology

(Pergamon 1961)

664124 Signlll Detectioll'~~ R. G. Keats

Prerequisite

flours

Examination

Content

Topic H.


One 2-hour paper

This topic will include the detcction and processing of signals with applications. The topic will discuss thc application of likelihood ratio, Bayes and other tests to signal detection and processing in a variety of situations including known signals in white Ganssian noise, and known signals in coloured Gaussian noise. The Shannon sampling theorem, Karhunen-Locve cxpansion, sequential detection and the effect of clipping will also be discussed.

61

Text

References Cramer, H.

Davenport, W. B. & Root, W. L.

Franks, L. E. Hancock, J. C.

Hancock, J. C. & Wintz, P. A.

Helstrom, C. W.

Middleton, D.

Middleton, D.

Papoulis, A.

Rowe, H. E.

Selin, I. Thomas, J. B.

Van Trees, H. L

Wax, N. (ed.)

Wong, E.

Woodward, P. M.

Nil

Mathematical Methods of Statistics (Princeton V.P. 1946)

Introduction to the Theory of Random Signals and Noise (McGraw-Hill 1958)

Signal Theory (Prentice-Hall 1969) An Introduction to the Principles of

Communication Theory (McGraw-Hill 1961)

Signal Detection Theory (McGraw-Hill 1966)

Statistical Theory of Signal Detection (Pcrmagon 1960)

Introduction to Statistical Communication Theory (McGraw-Hill 1960)

Topics in Communication Theory (McGrawHill 1965)

Probability, Random Variables and Signal Processes (McGraw-Hill 1965)

Signals and Noise in Communication Systems (Van Nostrand 1965)

Detectioll Theory (Princeton V.P. 1965) Introduction to Statistical Communication

Theory (Wiley 1969) Detection, Estimation & Modulation Theory

(Wiley 1967) Selected Papers on Noise and Stochastic

Processes (Dover 1954) Stochastic Processes in Information and

Dynamical Systems (McGraw-Hill 1971) Probability and Tnformation Theory with

Application to Radar (Pergamon 1960)

664125 Stochastic Processes -~ R. G. Keats

Prerequisite

Hours

Examination

Content

Topic H


One 2-hour paper

This topic will cover the theory of stochastic processes and some of its applications. The topic will include the concepts of stationarity,

62

covariance function, regular process, mean square continuity, differentiation, integration, ergodicity, spectrum, processes with uncOl'related or orthogonal increments, Wiener process, Poisson process, Ito integral. Applications to prediction, filtering or signal detection, will also be studied.

Text

References Bartlett, M. S. Cramer, H.

Doob, J. L. Feller, W.

Gikhman, I. I. & Skorokhod, A. V.

Grenander, U. & Rosenblatt, M.

Hannan, E. J. Laning, J. H. &

Battin, R. H. Loeve, M. Parzen, E. Phabbu, N. V. Solodovnikov, V. V.

Wong, E.

Yaglom, A. M.

Nil

Stochastic Processes (Cambridge D.P. 1965) Mathematical !vI ethods of Statistics (Princeton

u.P. 1946) Stochastic Processes (Wiley 1953) An Introduction to Probability Theory and its

Applications (Wiley Vol. I 1957 & Vol. II 1966)

Introduction to the Theory of Random Processes (Saunders 1969) (tr. Scripta-technica)

Statistical Analysis of Stationary Time Series (Wiley 1957)

Time Series Analysis (Methuen 1960) Random Processes in Automatic Control

(McGraw-Hill 1956) Probability 3rd edn (Van Nostrand 1963) Stochastic Processes (Holden-Day 1962) Stochastic Processes (Macmillan 1965) Introduction to the Statistical Dynamics of

Automatic Control (Dover 1960) Stochastic Processes in Information and

Dynamical Systems (McGraw-Hill 1971) Theory of Stationary Random Functions

(Prentice-Hall 1965)

664145 Viscous Flow Theory ~ W. T. F. Lan

Prerequisite

Hours

Examination

Content

Topic-Q


One 2-hour paper

Basic equations. Some exact solutions of the Navier-Stokes equations. Approximate solutions: theory of very slow motion, boundary layer theory, etc.

63

Text

Rejerences Batchelor, G. K.

Landau, L. D. & Lifshitz, E. M.

Langlois, W. E Pai, S. 1.

Rosenhead, L. (ed.) Schlichting, H.

Nil

An Introduction to Fluid Dynamics (Cambridge J %7)

Fluid Mechanics (Pergamon 1959)

Slow Viscous Flow (Macmillan 1964) Viscous Flow Theory Vol. 1 (Van Nostrand

1956) Laminar Boundary Layers (Oxford (963) Boundary Layer Theory (McGraw··Hill 1968)

664118 lP'eI1uJfbation 'l'heox'Y ~ D. L. S. McElwain

Prerequisites

Hours

Examination

Content

Topics C and E

About 27 .lecture hours

One 2-hour paper

An introduction to regular perturbation methods, including parameter and coordinate perturbations. A discussion of the sources of nonuni~ formity in perturbation expansions. The method of strained coordinates and the methods of matched and composite asymptotic expansions. The method of multiple seales.

':text

References Cole, J. D.

Nayfeh, A. H.

Nil

Perturbation Methods in Applied Mathematics (Blaisdell 1968)

Perturbation Methods (Wiley 1973)

664'106 Combinatol'ics~R. W. Robinson

Prerequisite

Hours

Examination

Content

Topic K


One 2-hour paper

Perm.utations, and combinations, inclusion-exclusion and generating f~lllctlOns. Polya's theorem and its application to counting various kmds of structures and graphs will be discussed. Also asymptotic analysis of many of the exact results.

64

Text

Rejerences Beckcnback, E. F.

(ed.) Hall, M. Harary, F. &

Palmer, E. M. Uu, C. L.

Riordan, J.

Nil

Applied Combinatorial Mathematics (Wiley 1964)

Combinatorial Theory (Blaisdell 1967) Graphical Ellumeration (Academic 1974)

Introduction to Combinatorial Mathematics (McGraw~Hi1l 1968)

Combinatorial Analysis (Wiley 1958)

664134 Recul(~ion Theory .o~·. R. W. Robinson

Prerequisite

Hours

Examination

Content

Topic 0


One 2 .. hour paper

Recursive functions and Turing reducibility are discussed, along with various more special reducibilities. The structure of the degrees of un solvability is investigated using various priority method constructions.

Text

Rejerences Kleene, S. C.

Rogers, H.

Sacks, G. E. Shoenfield. 1. R.

Nil

Introduction to Metamathematics (Van Nostrand 1952)

Theory oj Recursive Functions and Effective Computability (McGraw-Hill 1967)

Degrees oj Vnsolvability (Princeton 1963) Degrees oj Vnsolvability (North-Holland 1971)

664146 l~ational Number TheOJ(,Y W~ T. K. Sheng

Prerequisites

Hours

Examination

Content

Topic C


One 2-hour paper

Properties and distributions of rational. numbers. Approximation by rationals. Rational polygons. Linear operators over rationals. Dispersive and explosive mappings, super catastrophe. Lines dctcrmined by lattice points in Rn.

65

Text Nil

664103 Elliptic Functions and Integrals ~~. E. R. Smith

Prerequisite

Hours

Examination

Content

Topic B


One 2-hour paper

Doubly periodic functions, Wcierstrass's elliptic function and its integrals. Physical problems which give rise to elliptic functions and integrals. Elliptic integrals, Jacobian elliptic functions and their inverses, the connection between Weierstrass's elliptic function and thc Jacobian elliptic functions. The theta functions and their connections with other elliptic functions which are useful in their numerical evaluation, and on the application of elliptic functions to the study of physical phenomena.

Text

References Byrd, P. F. &

Friedman, M. D. Erdelyi, A.

Nil

Handbook of Elliptic Integrals for Engineers and Scientists 2nd edn (Springer 1958)

Higher Transcendental FUllctiolls Vol. 11 The Bateman Manuscript Project (McGraw-Hill 1953)

664109 Ergodic 'fhcm'Y~ E. R. Smith

Corequisite

Hours

Examination

Content

Rigorous Statistical Mechanics


One 2··hour papet

This course will be an introduction to the classical theorems of ergodic theory, and the ideas of Bernoulli systems, K-systems, mixing systems and ergodic systems. It is hoped to include a discussion of the recent work of Sinai on the ergodicity of hard-sphere gas systems.

Text

References Arnold, V. I. &

Avez, A.

Nil

Ergodic Problems of Statistical Mechanics (Benjamin 1967)

66

Halmos, P. R. Lebowitz, J. L. &

Penrose, O.

Lectures on Ergodic Theory (Chelsea 1955) Modem Ergodic Theory (Physics Today Feb.

1973 p.23)

664123 Rigorous ~jt)]ti5ticaI Mechanics ~ E. R. Smith

Prerequisites

Hours

Examination

Nil


One 2··hour paper

Content Maxwell-Boltzmann distributions. Equations of evolution of statistical systems. Gibbs distributions and ensembles. Ideas of ergod!cit~ a.nd mixinf2' in statistical mechanics. Existence of thermodynamiC lImits. The ideal gas. Convergence of high temperature series approximations. Lee-Yang theory of phase transitions. Exact calculations on some simple models.

Text Huang, K.

References Ruelle, D.

Thompson, C. J.

Uhlenbeck, G. E. & Ford, G. W.

Wannier, G. H.

Statistical Mechanics (Wiley 1963)

Statistical Mechanics: Rigorous Results (Benjamin 1969)

Mathematical Statistical Mechanics (Macmillan 1971)

Lectures in Statistical Mechanics (Amer. Math. Soc. 1963)

Statistical Physics (Wiley 1966)

664147 Nmnelical Analysis ~., W. Summerfield

Prerequisite

Hours

Examinatioll

Content

Either Topic F or Topic Z


One 2-hour paper

Often, one has to resort to a numerical method to "solve" a mathematical problem; before the resultant numbers can be interpreted in terms of the latter problem, one must analyse how their generation has been biased by the numerical method. The three major problem areas of numerical analysis involve rounding error, diseretisation error and convergence (in iterative methods) error. The effect of each of these lypes of error is often masked by "ill-conditioning" (instability) either in the numerical method or in the mathematical problem itself.

67

This course concentrates on the basic theoretical re;;uits pertaining to these areas, especially as they apply to linear systems of cquati~ns, eigenvalue problems and to differential equations.

Text

References Daniel, J. W. &

Moore, R. E. Forsythe, G. &

Moler, C. B. Gear, C. W.

Isaacson, E. & Keller, H. M.

Lambert, J. D.

Ortega, J. M.

Strang, G. & Fix, G. J.

Wilkinson, J.

Nil

Computation and Theory ill Ordinary Differential Equations (Freeman 1970)

Computer Solution of Linear Algebraic Systems (Prentice-Hall 1967)

The Numerical Solution of Initial Value Problems in Ordinary DifJcrential Equations (Prentice-Hall 1971)

Analysis of Numerical Methods (Wiley 1966)

Computational Methods in Ordinary DifJerefl~ tial Equations (Wiley 1973)

Numerical Analysi.l'---A Second Course (Academic 1973)

An Analysis of the Finite Element Method (Prell(ice~Hall 1973)

The Algebraic Eigenvalue Problem (Oxforc! V.P. 1965)

664148 Urban SIJalialTraffic PaUerns ~ R. J. Vaughan

Prerequisites

Hours

Examination

Content

Topics C and H


One 2-hour paper

~iscussion of transportation problems in cities. The advantages and dIsadVantages of the use of continuous and discrete models to describe traffic characteristics of urban areas. Distribution of homes and work places in urban areas. Mathematical properties of the distribution. Quadrivariate normal model. Structure of urban transportation net~ works. Routeing systems. Length of road per unit area and fraction of area occupied by roads related to the town centre. Intersection densities. Local traffi.c. measures. Wardrop's principle. Travel intensity. Data on travel denSItIes. Crossings intensity. Global traffic measures. Average distance travelled in theoretical cities. Summary of known results. Data on average distances. Expected number of crossings. Usc of traffic measures.

Text Nil

68

References Kendall, M. G. &

Morall, P. A. P. Marc!ia, K. V.

664149 Colling Theory

Prerequisites

Hours

Examination

Content

C comctrical Probahility (Griffin 1963)

Families of Bivariate Distributions (Griffin 1970)

W. D. Wallis

Topics D and K


One 2-hour paper

Introduction to codes; Hamming distance; linear codes; the Slcpian~ Moore-Prange algorithm; lLunming codes; perfect codes; polynomial codes; BeH codes.

Text Street, A. P. &

Wallis, W. D.

References Anderson, I.

Berlekamp, E. R.

van Lint, J. H.

Introduction to Combinatorial Theory Utilitas Math, 1977)

A First Course in Combinatorial Mathematics (Oxforc! 1974)

Algebraic Coding Theory (McGraw-Hill 1968)

Coding Theory (Springer-Verlag 1971)

664105 Combinatorial Designs ~-. W. D. Wallis

Prerequisites

Hours

Examination

Content

Topics D anc! K


One 2-hour paper

An introduction to various tYlies of designs and their properties. Pairwise balanced designs: the basic theory, some existence theorems. Wilson's theorems. Latin squares and balanced incomplete block designs; the existence theory using pairwise balanced designs, and various constructions. Partial balance. Room squares. Hadamard matrices. Block designs on graphs, such as handcuffed designs.

Text Street, A. P. &

Wallis, W. D. Introduction to Combinatorial Theory

(Utilitas Math. 1977)

69

References Denes, J. &

Keedwell, A. D. Hall, M. Jr. Mann, H. B.

Raghavarao, D.

Ryser, H. J. Vajda, S.

Latin Squares and their Appli,,·{/tiolls (English D.P. and Akademiai Kiado 1974)

Combinatorial Theory (Blaisdell 1967) Addition Theorems. The Addition Theorems of

Group Theory and Number Theory (Interscience 1965)

Constructions and Combinatorial .Problems in Design of Experiments (Wiley 1971)

Combinatorial Mathematics (Wiley 1963) Patterns and Configurations in Finite Spaces

(Griffin 1967) Vajda, S. The Mathematics oj Experimental Design.

Incomplete Block Designs and Latin Squares (Griffin 1967)

"Yallis, W. D. et a!. Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices (Springer 1972)

664102 Asymptotic Methods in Analysis ~ W. P. Wood

Prerequisites

Hours

Examination

Content

Topics B, C, E and P

About 27 lecture haUl'S

One 2AlOUl' paper

This topic will outline methods useful in the solution of a wide class of problems occurring in Applied Mathematics. Thc topic will include an introduction to asymptotics, asymptotic series, implicit functions, summation formulae, Mellin transforms, the Laplace method for integrals, the saddle point method, the method of steepest descents, indirect asymptotics, iterated functions, differential equations with a large parameter, singularities of differential equations, estimation of the remainder in an asymptotic expansion, numerical quadrature and asymptotic expansions, some examples of asymptotic problems in mathematical physics, e.g., motion in a stratified atmosphere, insta·· bility of shear flows, spiral structure of disc galaxies.

Text

Rejerences

Copson, E. T.

DeBruijn, N. G.

Erdelyi, A.

Nil

Asymptotic Expansions (Cambridge u.P. 1965)

Asymptotic Methods in Analysis 3rd edn (North Holland 1970)

Asymptotic Expansions (Dover 1956)

70

Evgrafov, M. A.

Feshchenko, S. F. et al.

JefIreys, H.

Lauwerier, H. A.

Wilcox, C. (ed.)

Asymptotic Estimates and Entire Functions (Gordon & Breach 1961)

Asymptotic Methods in the Theory of Linear Differential Equations (Elsevier 1967)

Asymptotic Approximations (Oxford D.P. 1962)

Asymptotic Expansions (Amsterdam Mathematisch Centrum 1966)

Asymptotic Solutions of Differential Equations and Their Applications (Wiley 1964)

664121 Random and Restricted Walks W. P. Wood

Prerequisites

Hours

Examination

Content

Topics C, E, Hand R


One 2··hour paper

Problem of random walk; lattice walks; walks in continuous time; spatial restrictions; correlated walks; self-avoiding walks; difIusion and Brownian motion; applications to polymer physics, astronomy, numerical analysis and solid state physics.

Text

References Barber, M. N. &

Ninham, B. W. Feller, W.

Spitzer, F.

Wax, N. (ed.)

Nil

Random and Restricted Walks (Gordon & Breach 1970)

lntroduction to Probability Theory and its Application (Wiley Yol. 1 1968, Vol. II 1971)

Principles of Random Walk (Van Nostrand 1964)

Selected Papers on Noise and Stochastic Processes (Dover 1954)

SCH.EDULE B

PART I

5:U206 Civil Engineering 1M

Prerequisites 2 .. unit Mathematics & multi strand Science at the 4··unit level (advisory)

71

Corequisite

Hours

Examination

Content (I) CEIU Statics

(ii) ME131 Dynamics

Mathematics 1

4 lecture hours & 2 tutorial laboratory hours per week

To be advised

(iii) CE231 lfluid Medmuics If or ME251 Fluid Mecbarnc§ (Iv) CE212 Mecbanics of Solids l!

(I) 521101 CEl11 Statics .~, B. Karihaloo

Hours

Examination

Content

1 lecture hour & t tutorial hour per week

One 3-hour paper

Two-dimensional force systems; equilibrium, funicular polygon, rigid bars, shear force, axial force, bending moment; pin .. jointed frames, analytical and graphical treatment; equilibrium of three-dimensional force systems, cables.

Text Hall, A. S. &

Archer, F.

References Beer, F. P. &

Johnston, E. R. Meriam, J. 1,.

Principles of Statics (Uni. of N.S.W. Students Union 1966)

Mechanics for Engineers: Statics 2nd edn (McGraw-HilI 1962)

Statics (Wiley 1966)

(ii) 541103 ME131 Dynamics K. L. Ritz

Hours 1 t hours per week

Examination Progressive assessment &. examination

Content Basic concepts required for study of motion: length, time, force and mass; Newton's laws of motion; systems of units; friction. Motion of point masses, rigid bodies and connected bodies in straight or curved paths, or in simple rotation. Relative motion using translating reference frames. General plane motion of rigid bodies. Momentum and impUlse, both linear and angular, related to point masses and rigid bodies.

72

Energy and the conservation principle applied [0 mechanical work, strain energy, kinetic energy and friction "losses", for particles and rigid bodies.

Text Meriam, J. L.

Reference Beer, F. P. &

Johnston, E. R.

Dynamics 7.nd cdn S.L vcrsion (Wiley 1966)

lVlechallics tor Engineers: Mechanics 2nd edn (McGraw-Hill 1962)

(ill) 522202 CE231 Fluid Mechanics I-W. G. Field

Hours

Examination

Content

1 lecturc hour &1 tutorial & laboratory hour per week

One 3-hour paper

Fluid properties and definitions. Fluid statics:-- statics of moving systems, forces on surfaces, buoyant forces, stability of floaling and submerged bodies. F''luid flow concepls:- types of flow, continuity equations, Euler's equation of motion along a streamline. Bernoulli equation, energy equation. Linear momentum equation. The moment of momentum equation. Linear and angular momentum applications. Introduction to dimensional analysis. Viscous elfects:-- fluid resistance, laminar and turbulent flow, flow in pipes and conduits. Fluid measurement.

Text Streeter, V. 1,. &

Wylie, E. B.

References Daugherty, R. L. &

Franzini, J. B. Vennard, J. K.. &

Street, R. L.

Or

Fluid Mechanics 6th edn (McGraw-Hill)

Fluid Mechanics with Engineering Applications (McGraw-Hill)

Elementary Fluid Mechanics 5th edn (Wiley)

(iii) 542202 ME251 Fluid Mechanics R. A. Antonia

Hours

Examination

1 j hours per week

Progressive assessment & examination

73

Content Fluid properties and definitions. Fluid statics:--· statics of moving systems, forces on surfaces, buoyant forces, stability of floating and submerged bodies. Fluid flow concepts:-Types of flow, continuity equation. Euler's equation of motion along a streamline. Bernouilli equation, energy equation. Linear momentum equation. The moment of momentum equation. Linear and angular momentum applications. Introduction to dimensional analysis. Viscous effects :-. fluid resistance, laminar and turbulent flow, flow in pipes and conduits. Fluid measurement.

Text Streeter, V. L. &

Wylie, E. B.

References Daugherty, R. L. &

Franzini, J. B. Streeter, V. L.

Fluid Mechanics 6th edn (McGraw-Hill)

Fluid Mechanics with Engineering Applications 6th edn (McGraw-Hili)

Fluid Mechanics 5th eeln (McGraw-Hill)

(iv) 522102 CE212 MechaniC!> of §olil!i .. J{ P. W. Kleeman

Hours

Examination

Content

1 lecture hour & ~. tutorial hour per week

One 3-hour paper

Uniaxial loading, states of stress and strain, stress and strain relationships; internal forces, internal stresses, deflection of beams, torsion, buckling.

Text Hall, A. S.

References

An Introduction to the Mechanics of Solids (Wiley 1973)

Crandall, S. I-I. et a!. An Introduction to the Mechanics of Solids 2nd edn (McGraw-Hill 1972)

Popov, E. P. Mechanics of Materials 2nel eeln (PrenticeHall)

522108 Materials Science I

Prerequisites

Corequisites

One Science 2,·unit subject or Science 28 (advisory)

Mathematics I & Physics IA

74

Hours

l;xamination

Content

3 lecture hours & 3 tutorial/laboratory hours pCI' week

Four 1 ±-hour papers plus assignments

(i) Mechanical Properties of Materials (ii) Microstmcillire of Materials

(iii) Atomic §tmcillre of Materials (iv) EITHER Cbemical Metallurgy OR Electrollic §tl'llctu!'e of Material§

(i) 111141 Mechanical Properties of Materials

Prerequisites

Hours

Examination

Content

Nil

About 21 hours of lectures & 21 hours of tutorial, demonstration & practical classes

II hour paper

Macroplasticity. The tension test, engineering stress and strain, true stress and strain, theories of strength, complex stresses, yielding, flow and fracture, effect of mctallurgical variables. Visco-elastic behaviour of matcrials, classical models. Heating a cold worked metal, recrystallization, hot working. Microp!asticity. Slip in single crystals, work hardening, multiple slip, deformation bands in polycrystals. Theoretical strellgth anomaly and dislocations, edge and screw types, their interaction, multiplication and pile ups. Fracture. Types of fracture under static loading, ductile, brittle, Creep dynamic loading fatigue. Ductile-Brittle transition in mild steel, the effects of variables, Mnl C ratio. Creep Test, shape of curve, microstructural aspects, creep rupture. Fatigue Test, S-N curve, effect of variables.

Text Wulff, J. et a1.

References Dieter, G. Polacowski, N. H, &

Ripling, E. Wyatt, O. H. &

Dew-Hughes, D.

Structure and Properties of Materials Vol. 3 (Wiley)

Mechanical MetalhlrRY (McGraw-Hill) Strength and Structure of Engineering

Materials (Prentice·Hall) Metals, Ceramics and Polymers (Cambridge

U.P.)

75

(ii) 111151 Miuosirw:ture of Materials

Prerequisites

flours

Examination

Content

Nil

About 21 hours of lectures & 21 hours of tutorial, demonstration & practical classes

11 hour paper

The generation of microstructure and its relationship with material properties. Statcs of malter, bonding in solids, crystal structure, phases, surfaccs, grain boundarics and interfaces, atom development. Phase rule allCl microstructures in binary systcms for equilibrium conditions and for near equilibrium transformations including: isomorphous, eutectic, peritectic and eutectoid types, the lever rulc. Microstructures of ceramics and polymers. Tcchnically important systems including iron-carbon, copper-zinc, aluminium-silicon, aluminium-copper. Modification of euteclics, normalizing and annealing. Non-equilibrium microstructures, quenching. M arlCilsitc and bainitc, TTT diagrams, age hardening tempering.

Text

Wulff, J, et a1.

References

Rhines, F. N.

Rollason, E. C. Van Vlack, L. H.

Wyatt, O. H. & Dew-Hughcs, D.

Structure and Properties of lvfatCl'ials VoJ. I (Wiley)

Phase Diagrams in Metaliurgy (McGraw·· Hill)

Metallurgy jor Engineers (Arnold)

LJemel1ts of Materials Science (AddisonWesley)

Metals, Ceramics and PolYlIlers (Cambridge U.P.)

(iii) '111181 Atomic Structure of Materials

Prerequisites

Hours

Examination

Content

Nil

About :'.1 hours of lecturcs & 21 hours of tutorial, demonstration & practical classes

1 t hour papcr

Introductory crystallography; crystal systems, lattices and unit cells. Miller indices and stcreographic pi'ojection. The periodic table and atomic bonding.

76

The mctallic structun;~;, b.c,c" 1'.c.c., ('.p.11. [n'm st::Jcking equal sphercs. Metallic solid solutions, HUll1(>Rothcry rulcs, short and long rangc order. Defects. Ionic structures, from stacking coordination polyhcdra. Pauling's rules. Covalent structures.

Structurcs with more than one type of bond, silicates and polymcrs.

Text

Wulff, J. (cd.)

Rejerences

Crackncll, A. P. Van Vlack, 1.. H.

Structure and Properties of !'vIa/erial.\' Vols. 1 & 3 (Wilcy)

Crystals and their Structure (Pergamon) Elements oj Materials Science (Addison

Wesley)

(iv) 111122 Chemical Metallurgy

Prerequisites

Hours

Examinatioll

Content

Nil

About 21 hours of lectures & 21 hours of tutorial, dcmonstration & practical classes

11 hour paper

Introduction to chemical thcrmodynamics and thc rates of homogeneous and heterogeneous chcmical reactions. Extens!ol1 to electrochemical and photochemical reactions, thcrmodynatTI!~s and kinetics of chemical change illustrated by referencc to the envlronmcntal degradation of materials. \Vet and dry corrosion of metals. Chemical attack on refractorics, ccramics and cement. Photochemical breakdown of polymers, stress corrosion of metals and plastics. Internal chemical brcakdown of materials.

Texts

Ives, D. J. G.

Chilton, J. P. Guggenheim, E. A.

Reference

Guy, A. G.

Principles 0/ FXirrzcliol1 oj Metals (Chem, Soc.)

Princip-Zes of A1etallic Corrosion (Chcm. Soc.)

Elements of Thermodynamics (Chern. Soc.)

Introduction to Materials Science

77

01'

1111t!2 Electmnic Stmcture of Materials

Prerequisites

Hours

Examination

Content

Nil

About 21 hours of lecturcs & 21 hours of tutorial, demonstration & practical classes

It hour paper

Atomic bonding and electron mobility. Electron~ in a potential box, free electron model of a metaL effects of the lattIce, alkali, nobJc and transition metals, insulators and semi conductors.. . Specific heat and thermal cO!1(~uctivity of clc?trons ~:l(:. lattIces: Thermal and Electronic properties of metals, 1l1sulators a.1d semI conductors. Magnetic properties of metals and insulators. Optical properties of metals, insulators and semi conductors.

Text Wulff, J. et al. The Structure and Properties oj Materials

Vol. 4 (Wiley) References To be advised

PART !Il!

522700 Civil Engineering lIM

Prerequisites

Hours

Examination

Content (i) 523105

(ii) 523301 (iii) 543101

Mathematics I & Civil Engineering 1M

5 lecture hours & U tutorial & laboratory hours per week

Two 3-hour papers & progressive assessment

CE313A Strudural Analysis I CE332 Fluid Mechanics II ME301 Engineering Computations

(i) 523105 CE313A StmduJ:'al Analysis l{ <~- A. W. Page/No O. Bf)tts

Hours 2 lecture hours & 1 tutorial hour per week


78

Content

Analysis component of CE313 -- Structural Analysis and Design l. Analysis of elastic statically determinate and indeterminate systems by classical methods; limit analysis.

Text

References Coates, R. C. ct a1. Heyman, J.

Horne, M. R. Norris, C. H. &

Wilber, J. B. Raz, S. A.

Nil

Structural Analysis (Nelson 1972) Plastic Design oj Frames (Cambridge U.P.

Vcl. 1 1969 & 2 1971) Plastic Theory of Structures (Nelson 1971) Elementary Structural Analysis (McGraw~HiIl

1960)

Analytical Methods in Structural Engineering (Wiley 1974)

(li) 523301 CE332 Fluid Mechallics II ~ W. G. Field

Hours

Examination

Content

2 lecture hours & 1 tutorial & laboratory hour per week

One 3-hour paper

Similitude; flow nets, boundary layers; closed conduit flow; pipe networks; unsteady flow; waterhammer, hydraulic machinelY, open channel hydraulics, backwater curves.

Preliminary Reading

Rouse, H. & Ince, S. History of Hydraulics (Dover 1963)

Texts Henderson, F. M. Olson, R. M.

References Davis, C. V. &

Sorenson, K. E. Morris, H. M.

Rouse, H. Streeter, V. L.

Vallentine, H. R.

Open Channel Flow (Collier Macmillan 1966) Engineering Fluid Mechanics 3rd edn (Tutext

1973)

Handhook of Applied Hydraulics 3rcl edn (McGraw-HilI 1969)

Applied Hydraulics in Engineering (Ronald 1963)

Engineering Hydraulics (Wiley 1958) Handbook of Fluid Dynamics (McGraW-Hill

1961 )

Applied Hydrodynamics (Butterworths 1959)

79

(iii) 543UH ME301 EJiginccl'mg Compnmtionf§ co~~, :L. W. B. Browne

Hours 1 t hours per week

Examination Progressive assessment

Content ., . Solution of equations. Sets of linear algebraic equations b~ elm11?a~!On and iteration methods. Numerical inte~ration a.nd cll.ff~l:entIa.tJOn. Numerical solution of ordinary differential equatlOns, mltJa~ v"llue, boundary value and characlcri~tics. value pro~lerns. SoiutlOns of partial differential equations by fimte dlffe~cnce rn~lho~s. Introduction to linear programming, wIth engmccnng applications.

Texts McCracken, D. P. &

Dorn, W. S.

References Forsythc, G. &

Moler, C. B. Ralston, A.

752300 Psychology lIC

Prerequisites

Hours

Examination

Content

Numerical Methods with Fortran IV Case Studies (Wiley 1972)

Fortran (Dataset 1973)

Computer Solution of Linear Algebraic Systems (Prentice-Hall 1967)

A First Course in Numerical Analysis (McGraw-Hill 1965)

Psychology I & Mathematics I

3 lecture hours, one 2-hour practical session & 1 tutorial hour per week.

Two 3-hour papers plus an assessment of practical work

1. Statistics, Scientific Method, Quantitative psych.ologyp (Mat~he" matieal Models and Individual Differences), l.carnmg,-ercep IOn.

Z. Two other topics chosen from Physiological Psychology, Ah 11

limal

Behaviour, Motivation, Cognition, Developmental P~yc oogy, Social Psychology, Personality, Developmental PsychoblOlogy.

3. Mathematical Psychology

Texts } To be advised

References

]['sychology l!IC will be a Prerequisite fm' Psychology IHC in 1978

80

I'ART In

413900 A!:cmmting l!J(J!C

Prerequisites

Hours

Examination

Content

Mathematics ITA & lIC & either Accounting IlA or IJB

4 lecture hours & J tutorial honr per week

Two 3-hour &. two 2-hollr papers

Either Accounting IlIA or Accounting HIB and two appropriately chosen Part III topics (e.g. topics U and R) otrered by the Department of Mathematics and approved by the Head of the Department.

Either

(i) 413100 Accollnting mA

Prereqllisites

Hours

Examination

Content

Accounting IIA & JIB

2 lecture hours per week

Two 3-hour papers

Selected contemporary problems in the theory and practice of financial accounting, company financial reporting and public practice including a study of current approaches to the formulation of accounting theory; governmental and institutional accounting.

Texts

References

Nil

Accounting Standards The Corporate Report (Acc. Stand. Steer. Steering Committee Comm.)

American Accounting Assn

Backer, M. (cd.)

Barradell, M. Baxter, W. T. &

Davidson, S. Beck, G. W.

Bray, F. S. Chambers, R. J.

A Statement of Basic Accounting Theory

Modern Accoullting Theory (Prentice-Hall 1966)

Ethics and the Accountant (Gee 1969) Studies in Accounting Theory (Sweet &

Maxwell 1966)

Public Accountants ill Alistralia-,Their Social Role (Aust. Accounting Research Found.)

The Accounting Mil'sion (Melbourne U.P.) Accounting Evaluation and Economic

Behaviour (Prentice·-Hall 1966)

81

Davidson, S. et al.

Edwards, E. O. & Bell, P. W.

Garner, P. & Berg, K. B. (eds)

Gilman, S. Goldberg, L.

Goldberg, L. Henderson, S. &

Peirson, G. Hendriksen, E. S. Hendriksen, E. S. &

Budge, B. P. Jay, W. R. C. &

Mathews, R. L. Johnston, T. R. et a1.

Levy, V. M.

Littleton, A. C.

Mattessich, R.

Moonitz, M. & Littleton, A. C.

Mueller, G. G. Murphy, M. E.

Normanton, E. L.

Paton, W. A. & Littleton, A. C.

Ross, H.

Staubus, G. J.

Storey, R. K.

Vatter, W . .T.

Wixon, R. et al. (eds)

An Income Approach to Accounting Theory (Prentice-Hall 1965)

The Theory and Measurement and Business Income (California U.P. 1961)

Readings in Accounting Theory (Houghton Mifflin 1966)

Accounting Concepts of Profit (Ronald) An Inquiry into the Nature of Accounting

(American Accounting Assn ]965) Concepts of Depreciation (Law Book Co. 1960) Issues in Financial Accollnting (Cheshire)

Accounting Theory (Irwin 1970) Contemporary Accounting Theory

(Dickenson) Government Accounting in Australia

(Cheshire 1967) Law and Practice of Company Accounting in

Australia (Butterwol-ths 1973) Public Financi(il Administration (Law Book

Co.) Structure of Accounting Theory (Amer.

Accounting Assn 1953) Accounting and Analytical Methods (Irwin

1964) Significant Accounting Essays (Prentice-Hall

1965) International Accounting (Macmillan 1967) Advanced Public Accounting Practice (Irwin

1966) The Accountability and Audit of Government

(Manchester V.P. 1966) An Introduction to Corporate Accounting

Standards (Amer. Accounting Assn 1965) Financial Statements: A Crusade for Current

Values (Pitman 1969) A Theory oj Accounting to Investors

(California V.P. 1964) The Search for Accounting Principles

(A.I.C.P.A. 1964) The Fund Theory of Accounting (Chicago

V.P. 1951) Accountants' Handbook (Ronald 1970)

82

011'

Illjlation Accounting: Report oj the In/latioll Accounting Committee (HMSO)

Inflation and Taxation: Report oj Committee of Enqliiry ill the Inflation and Taxation, May, 1975 (Aust. Govt Publishing Service)

(ll) 4132011 Accm!Wtin~ ruB

Prerequisite

Hours

Examination

Content

Accounting lIB


One 3-hour paper

Selected contemporary problems in the theory and practice of managerial accounting. Topics studied include the development of management accounting, decision theory and information systems, profit planning, cost-volume profit analysis, incremental analysis, intra company pricing and divisional performance evaluation, product pricing direct costing, allocation of costs, cost accounting for income determination, feed-back for accounting control, behavioural COI1-

siderations in management accounting and general concepts of managemeIlt accounting including decision making for small and medium sized manufacturers, management accounting and statistics; production and operations management.

Texts

References Arney, L. R. &

& Egginton, D. A. Anton, H. R. &

Firmin, P. A. Benston, G. J.

Broom, H. N. & Longenecker, J. G.

Broster, E . .T.

Chase, R. B. & Aquilanci, N. J.

De Coster, D. T. & Schafer, E. L.

To be advised. Articles arc selected from Abacus, The Accounting Review, Journal of Accounting Research, .TournaI of Business, etc.

Management Accounting: A Conceptual Approach (Longman)

Contemporary Prohlems in Cost Accounting (Houghton Mifflin 1966)

Contemporary Cost Accounting and Control (Dickenson 1970)

Small Business Management 4th edn (South Western)

Management Accounting and Statistics (Longman)

Production and Operations Management (Irwin)

A1anagement Accounting: A Decision Emphasis (Wiley/Hamilton)

83

Greenwood, W. T.

Hofstede, G. H.

Horngrell, C. T.

Li,D.H.

Nalional Assn of Accountants

Parker, R. H.

Rappaport, A. (ed.)

Rosen, L. S.

Schiff, M. & Lewin, A. (ed.)

Solomons, D. (ed.)

Stedry, A. C.

Thomas, W. E. (cd.)

Decision Theory and Information Systems (South Western 1969)

The Game of Budget Control (Assoc. Book Publishers 1(67)

Accolillting for Management COlltrol (Prentice~Hall 1965)

Accounting Computers, lvfanagenzent Information Systems (McGraw-Hill)

Research Reports and Research Monographs

ll,1anagement Accounting: An Historical Perspective (Macmillan 1969)

Information for Decision Making (PrellticeHall 1970)

Topics in Managerial Accounting (McGrawHill 1970)

Behavioural Aspects of Accounting (PrenticeHall 1974)

Studies in Cost Analysis 2nd edn (Sweet & Maxwell 1968)

Budget Control and Cost Behaviour (Prentice·, Hall--- Ford Foundation Series 19(1)

Readings in Cost Accounting Budgeting and Control (South Western 1968)

713200 Biology nIB ~- D. Angus/B. A. COllToy/R.. C. Jones/J. W. Patrick

Prerequisites

Hours

Examination

Content

Mathemalics IIA & lIC & either Biology IIA 01' UB

Ii lecture hours & 8 tutorial & laboratory hours per week & a field excursion

Two 3-hour papers

Fundamentals of Population and Quantimtive Genetics Equilibrium, changes due to selection and mutation. Small populations., Adaptations. Average effects, breeding values, phenotypic variance. Covariance of relatives. Selection and inbreeding. Neutral traits.

Commun.ity Analysis Structure and dynamics of biologicaJ communities.

Emrironmental Physiology Functional adaptations (homeostatic and developmental) of organisms to their environments.

84

Texts

Falconer, D. S.

Krebs, C. J. Milthorpe, p. L. &

MOQl'by, J. Schmidt-Nieben, I": ..

Zar, J. H.

References

Connell, P. ,V. C.S.I.R.O.

fiord, E. B. Gordon, M, S.

Kershaw,K. A.

Leopold, A. C. & Kriedeman, P. E.

Pianka, E. R. Phillipson, J. Poole, R. W.

Sehmidt-Nielson, K. Swenson, M. J. (cd.)

Introductiol/ to Qliantitative Gcnctics (Oliver & Boyd 1975)

Ecology (Harper & Row 1973) An Jntroduction to Crop Physiology

(Cambridge U.P.) Anima! Physiology: Adaptioll (lild Environillent

(Cambridge UP. J975) fJiu,'.lrlti.l'lica/ Analysis (Prcnticc+lall)

Water Pol/ution (Queensland D.P. 1970) The A ustrattan 1,'!lvil'Ol1l1?cnt (Melbourne

UP. 1970) Ec%[Zical Genetics (Methuen 1975) A !limal Physiology: Principles and Adaptions

(Macmillan) Quantitative ([fld Dynamic !,lant Ecology

2nd edn (Arnold 1973) Plant Growth and Dcve!opm('nt

(McGraw-Hill 1975) l:'l'olutionary Ecology (Harper & Row) Ecological Energetics (Arnold) introdllction to Quantitative Ecology

(McGraw<oHill) HolV Animals Work (Camhridge U.P,) Dukes Physiology of Domestic Animals

(Cornell U.P. 1970)

513900 Chemical Ellgineerh11~ :mc

Prerequisites

Hours

Examination

Content

Cl:lcmical Engi~ecring J, (hilt s('e note on page 15), MathematiCs {fA ,,91. He (indudil1l' topics E & F) .

See under individual topics below

To be advised

Six of the following topics: (I) ChE301 COmlllJtations ~~~) CbE3'12 Reaction Engineering (~1I) ChE313 Transport Principles (2 tOllic§) (Iv) ChE314 Process Control (v) ChF~322 Particulate Systems (2 topics)

(vi) ChE331 l'rocess Economics (vii) ChE412 Radiant Heat TransfeR'

85

(1) ChE301 ComputatiOl!lil-' J. Roberts

Hours

Content

Approx. 21 hours

Computations for heat and mass transfer, thermodynamic functions and data processing will be used as an introduction to numerical methods emphasing iterative techniques. Extensive use of FORTRAN IV and Input! Output operations, sub-programs, subroutines, lCL computer packages and efficient programming in FORTRAN will be made.

Topic Outlines Curve fitting by classical graphical methods. Curve fitting with data transforms by least squares polynomial approximation, mini-max polynomials; coefficient errors. Iterative solution of algebraic and transcendental single-simultaneous equations by first or second order methods, weighting factors on convergence efficiency, Matrix methods in solving sets of equations. Solution of single/simultaneous differential equations of first or higher order. ICL Analogue Simulation package.

Texts Darn, W. &

McCracken, D. Kemeny, J. C. &

Kurtz, T. E. Scheid, F.

References Carnahan, B. et al. Smith, G. D.

(ii)

Hours

Examination

Content

Numerical Methods for FORTRAN IV Case Studies (Wiley 1972)

Basic Programming 2nd edn (Wilcy 1971)

Numerical Analysis (McGraw-Hill 1968)

Applied Numerical Methods (Wiley 1969) Numerical Methods for Partial Differential

Equations (Oxford U.P. 1965)

1 T hours a week for J year

To be advised

Design and operation of chemical reactors for homogeneous and heterogeneous reacting systems. Elementary reaction kinetics leading to interpretation of experimental data needed to design batch and continuous reactors, Effect of heat of reaction and changes of

86

temperature and pressure on design, use of catalysts and residence time estimation. An introduction to design for heterogeneous reacting systems.

Text Levenspiel, O. Chemical Reaction Engineering 2nd edn (Wiley

1972)

(iii) CbE313 Trallsport Prim:iple&

Hours

Content

I! hours per week

Heat and mass transfer in unsteady state conditions, transport theory for momentum, heat and mass transfer in laminar and turbulent flow conditions. B~:)lJndaIY layer theory. The course stresses the application of mathemattcs to the solution of engineering problems. Analogies between heat mass and momentum transfer.

Text Bird, R B. et a1. Transport Phenomena (Wiley 1960)

(Iv) C11E314 Process Conkol W. G.Kirchner

Hours

Examination

Content

1:\ hours a week

To be advised

Introduc~ion to process dynamics, the well stirred vessel, treatment of e~penmental data, Laplace Transform Applications. Block diagram rotatIOn, open loop and closed loop systems, the transfer function application and limi~ations. Control modes. Stability of closed loop system, elementary. no locu.s., ~ode diagram. Feed forward. Control, cascade control WIth applIcatIOns to control of temperature flow pressure and composition, '

Text

Couganowr, D. R. & Koppel, L. B.

Process SYstems A nalysis and Control (McGraw-Hill 1965)

(v) ChE322 Pllrticuillte SYsU1I1i1Ei ~~~~, J. Roberts/I. MeC. Stewaxt

Hours 11 hours per week

Examination To be advised

87

Content Definition of size and shape of solid particles, laws of brePlkage, analytical description of size distributions, matrix description of breakage and classification operations, crushing and grinding equip·· ment, separation of solid~); partition curves; pressure and flow of granular material. Drying operations, movement of moistnre in solids; drying systems, drying equipment; design methods. Furnace and kiln analysis by heat and mass balance on well-stirred and parallel flow reactors. Size and solids separation in gas or liquids; action of gravitational :md centrifugal fields, design and performance of separation and pollution control equipment under these conditions-settling chambers, gas and liquid cyclones, centrifuges; flocculation, hindered settling, sludge thickening; Flow through fixed beds-Fluid is .. ation-Filtration .. analytical and design methods. Agitation and mixingscale-up and shape considerations; EVaporation and crystallisation. Dust and gas removal for environmental control.

Text

Coulson, J. M. & Richardson, J. F.

References

McCabe, H. L. & Smith, S. C.

Perry, J. H.

Chemical Engineering Vol. II 2nd edn (Pergamon 1970)

Unit Operations of Chemical Engineering (McGraw-Hill·196?)

Chemical Engineers' Handbook 5th edn (l\1cGraw-Hill 1973)

(vi) CbE331 PrO£eoo FICOIlOmics ~ B. D. Henry

Hours 11 hours a weck for half a year


Content 1. Process Plant Costs --- fixeel, variable, direct, indirect --- review of cost accounting procedures applied to above. Balance sheet and in·· come statements. 2. Cost estimation procedures - cost indices -- six tenths rule and economy of scale. 3. Ecol1omic production charts (break even analysis). Capacity factors, incremental costs. 4. Depreciation '-- Purpose of depreciation studies in process costs-types and requirements of depreciation methods -- taxation allowances in proce~;s plant and equipment -- economic life - depIction. 5. Project profitability - .. Concept of equivalence and discounted cash J'!ow~ -- methods for measuring project profitability including rate of return, payout time, interest rate of return (DCF) net present value, anmwl co~t and capitalised cost - continuous discounting.

88

6. E~o~l~mic Balances -- General considerations for economic balance ~ b.net 1l1trodu.ction .to optimisation - Economic balances applied to selected operatl.ons, I.e. mass transfer, cyclic operation, yicld and recovery operatIOn.

7. Feasibility studies - selected examples.

Text

Jelen, F. C.

References

Buchanan & Sinclair

Peters, M. S. & Timmerhaus

(vii)

Hours

Examination

Content

Cast and Optimization Engineering (McGraw.,Hill 1970)

Costs and Economics of the A llstmlian Chemical and Process Industries ~nd cdn (Wests 1967)

Plant Design and Economics for Chemical Engineers (lVIcGraw-IIill 1968)

I} hours a week for half a year

To he advised

A study of f~ndamentaIs and of computational methods for r2dhtive transfer nartJcularly fo . I b ' , . M' ~ _ r gICy am crt surfaces and ncn··luminous gases. edlOds of repreoentl'n" - J ., 1 Mat', " d b lea gases )y grey gas components. d " fiX methods of soIvmg for multi.-surface systems. Application 10

~slgn of furnace enclosures. Sunphfied overall equations for welJ stIrred and plug-flow furnaces.

Text

Hottel, H. C. & Sarofim, A. C.

Radiative Transfer (McGraw.,Hill 1968)

5237()O Civil Engineering ruM

Prerequisites

Hours

F:xamination

Content

Mat~e:nat,ics. IIA & HC (including Topic E) & CIVIl Engmcering 11M

7 ieclure hours and 4 tutorial/laboratory hours per week

To be advised

Topics CE324 and CE414A, and any 2 of the other topics. (i) CE3l4 Soil Mechanics

(ii) CE414A §tmctllral Analysis II

89

(ill) ClI<~41§

(Iv) CE416 (v) CI<:43;~

(vi) CE434

Elastic Continua Plastic I,'rame IJiesip Theoretical Hyili'odymlmics OlJlm Channel Flow

(i) 523102 CE324 S{lil Mechanics .. ~ J. B. Merrill

Corequisite

Hours

Examination

Content

CE332 Fluid Mechanics II

2 lecture hours & 1 laboratory hour per week

One 3~hour paper

Index properties, classification of soils; permeability, capillarity:, s~epage and flow nets; stresses in soils; set~le~ent a~~ consohd~tl?n; compaction, shear strength and failure cntena; stabIlIty of retammg walls.

Text Scott, C. R.

References Lambe, T. W. SAA

Wu,T.H.

An Introduction to Soil Mechanics and Foundations 2nd edn (Applied Science)

Soil Testing for Engineers (Wiley 1961) Methods of Testing Soils for Engineering

Purposes A.S.A. 89 Soil Mechanics (Allyn & Bacon 1966)

(J.i) 524193 CE414A Stmciural Aualysis 11 ~ P. W. Kleeman

Hours n lecture hours & H tutorial hours per week


Content Matrix displacement method of analysis, stabili!y of .fra~es, dyn~mic behaviour of beams and frames, influence hnes m mdetermmate structures, non~uniplanar bending and torsion.

Text

References Bresler, B. et aI. Coates, R. C. et al. Horne, M. R. &

Merchant, W.

Nil

Design of Steel Structures (Wiley 1968) Structural Analysis (Nelson 1972) The Stability of Frames (Pergamon 1965)

90

Martin, H. C.

Morris, C. H. & Wilbur, J. B.

Introduction to Matrix Methods of Structural Analysis (McGraw~HiII 1966)

Elementary Structural Analysis (McGraw··Hill 1960)

(ill) 5:24029 CE415 EIllStic Continua ~ P. W. Kleeman

Corequisite

Hours

Examination

Content

CE414A Structural Analysis II

1! hours per week

One 2~hour final paper

Equilibrium and compatibility in solids, plane stress and plane strain solutions for solids with rectangular and circular boundaries, finite element method of solution, study of a simple finite element program. Bending of plates with rectangul ar boundaries, plate bending finite elements.

Text Nil

Ref.erences Desai, C. S. & Introduction to the Finite Element Method

Abel, J. F. (Van Nostrand Reinholt 1972) Timoshenko, S. P. & Theory of Elasticity 3rd edn (McGraw-Hill

Goodier, J. N. 1970) Timoshenko, S. P. et al. Theory of Plates and Shells 2nd edn

(McGraw-Hill 1965)

(iv) 524030 CE416 PIllStic Fmme IJiesign - P. W. Kleemau

Corequisite

Hours

Examination

Content

CE414A Structural Analysis II

1} hours per week

One 2~hour paper

Review of upper and lower bound theorems, beams, columns, connections, design of braced frames, column deflection curves, subassemblages, unbalanced frames.

Text

References Heyman, J.

Nil

Plastic Design of Frames Vol. 2 (Cambridge V.P. 1971)

Plastic Design of Multi--story Frames (Lehigh University 1965)

91

(v) 524038 CE433 l'heoA'et.icallHfydwdynamics -- F. M. Henderson

Prerequisite

Hours

Examination

Content

CE332 Fluid Mechanics 11 is advisory

H hours per week

To be advised

General treatment of stresses and rates of strain in a moving fluid, derivation of the Navicr-Stokes equations, the vorticity equation; Kelvin's circulation theorem, the generation and diffusion of vorticity, with ,~ngineering applications. Irrotational flow theory in two and three dimensions, with engincering applications.

Text Vallcntine, H. R.

Reference Milne-Thompson,

L. M.

Applied HydrodynamiCS (llutterworths)

Theoretical Hydrodynamics (Macmillan)

(vi) 524039 CF:434 Open Cbllnnel Flow - F. M. Henderson

Prerequisite CE332 Fluid Mechanics II is advisory

Hours 1 i hours per week


Content Numerical methods for the solution of unsteady non-uniform flow problems in irregular chann.els. T~e cq.uations .of ~nsteady flow, the method of characteristics, with engll1eermg applIcatIOns, e.g., the dam break problem. Theories of Hood wave movement an~l technique~ !or its prediction. Sediment transport, river channel formatIOn and stablhty.

Text Henderson, F. M.

References Davis, C. V. &

Sorcnson Morris, H. M.

Rouse, H. Streeter, V.

Vallentine, H. R.

Open Channel Flow (Collier-Macmillan 1966)

Handbook at Applied Hydraulics 3rd edn (McGraw-Hill 1961)

Applied Hydraulics in Engineering (Ronald 1963)

t,'ngineering Hydraulics (Wiley 1951) Handbook of Fluid Dynamics (McGraw-·Hill

1961) Applied Hydrodynamics (Butterworths 1967)

92

533900 CommumicatioID!ll ami Automatic ConiU'OI

Prerequisites

Hours

examination

Content

Mathematics HA & HC (including Topics C, D, E)

6 lecture, tutorial & laboratory hours per week

Progressive a:;sessment & final examination

(0 533213 EE341 Automatic Control (ii) 533'110 EE342 :lLinear System Theory

(iii) 534132 lEE443 OjJtil1l1llz8.tiol1l Tecbniques (iv) 534136 ElE344 ConmnmicatioJls

(i) 533213 lElE341 Automatic 1C00lirol ~o~. G. C. Goodwin

Assumed Standard of Part II Mathematics Topics C. D, E, H Attainment

Hours 3 lecture, tutorial & laboratory hours per week for the 1st half year

Examination Progressive assessment & final cxamination

Content

Mathematical models of systems and components: linear differential equations, block diagrams, Laplace transforms, state-space formulation. Transient response: characteristic rools, transition Im:trix, system stability. Forced response: transfer functions, impulse and step res .. ponses, input-output stability, steady-state beh:wiour. Fcedbaek and compensation: effects of feedback on charactcristie roots, root-locus technique, Nyquist stability criteria, series and feedback compensation.

Text Fortmann, T. E. &

Hitz, K. L.

References Chen, C. T.

Desoer, C. A.

Gupta, S. C. & Hasdorff, L.

Melsa, J. L. & Schultz, D.

Introduction to Linear Control System Theory (Dckker 1976)

Introduction to Linea/' SYstem Theory (Holt, Rinehart & Winston 1970)

Notes for a Second Course on Linear Systems (Van Nostrand 1970)

Fundamentals of A utomalic Control (Wiley 1970)

Lineal' Control Systems (McGraw-Hili 1969)

93

Ogata, K.

Raven, F. H.

Modern Control Engineering (Prentice"Hall 1969)

Automatic Control Engineering 2nd edn (McGraw"HilI 1968)

(ii) 533110 EE342 l.ineal' System Theory ~ K L. lUtz

Prerequisite

Hours

Examination

Content

EE341

3 lecture, tutorial & laboratory hours per week for second half year

Progressive assessment & final examination

Multivariable control systems. Frequency domain design methods. Controllability. Observability. Canonical decomposition. Minimal realisations. Pole positioning by state variable feedback. Lucnburger observers. The type 1 servomechanism problem. Introduction to Kal" man filtering. Nonlinear control systems. Popov criterion and describ·· ing functions.

Text

Reference } As for EE341 Automatic Control

(iii) 534132 EE443 OptimizatiOl:t Techniques ~ B. D. O. Anderson

Prerequisites

Hours

Content

Part II Mathematics Topics C, D, E

3 hours pcr week for 2nd half year

Mathematical background to optimization. Comparison of optimization methods; engineering applications-such as to problems of identification, control, pattern recognition and resource allocation.

Texts Aoki, M.

Luenberger, D. G.

Reference Luenberger, D. G.

Introduction to Optimization Techniques (Macmillan 1971)

Introduction to Linear and Non-linear Programming (Addison-Weslcy 1973)

Optimisation via Vector Space Methods (Wiley 1969)

94

(iv) 534136 EE344 Communications <~" G. C. Goodwin

Prerequisite

Hours

Examination

Content

EE331 Circuits & Part II Mathematics Topic II

3 hours per week for 2nd half year


Introduction t? the common forms of analog modulation, as well as pulse modulatIOn systems including pulse code modulation. Perform" ance in the presence of noise is considered.

Text Carlson, A. B.

Reference Taub, H. &

Schilling, D. L.

Prerequisites

Hours

Examination

Content (i) 533213 EE341

(ii) 533210 EE342 (iii) 533211 EE361

(iv) 533212 EE362

Communication Systems (McGraw··Hill 1975)

Principles of Communication Systems (McGraw-Hill 1971)

Mathematics IIA & lIC (including Topics C, D, E)

6 lecture, tutorial & practical hours per week


Antomatk Contl'ol ~ see pages 93-94 Unear System Theory -~ see pages, 93-94 Computer Structure: Machine and Assembly Languages .~" see pages 119-120 Log.ical Design ami Switching Theory~" see pages 119,,120

423800 Economics me

Prerequisite

Hours

Examination

Content

Mathematics IIA & IIC & Economics IIA

As indicated in the description of the components

To be advised

Two of the following so as to include Econometrics I or Mathematical Economics or both:

(1) 423208 Econometrics l!

95

(ii) 423:1.04 Mathcmatical Economics (iii) 423104 Growth and Development (iv) 423102 lli1tcmatiomd Economics (v) 423103 Public Economics

(I) 423208 ]B'.cOJIOlI1CtriC§ l! ~~~ R. W. McShane

Prerequisite Economic Statistics II or Statistical Analysis

!lours 2 lecture hours per week


Content A knowledge of matrix algebra and of the mathematical statistics dealt with in Statistical Analysis is recommended. The course examines the usefulness of single equation rcgres:,ion an8.lysis in applicd economic research and also provides an introduction to simultaneous cstimation procedures.

Text Johnston, J.

References Fox, K. A. Goldberger, A. Hadley, G. Huang, D. S. Kmenta, J. Koutsoyiannis, A. Wonnacott, R. J. &

T.R.

Econometric Methods (McGraw-Hill 1972)

Intcrmcdiate Economic Statistics (\Viley)

l~'Collomctrics (Wiley) Linear A 1gehra (Addison-Wesley) Regressio/1 (lnd Econometric Methods (Wiley)

Elements of Ecol1ometrics (Macmillan)

Theory of Ecol1ometrics (Macmillan)

lc,'col1ometrics (Wiley)

(ii) 423204 Mathematical Economics ~~ P.e. III

Hours 3 lecture hours per week


Content (i) The mathematical reformulation and interpretation of traditional

micro .. and macroeconomic theory.

(ii) Modern capital and growth theory and mathematical programming.

96

Texts Dernburg, T. F.

Henderson, J. & Quandt, R.

References Benavie, A.

Chiang, A. C.

Gandolfo, G.

Hadley, G. & Kemp, M. C.

Intriligator, M. D.

Naylor, 1'. H. & Vernon, J. M.

Itfacroecollomic Analysis: A II introduction to Comparative Statics and Dynamics (Addison-Wesley 1969)

lVlicrocconomic Theory -~- A M'{(lhcl1laticai Approach 2nd eeln (McGraw-Hill)

l\llathematical Techniques for Ecollomic Analysis (Prcntice-·Hall 1972)

Fundamental j\1ethods of IvlatJlCmatical Economics 2nd edn (McGraw-Hill)

Mathematical j\1:;t/lOds and lvIodels in Economic DYllllmics (North .. Holiancl 1971)

Finite Mathematics in Business {{lid Economics (North-Holland 1972)

Mathematical Optimi;:,ation {flld Economic j'heory (PreJltice-HaH 1971)

Microeconomics alld Decision lvlodels of the Firm (Harconrt, Brace & World 1969)

Read, R. C. A IvfathcmalicallJackgroulld for Economists (lnd Social Scientists (Prentice··Hall 19'12)

Vandermeulen, D. C. Linear l':col1omic Theory (l'r(,Dtice·~Hill! 1971)

(iii) 423104 Gl'Owth .lIm~ Developmei1t~~,N. J. Dickinson/C. W. Stahl

Hours

Examination

Content


Two 3-hour papers (i) end of 1st half of academic yea r (ii) end of year

The first half of this course will deal wilh the dynmnics of fluctuations and growth in the framework of an advanced economy. A critical apprai.saJ is undertaken of leading contributions in this fidd. Topics such as the procJurtion function, t('chnical progress and variilUs Hlndd, of growth ar'~ df~alt with in dr·tail.

The second half of the course will study some underdeveloped countries with spceific focus upon their dualistic nature. The struct~ure of the rural and urban economies of the lypical llnderdevelopcd country will b~ investigated in order to understand undcrdevl:]opmcnt and hence deSIgn devc!opment strategies. Theoretical models will be supplemented with case studies from Asia.

97

Preliminary Reading

Bober, S.

Clark, J. G. & Cohen, M. (cds)

Hicks, J. R.

Meade, J. E.

Neher, P. A.

Text

Hamberg, D.

References

Bauer, P. T.

Enke, S. Gill, R. T.

Higgins, B.

Kindlcbcrgcr, C.

Meier, G. M. (cd.)

Myrdal, G. lVfyint, H.

Szentes, T.

The Economics of Cycle and Growth (Wiley 1968)

Business Flucillations, G rowlh and Economic Stabilis({iiul1: A Reader (Random [-louse

1963) A Contribution to the Theory of the Trade

eycl e (Clarendon 1967) A Neoclassical Theory of Ecollomic Growth

(Allen & Unwin 1962) Economic Growth and Development --- A

Mat/zelJlaliC(lI Introduction (Wiley 1971)

lvlodels of L'conol1Jic Growth (Harper IntcrnaL Edns 1973)

Dissent 011 Development (Wcidenfeld & Nicolson 1971)

Economics for Development (Dobson 1963) L'conomic Development: Past and Present 3rd

eeln (Prentice-Hall 1973) Economic Development rcv. edn (Norton

19(8) economic Development 2nd edn (Ivr eGraw ..

Hill 1965) Leadil1R Issues in Jc'conomic Development 2nd

edn (Oxford U.P.) Asian Drama (Twentieth Century Fund 1968) The L'corlol1!ics of Developing Countries 3re!

edn (Hutchinson) The Political Fconomy of Underdevelopment

(Akademiai Kiado 1973)

(Iv) 423102 International I!:collomics ~~ P. W. Sherwood

Hours

Examination

Content

2. lecture hours per week & I scminar hour per fortnight

One 3-hoUl' paper

(i) The pure theory of international trade. Comparative costs, the Heckscher~Ohlin theorem. Critical assessment of these and other theories of trade. The theory of protection; tariffs and quota restrictions on imports. Australian protection policy. Customs union theory. Relationships between economic growth and trade.

98

(ii) International monetary economics. The foreign exchange market. The balance of payments. The foreign trade mUltiplier. Balance of payments disequilibrium and acijl.!stment policies. Effects of internal expenditure changes. Analysis of rate chan.f"cs under adjustable peg ane! floating rate systems; optimum currency areas. Exchange controls. Tlitem'll and external balance. The international mOlllotary system and its rcform~. Theoretical aspects of international capital movements and the implications of overseas investment in Australia. Foreign aiel.

Texts

Ellsworth, P. T. & Leith, J. C.

or

Seammcll, W. M.

Snape, R. H.

Wells, S. J.

References

Bhagwati, J. (eel.)

The Internatiollal Economy 5th edn (Mac~ millan 1975)

International Trade ([lid Payments (Macmillan ] 974)

International Trade and the Allstralian Economy 2nd edn (Longman 19'13)

Internrttionai L'collomics rev. edn (Allen & Unwin 1973)

I ntcrnational Trade (Penguin 1972.)

Caves, R. E. & Readings in International Economics Johnson, H. O. (eds) (Allen & Unwin 1968)

Clement, M. D. et aL Theoretical Issues in International Economics (Constable 1967)

Cooper, R. R. (cd.)

Heller, H. R.

Heller, H. R.

Kindleberger, C. p.

McColl, O. D. (ed)

Intematiollal Finance (Penguin 1969)

International Trade: Theory and Empirical Evidence 2nd cdn (Prentice-Hall)

International ;Wol7etary Economics (Prentice·· Hall 1974)

International Economics 5th edn (Irwin 1973) Overseas Trade alld Investment (Pelican 1972)

(v) 423H)3 Public Economics ,~~ N. J. Dickinson/W. J. Sheehan

Hours

Examination

Content

2 lecture hours plus seminars

One 3-hour paper

The effects of government intervention in the economy through the budget ane! through the operation of publicly·,ownec! business undertakings. Inter-governmcntal fiscal relationships are examined. At the mieroeeonomic level, an analysis of the ciIects of tax and expenditure policies, in particular, community welfare and incentives.

99

At the macroeconomic level, models afe used 10 analyse the relation of fiscal policy 10 other economic policies for stability and growth.

Preliminary Reading Eckstein. O. Public Finance 3rd edn U'rentice-Hall 1973)

Texis Nil

References Buchanan, J. 1v1.

& Flowers, lilt R. Culbertson, J. M.

Fromm, G. & Taubman, P.

Houghton, R. W. (cd.) Johansen, L. K.eiser, N. F. IVlathcvv's, 1< __ , L. (~

Jay, W. R. C. Musgrave, R. A. &

P. n. Peacock, P,. Sf.

Shaw, G. K. Shoup, C. S.

733300 Geology me

Prerequisites

Hours

Examination

Content

The Public Finances (Irwin)

Macroeconomic Theory and Stahilisation Policy (McGraw-Hili)

Public ,";collomic Theory (lnd Policy (CoHill-Macmillan)

Public Finance (Penguin) Public Economics (North Holland 1971) Readillg iii Ivfacroi'collolJ1ics (Prentice-llnll) Federal l"ina!/ee (r".fc] ';0 Ii )

Public Finance in Theory and Practice ((1vv-lTiH)

The Ecollomic Theory of Fiscal Policy (Allen & Unwin)

Public Fin(l)lce (Weidenfcld & I'<.]icholson)

Physics lA, Mathematics IIA & He & Geology llA

3 lecture he\lrs & 6 laboratory hours pef week and 12 clays field work

Two 3-hour papers plus assessment

Sedimentology -- the petrogenesis of sedimentary rocks. Economic geology - principles of formation of economic mineral deposits; major Australian ore deposits; ore mineralogy. Structural geology···structural aspects of geosynclinal concept; orogenies; continental drift; global tectonics. Photogramrnetry and Photogeology _._. basic principles of interpretation; aerial photographs and their use in stratigraphic and structural studies. Exploration Geophysics: geophysical techniques - .. their interpretation and application in petroleum ,md mining explor·· at ion, and hydrogeological and engineering investigations as well as scdimentmy basin and tectonic studies.

100

Texts

Prerequisites

Hours

Examination

Content (i) 543501

(Ii) 543502 (iii) 543503 (iv) 544104

Hours

Examination

Content

MJL:~81

ME383 ME384 l\;lDE483

Consult lecturers concerned

Mathematics IIA & He

6 lecture hours per \vcck

Progre~isivc assessment

MetilJmb lEngiJleeriug Quality Engineering Design I'm: JP'rodllcition It'mliucltiml lKugi!LIcel'ill!;

I} hours per week

Progre:)~;ive assessment

The integration of man, machines and materials to aehirve maximum dliciency of operation. The critical questioning attitude. Charting methods. V"ork study. Ergonomics. Activity sampling. Calle studies.

Text Niebe!, B. W. Motion (lnd Time Study (Invin)

References Alford, L. P. & Productioll Handbook (Ronald)

Bangs, J. R. (eels) Barnes, R. M. Motion and Time Study (Wiley) Krick, E. V. IVIethods Engineering (Wiley) Maynard, H. B. (eel.) Industrial Engineering Handbook

(McGraw-Hill)

(Ii) 543502 lVfE383 Qmllity Engineering .--~ D. S. R. Karamchotty

Hours 1;\ hours per weck

Examination Progressive asse,;sment & examination

Content Concepts of quality. Sampling plans. Inspection by attributes, by measurement. Operating characteristic curves, control charts. Design of experiments. Analysis of variance.

101

Text

References

Amer. Soc. of Tool & Mfg Engs

Duncan, A. J.

Grant, E. L. Juran, J. M. &

Gryna, F. M. Kirkpatrick, E. G.

Nil

Handbook of Indll.,trial l'vietrology (PrenticeHall)

Quality Control and Illdustrial Statistics (Irwin)

Statistical Quaiily Con/rol (McGraw-Hill) Quality Planning (llld Analysis (McGraw-Hili)

Quality Control for Managers and Engineers (Wiley)

Maynard, E. G. (cd.) Indllstrial Engineering Handbook (McGrawHill)

(iii) S43S03 ME3M Design foil' Plwduction .~. J. W. Hayes

Hours 1 J hours per week

Examination Progressive assessment & examination

Content The application of economics, methods engineering, ergonomics :md mechanical engineering to the development and design of a product. Production distribution and marketing of engineering products. Production, assembly and inspection mcthods in relation to scale of output. Principles of metrology ane! tool, jig and fixture design.

Text Nil

References

Gladman, C. A. Geometric Analysis of Engineering Designs (Aust. Trade Publications 1972)

Kempster, M. H. A. Principles of Jig and Tool Design (English u.P.)

McCormick, E. J. Human Factors Engineering (McGraw-Hill 1964)

(iv) 544104 MlE433 Plrodm~tiol.l Engineedng -~ J. W. Hayes

Hours J 1 hours per week


Content Production planning and control, Forecasting, inventory, scheduling. Dynamics of production-inventory systems. Simulation of production systems.

102

References

Baker, K. R.

Box, G.E. & Jenkins, G. M.

Forrester, J.

Prerequisites

Hours

Examination

Content

Introduction to Sequencing (lnd Scheduling (Wiley 1974)

Time Series A nalysis, Forecasting and Control (:Holdcn-Day)

Industrial Dynamics (M.I.T. Press 1961)

Mathematics IIA & lIC (including Topics E, F & H)

G hour" pcr wcek

Progressive assessment

Students may choose one of the following alternatives (a), (b), (c) or (d) but all 4 alternatives may not be available each year. (a) (i) ME361 Automatic Control

(ii) ME401 Systems Analysis (iii) ME402 Systems Planning, Organisation & Control

(viii) ME481 Operations Research-Deterministic Models (b) (iii) ME402 Systems Planning, Organisation & Control

(viii)ME487 Operations Research·- Deterministic Models (ix) ME488 Operations Research - Probabilistic Models (x) ME489 Operations Research - Applications in Industry

(c) (iii) ME4m Systems Planning, Organisation & Control (iv) ME404 Mathematical Programming (ix) ME488 Operations Research - Probabilistic Models

(d) (i) ME361 Automatic Control (v) ME434 Advanced Kinematics & Dynamics of Machines

(vi) ME448 Introduction to Pholomechanics (vii) M£449 Reliability Analysis for lVIeehanieal Systems

(i) S43204 ME361 i\lUtomaiic COl"liroi---K L. Hitz

Hours [i hours per week


Content

An introductory course in linear control ~ystems. Mathematical models of systems and components; differential equations and transfer functions. Discussion of analog computers and their use in thc solution of equations and simulations of systems. Simple systems of flrst and

103

second order. Analysis of steady state performance. System stability and transient response by al~cbraic, root~locus and frequency response methods. Introduction to compensation techniques. Description of components of servo··mechanisms and process control systems.

Text Fortmann, T. E. 8:.

Hitz, K. L.

T-?eferences Desoer, C. A.

Gupta, S. C. & HasdorfT, L.

Mc]sa, J. 1 .. &. Schultz, D. G.

Raven, F. H.

Introductioll to Linear Control Systell1s Theory (Dekker 1976)

Notes for a Second Course ill Linear Systems (Van Nostrand··Reinhold 1970)

Fundamentals of Automatic Control (Wiley 1970)

Unear Control Systems (l\lcGraw-Hill 1967)

Automatic Control Engineering 2nd edn (McGraw-Hili 1968)

(ii) 544451 lVLll~401 Systems Alilalysis .. ~ A. W. Roberts

f1 ours I} hours per week


Content System concepts and system classification. Mathematical modelling. Deterministic aud probabilistic models, Stochastic models. Deterministic systems···-Linear Graph theory and Network Analysis; Classical time and frequency domain analysis of continuous and discrete systems; Matrix methods in systems modelling and analysis. Stochastic Processes--Random data and signal analysis; Response of systems to random excitation; System identification.

Text

References Bendat, J.S. &

Piersol, A. G. Busaeker, R. G. &

Saaty, T. L. De Russo, P. M. et a1. Machol, R.

M dvIillan, C. & Gonzalez, R. F.

Nil

Al eaSllfemCl1t and Analysis of Random Data (Wiley 1968)

Finite Graphs and Networks (McGraw·Bill 1965)

State Variables for Engineers (Wiley 1965) Systems Engineering Handbook (McGraw

Hill 1965) Systems Analysis: A Computer Approach to

Decision Models (Irwin-Dorsey 1968)

104

Meredith, D. D. et '11. Design and Planning of Engineering Systems (Wiley 1967)

Raven, F. H. Mathematics of Engineering Systems (McGraw-Hill 1%6)

(iii) 544452 lVffi40~ Systems Phuming, OI'gallizatlim amI CO!(ltml.~<o A. Roberts/G. D. Butler

Hours H hours per week


Content

Goals and structure of systems. Mathematical modelling and system ~imulation. Hierarchial control systems. System performance criteria, concepts of optimization. Formal organisation and decision theory. Application of systems techniques to organisational analysis and design. Examples of industrial and business systems.

Text

References Aekoff, R. L.

Battersby, A.

Carzo, R. & Yanouzas,

Citron, S. J. J. V.

KUester, J. L. & Mize, J. H.

Machol, R.

Nil

A Concept of Corporate Planning (Wiley 1970)

Network A nalysis for Planning Schedlllillg (Macmillan 1970)

Formal Organisation, A Systems Approach (Irwin-Dorsey 1965)

Elements of Optimal Control (Holt, Rinehart & Winston 1969)

Optimization Techniques with Fortran (McGraw-I'IiIl 1973)

Systems Engineering Handbook (McGrawHill 1965)

McMillan, C. & Systems Analysis: A Computer Approach to (Irwin·Dorsey 1968) Gonzalez, R. F. Decision Models

Meredith, D. D. et al. Design and Planning (Wiley 1967)

of Engineering Systems

Wayne-Weymore, A. A Mathematical Theory of Systems E'ngineer~ ing (Wiley 1967)

(iv) 544417 ME404 Mathematical PmgmnnnilIg -~- Ie. L. Hitz

Hours

Examination

H homs per week


105

Content Introduction to the solution of static optimisation problems. Dynamic programming; computational refinements of the basic algorithm. Line.at programming; the Simplex algorithm and its revised form; duality theory; sensitivity analysis; decomposition algorithms. Transportation and assignment problems.

Texts Gass, S. 1.

Nemhauser, G. L.

References Bellman, R. E. &

Dreyfus, S. E. Kunzi, H. P. et al. Macmillan, C. Taha, H. A.

Note

Linear Programming 3rd edn (Internal. Studcnt Edn, McGraw~HiIl 1969)

Introduction to Dynamic Programming (Wiley 1966)


Non-Linear Programming (Blaisdell 1966) Mathematical Programming (Wiley 1970) Operations Research (Macmillan 1971)

This subject is identical with the first part of ME581G.

(v) 544419 Ml<:434 Advanced Kinematics and Dynamics of Machines .~ .. E. Bctz

Hours

Examination

Content

1 t hours per week

To be advised

Dynamic Motion Analysis: energy distribution method, equivalent mass~and-foree method, the rate-of-change··of-energy method. Advanced Kinematics of the Plane Motion: the inflection circle, Euler-Savary equation, Bobillier's construction, Hartmann's construction. Introduction to synthesis: graphical and analytical methods.

Text Hirschhorn, J.

References Hall, A. S.

Holowenko, A. R.

Mechanics of Plane Motion (McGraw-Hill 1962)

Kinematics and Linkage Design (PrenticeHall 1960)

Dynamics of Machines (Wiley 1955)

106

(vi) 544411. ME448 Introduction to If'hotomechanks· ~. D. R. A. Budney

Ii ours lel hours per week


Content Concepts of bi~refringence. Polarized light~plane, circular and elliptical polarization. Fundamentals of photoelastic method _. stres£~optic law in two dimensions. Isochromatics, isoclinics, isopachics -~~ fundamental equations for linear and non-linear model materials. Model analysis for two and three dimension problems which may involve static, dynamic or thermal loading conditions. Calibration of material and solution of disc problem.

Text

References Dally, J. W. &

Riley, W. F. Durelli, A. J. &

Riley, W. F. Frocht, M. M.

Nil

Experimental Stress Analysis (McGraw-Hill 1965)

introduction to Photo~Mechanics (PrenticeHall 1965)

Photoelasticity (Wiley Vol. I 1945 & Vol. II 1948)

(vii) 544418 ME449 Reliability Analysis for IVlechanical Systems A. J. Chambers/ A. W. Roberts

flours 1 t hours per week


Content Some important probability concepts. Fundamental concepts of the theory of reliabiiity. Some quantitative aspects of reliabiliLy. Component reliability and reliability of assemblies of components, gradual and sudden failure. Matrix formulation of problems. Spectral method for calculation of reliability. Basic concepts of systems. Reliability analysis of systems. Methods for improving the reliability of systems. Cost~Benefit analysis. Reliability Case Studies. Automobile suspension ignition system. Measuring system.

Text Shooman, M. L. Probabilistic Reliability. An Engineering

Approach (McGraw-Hill 1968)

107

References Haviland, R. P.

Polovko, A. M.

Engineering Reliability and Long Life Design (Van Nostrand 1964)

Fundamentals for Reliability Theory (Academic 1968)

(viii) 544841 ME4!!7 Operations Research ~~~ Detel'l!lIiuistic Models -~ G. D. Butler

Hours

Examination

Content

I} hours per week


Concept of optimisation; optimisation approaches; formulation of models; linear programming; allocation and assignment; simplex method; duality; theory of games, parametric programming; integer programming; zero-one programming; quadratic programming; decomposition principle. Network theory; dynamic programming. Geometric programming. Applications.

Texts Ackoff, R. L. &

Sasienji, M. W. Hillier, 1. S. &

Lieberman, G. J. Taha, H. A.

References McMillan, C. McMillan, C. &

Gonzalez, P. F. Wagner, H. W.

Fundamentals of Operations Research (Wiley)

Introduction to Operations Research (Holden-Day)

Operations Research (Macmillan)

Mathematical Programming (Wiley) Systems A f/alysis-A Computer Approach to

Decision Models (Irwin-Dorsey) Principles of Operations Research (Prentice

Hall)

(ilK) 544842 ME488 Opemtiolls Research ~ Pmbabilistic Models ~-- G. D. Butler

Hours

Examination

Content

1 t hours per week


Statistical decision theory; forecasting, methods moving average, exponentially smoothed average. Inventory control theory. Fixed order quantity; fixed order cycle systems; production c __ inventory systems. Queueing theory; simple queue, multiserver queues. Queues in series. Transients in queues; simulation of systems. Applications.

108

Text Saaty, T. L.

References Brown, R. G.

Dychman, T. R. et al.

Hadley, G. & Whitin, T. M.

Taha, H. A.

Elements of Queueing Theory (Prentice.Hall)

Smoothing, Forecasting and Prediction of Time Series (Prentice-Hall 1963)

Ai anagement Decision Making ullder Uncertainty (Macmillan 1969)

Analysis for Inventory Systems (Prentice.Hall 1(63)

Operations Research (Macmillan 1(71)

(,,) 544843 ME48,) Operations Research ~c~ Allplkatio11ls in Jmillstry ~. G. D. Butler

Hours

Examination

Content

Ii hours per week

To be advised

The case study approach to industrial cases. The application of operations research to industrial problems.

Text Nil

References

Dooley, A. R. et al.

DUCkworth, E.

Eilon, S. ct al.

McKenny, J. L. & Rosenbloom, R. S.

Rivett, B. H. P. & Ackoff, R. L.

SchnelIe,K. E.

743100 Physics InA

Prerequisites

Hours

Examination

Casebooks in Production Management (Wiley 1968)

A Guide to Operational Research (Methuen ]965)

Exercises in Industrial Management (Macmillan 1966)

Cases in Operations Management (Wiley 1969)

A lV/anager's Guide to Operational Research (Wiley 1(63)

Case Analysis and Business Problem Solving (McGraw.,Hill 1967)

Physics II, Mathematics IIA, Of lIe (Topics C, E, G & H or B or D desirable)

4- lecture hours & 8 laboratory hours per week

Assessment to the equivalent of three 3~hour papers

109

Content The areas of classical and quantum physics cssential to the understanding of both advaneed pure physics and also the many applications of physics. Some electronics is also included. A. Classical Physics Mathematical methods, advanced mechanics, special theory of relativity, electromagnetics including waveguide and antenna theory. B. Modern Physics Quantum mechanics, atomie and molecular physics, statistical physics, solid state physics, nuclear physics, electronics. C. Laboratory Parallels the lecture course in overall content with at least one experi~ ment availahle in each topic, although students are not cxpected to carry out all the experiments available.

Texts A list is available from the Physics Department office. Students should retain thcir Physics II texts.

'153300 Jl>gychology llII!C

Prerequisites

Hours

Examination

COlltent E"lKperimentaI Desigrl Pel'soillality Assessment

Mathematics IIA, He & Psychology ITA or lIB

4 lecture hours & 3 laboratory hours per week

To he advised

Mathematical Models ill!. Jl>en:elltioll mId llA!!uuulg Cognitioll Pen:eptioll amI Physiological Psychology.

One or more additional topics to be selected from Psychology IlIA or HIB. Students will also be required to complete an independent investigation in mathematical psychology under supervision.

Text

References Coombs, C. H. et aJ. Flavell, J. H.

Harman, H. H. Jackson, D. N. &

Messick, S. Laming, D. Mandler, J. M. &

Mandler, G.

Nil

Mathematical Psychology (Prentice·.Hall 1974) The Developmental Psychology of Jean Piager

(Van Nostrand 1963) Modern Factor Analysis (Chicago U.P. 1960) Problems in Human Assessment (McGraw

Hill 1967) Mathematical Psychology (Academic 1973) Thinking: From Association to Gestalt (Wiley

1964)

110

Prerequisites

Hours

ExaminatirJn

Content

SCHEDULE C

Mathematics IlIA & Physics IlIA and such additional work as is required for combined honours students by the Department of Mathe. ematics.

A student desiring admissiun to this subject must apply in writing to the Dean of the Faculty of Mathematics before 7th December of the preceding year.

To be prescribed bJ the Heads of the Departments ~f Mathematics and Physics. Project work WIll normally bCsin in the first week of February.

Examll1ations will be held in th" Mathematics (md Physics topics selected by foe student.

The st~dcnt s~QU. complete four topics from Mathematics IV, chosen ~or theI~ applIcatIOn t? Physics; he must also attend selected topics Ifl Ph~SICS . ry. A project of mathematical and physical significance supervIsed JOI~tly. by the Department of Mathematics and the Depart. ment of PhYSICS ]S also required.

664200 Matbematics/psychology IV

Prerequisites

Hours

Examination } Content

Mathematics lITA & Psychology HIC. A student desiring admission to this subject n;ust apply in writing to the Dean of thE: Faculty of Mathematics before 7th December of the preceding year.

To be advised

4 Mathematics topics chosen from the Part IV Mathematics topics (see page 53 et seq.)

Psychological Measurement (see below).

Mathematical MOdels in Perception and Learning (see below).

HI

(0 i'§ycboiogkal Memmrcment J. A. Keats

Prerequisites

Hours

Examination

Content

Nil

1 ~~ hours per week

To be advised

The logic of measurement and its application to psycholoBical phenomena and at least one paper on one of' the rn0re recently developed psychological scaling methods.

Text

References Atkinson, R. C. (ed.)

Campbell, N. R.

Coombs, C. H. Lord, F. M. &

Novick, 1\1. R Ross, S.

Torgerson, W. S.

Nil

Studies in Mathematical Psychology (Stanford U.P. 1964)

Foundations of Science: The Philosophy of Theory and Experiment (Dover 1957)

A Theory of Data (Wiley 1964) Statistical Theories of Mental Test Scores

(Addison-Wesley 1968) Dogical Foundations of Psychological

Measurements (Aarhuus Stiftsbogtrykkerie A-S 1964)

Theory and Methods of Scaling (Wilcy 1958)

(ii) Mathematical Models in Perception and lLeaming c"~~ R. A. Heath

Prerequisites

Hours

Examination

Content

Part II Mathematics Topic H recommended

1 t hours pcr week

To be advised

An introduction to the application of stochastic process models to the analysis of psychological processes involved in perception and le;Jrning. Use of a real-time computer.

Text Nil

References Atkinson, R. C. et al. An Introduction to Mathematical Learning

Theory (Wiley 1965)

112

Coombs, C. H. et a!. Mathematical Psychology (Prenticc>llall 1970)

Cox, D. R., & Miller, H. D.

The Theory of Stochastic Processes (Methuen 1965)

Laming, D. Mathel7wtico/ Psychology (Academic 1')73)

A GUIDE TO STUDENTS ENROLLING IN THE FACULTY OF MATHEMATICS

1. 1110 following n01Hn,lthematics wbjocts have been approved.

Part I Accounting I Geology I Biology I German IS or IN Chemistry I G reek I Classical Civilisation I Japanese [ Drama I Legal Studies I & II Economics IA Linguistics J Engineering I Philosophy I English I Physics IA 01' IB French IN or IS PsycIwlo8Y I Geography 1 ~anskr;t I

Sociology I

Pad l!J! Biology UA, lIB & IlIA Chemistry JJ A Economics IIA & lIB l:dnc~lion 11 Electronics & Instrumentation II English HA French IIA Geography IrA, lIB & nIB (;cology lIA & lIB lli,tuIY IIA, lIB &. TIC J '!]Jancsc IlA l'hilo,,()phy llA &. llil Physics II P,ychology IlA & lIB

2. Enrolment in the following subjects is restricted as indicated below.

Accounting 1·- Students who include this subject in their course as a Part I subject are advised to discuss with the Dean the possib·· ility of including Accounting IIA or Accounting lIB in their Parl n subjects. However, both Accountinl', HA and Acccunling lIB must be passed to gain credit for one Part II subject; in cxcep~

tional cases one of these subjects phIS additional work, e.g. Matlle" matics lIB Part (i), may be acceptatjlc~. Economics llA - Students should also include the Part II I'vfathematies Topic H, Probability and Statistics, in their course. Economics /IB -- This subject would not normally be included in the Bachelor of Mathematics course. However if permission is given to include this subject then the content should be discussed with the Dean.

A student may not include both Physics 11\ and Physics IE in his course. A student may not include both Engineering I and Civil Engineering 1M in his course.

3. Perrrlission "vill nOflnally be given for the inclusion in a student's course of subjects which are prerequisites or corequisites of subjects appearing in the schedules.

113

RE'QUlR1:Jl1El'JTS FOR/HE' DIPLOMA IN COMPUTER SCIENCE'

1. In these Requirements, unless the context or subject matter otherwise indicates or requires, "the Faculty Board" means the Faculty Board of the Facultv of Mathematics and "the Board" means the Board of Studies ;~stab]isbed to supervise the course of the Diploma in Computer Science.

2.. An r.pplicant for registration as a candidate for the Diploma shall: (i) have satisfied ail the requirements for admission to a degree

in the University of Newcastle, or (ii) have satisfied all the requirements for admission to a degree

in another university or institution approved for this purpose by the Board, or

(iii) hold other qualifications approved for this purpose by the Senate on the recommendations of the Board and the Faculty Board.

3. The Board may require a candidate to complete additional work and/ or examinalions if, in its opinion, he has not reached the assumed standard of attainment on which the content of any of the 1]ubjects is based.

4. An applicant for registration as a candidate for (he Diploma may be granted standing by the Board for work completed in this Univcrsity, or in another university or institution approved for this purpose by the Board. Such standing shall not be eivel1 for more than half d the course and shall not be given for work on the basis of which a degree or diploma has already been conferred or awarded or approved for conferment or award.

S. (a) To complete a subject qualifying towards the Diploma, a candidate shall attend sllch lectures, tutorials, seminars and laboratory classes, and submit such written work as the Board may require.

(b) To pass a subject, a candidate shall complete the subject and pass such examination~ as the Board may require.

6. The Board shall approve a programme of studies for each candidate. This programme may be varied only with the approval of the DOllrd.

7. (a) A candidate may withdraw from a subject only by informing the Se:::retary to the University in writing and the withdrawal shall take effect from (h, date of receipt of such notification.

(b) A candidate who after: the eighth Monday in First Term, in the case of a suhject lasting only the fir~t half-year; the sixth Monday in Seccnd Term, in the case of a subject lasting the whole year; the second Monday in Third Term, in the case of a subject lasting

114

only the second half.,year; withdraws from a in which he has enrolled shaH be deemed to have failed in that subject, unless granted permission by the Dean of the Faculty lOf Mathematics to withdraw without penalty.

8. In order to qualify for the Diploma, a candidate shall, in not less than two years of part··time or one year of fell-timc enrolmcnt, complete satisfactorily a course of studies, comprising 11 unit; of work chosen from the Schedule of Subjects provided thM the subjects passed:

(a) shall include all the subjects in Group I, unk~s, in order to satisfy provisions of sub-section (c) of this Section, the Board has prescribed for the candidate concerned an alter .. native subject or subjects for one or lTlOre of the subjects 111

this Group; (b) shall not include more than two units from subjects In

Group Ill; (c) shall not include a subject which, in the opinion of the

Board, substantially overlaps the content of a COllEe completed or work presented for another degree or diploma; and

(d) shall be those prescribed in the programme approved by the Board.

9. The Diploma shall be awarded in two grades, namely: Diploma in Computer Science with merit, Diploma in Computer Science.

10. Group I subjects shall be offered each year, but subjects listed in Groups II and III may not necessarily all be ofTered in anyone year.

11. Notwithstanding the provisions of Scction 8, the Board may from time to time approve a subject to be coun(cd as a Group II or Group III subject for one specific year.

12. In order to provide for exceptional circumstances arising in particular cases, the Senate, on the recommendation of the Faculty Board, may relax any provision of these Requirements.

SCHEDULE OF SUBJECIS

1 The lecturer in the subject will assume that all students ha,ve a good understanding of the content of items in this column.

2 Subjects with a prefix CS are subjects offered in the Faculty of Mathe, matics specifically for the Diploma in Oomputer Science.

GllWUPl!

Core Subjects

Subject2

CS~-Commcrcial Programrning

Department OjJering Assumed Standard Subject of A ttainment1

Commerce

115

Mathematics I. Topic NM. OR Commercial Electronic Data Processing

No. of Units

EE361~-,Computer Strllcture: Machine & Assen1bly Langu8.eCS

RE36?""Logieai Design & Switclu:lg Theory

CS--Prourammlng & Algorithms C5 -- Data S{mcttlre~-; 8:,

Programming

CS ,-Numerical AuaJysis

GHOUl!:' J!J(

Department O f" Assumed Standard

uerzng fA' I S' I' t 0 tillliliJlellt

11 )Jce

Electrical Engineering Electrical Engineering Mathematics

Mathematics

Mathematics

Mathematics I

Mathematics I

Mathematics I CS-·Prngr~Hnmilig &

AlgorithrCis II Mathematics, Topics D. F

No. oj Uni(\

§,lbject§ in the mailll"S!l'eam of cOlllllm[er science Quantitative Business Analysis II Infonnation Systems

Sueial Implications of Compnters

Systems Analysis &. Design A

Systems Analysis & Design B

EE341--·Au(0111atic Control

FfJ45--Sarnplc Datu & Digital Control

EE425~--Digital Electronics

EE463~Computef Operating Systems

EE464-"~,Compilers, Assemblers ,'",_ Interprmcrs

EE44FJ~Digilal Communicatio113

EE462---To;oics in Switching Thcory

EE565-Pattern Recognition

EE56G-Automata & Computing l\1rtchincs

EE567-~Computer Process Control

EE568---Advanced Computer Architecture

EE569-I'ormal Languages & Automata

CS-,--Topic in Applied Probability e.g" InfonnaLion 'Iheory

CS-Thcory of Computing

CS-Mathematical Principles of Numerical Analysis

ME402-Systems Planning, Organization & Control

ME404--'Mathematical Pf()gramming

ME581G-Mathematical J)rogrammin1!,

GROUP m

Cornlnerce Commerce

COtnlnerce

Comnlercc

Commerce

Electrical Engineering Electrical Engineering

Electrical Engineering

Electrical Engineering Electrical Bngineering Electrical J ~n?,inccri!1g Electrical Engineering Electrical Engineering Electrical Engineering Electrical Engineering Electrical Engineering Electrical Engineering

MathematiC!)

Mathematics

Mathematics

Mechanical Engineering

Mechanical Euginecrin8 Mechanical Engineering

Commercial EOP Mathematics 1 or Commercial

EDP

CS-Conllllcrcial llrograrmning Systems Analysis & Design A Part II Mathematics, Topics

C, D,E,H

EE341---Automatic Control

FP421-Elcctronics EE4231r--ElcctroniC!) !~abol'atory EE332--Circuits EE361-----Computcr Slrnclll1'o:

Machine & Assernbly Langnages 1 EE361-Computer Structure:

.iVlachinc: &. Assembly Languages 1

EE362---LogicaJ Design & Switching TheOIY

Part II Mathematics, Topics C, D, E, II

Mathematics I

EE341~-Automatic Control

EE361~Compntcr S(rllcture: 1 lVL_1clIine & As~embly Lallguagc~, 1

Mathematics I

Part 1I Mathematics, Topic H

Part II Mathematics, Topics C, D, F or equivalent

Part II Mathematics, Topics C, D, F

Part II Mathematics, Topics C,D, E,H

ME361--Automatic Control Part II Mathematics,

Topics C, D Part II Mathematics,

Topics C, D 2

§ubjeds wbich have somc aIJplic;l;tiolii to compllter science

CE5IS--Elastic Continua Civil Engineering

116

CE212~---Mechanics of Solids I Part II Mathclllatics, Topic D

Subject2

Theories of Organisation

EE323--Linear Electronics

El'J24L'~",Electronics Laboratory

EE342-,,-Lillear System Theory

EFA21~Electronics

EE423Ir-~E1cctro!lic~ 1.:~bon~ tury

f~ E344--Communic(l tions

EE442-Modern Control

EE44J~Optill1izatio!l Techniques

EE44.5,--~--Co!l1mt1nication Systems

EE516--Compllter Aided Analysis of Po'-vcr··Systel11:,

CS--Probo.bility & Statistics CS---Asymptotic Methods in

All,dy'ds

CS--Randnrn & Restricted \\Talks

CS~,signal Detection

CS--Stochastic Processes

CS~-Combinatorial Designs

CS--Combil1atorics

CS--Population Dynamics

CS-Graph Theory

CS~~Mathcm"tical Logic

CS--Operations Research

ME449·~Rcliability Analysis inr Mcchankal Systems

ME503G-Dcsign of Experiment:; fnr Engineering Re~iearch

MFA87~-Opcratiol1s Research .~Deterministic Models

ME488-0perations Research~Probabilistic Ivloclels

ME489---0perations Research Applications in industry

f"Tet 312-~--Optimization & Control CS-""~-Illstrumentatiol1 Techniques

The Board may approve the projoct. This project would be count more than two units.

Department Oltering Assumed.Standard Subject of Attamment1

No, of Units

Commerce

BiectIkal Bngineerillg

Electrical Engineering

Electrical Engineering Electrical Engineering Electrical Engineering Electrical EngilleeI'ing Electrical Engineering Electrical Engineering Electrical Engineering Electrical Engil1ccriog Mathematics

Mathematics

Mathematics

Mathematics

Mathematics

Mathcmatics

Matnematlcs

Mathematics

l'.'latl1cmati(:s

IV'iathcmatics

Mechanical Engineering Mechanical Engineering

Mech.1.nical El1gineering

Mechanical Engineering

IV1etall11rgy Physics

Organisational Uchavjoul' EE2.03~" ~-Introdnction to

Electrical Information EE321-~'Electronics

PI-I221-E!cctromagnetic21 & Quantum Mechanics

EE322.-~Electronics

EEJ41'"~-"Automatic Control

EE323-~-Lillcar Electronics

EE32AL-ElcCif(ll1ics Laboratory EE421,","c--ElectfOllic§ EE331 ~""Circuits Pert II Mathematics, Topic H

EE34?-Lincar System Theory

Part n M'athcmatics, Topics C, D, E

FEJ42~-Linear SY~itcm Theory

EE731· -~CElectrkHl Circuits

Part II Mathematics, Topic II Part !l Mathematics,

Topics B, C, E PilTt T r Mathematics,

Temits n, C, n Part n Mathematics, Topic II Part III Mathematics, TopicR Part II Mathematics, Topic H Part III Mathematics,

Topics R, V Part II Mathematics,

Topics D, IC Part H Mathematics,

Topics n, C

rart II Mathematics, T<Jpics 0, Ie

Part n Mathematics, Topics D, Ie

rart n Mathematics, Topics C, D

Part II Mathematics, Topic H

Part II Mathematics, Tunics C, D

;'art If Mathematics, Topics C, D. H

Part II :rvlathematicsJ

Topics C, D, H ivlE487--0pcrations Research

Deterministic 1Vlodels ME488-- --Operations Research

Probabilistic Models

Physics IA or IB 1 1

indus ion in a student's programl',le of a in lieu of Group HI subjects and may not

117

A student may suggest to the Dean for consideration by the Board the inclusion in his programme of a subject not listed in the Schedule of Subjects.

Students interested in positions as Computer Systems, Officers in the Australian Public Service are strongly advised to include the subjects Systems Analysis and Design A and B in their course.

SUBJECTS OVERLAPPING IN CONTENT

The Board of Studies in Computer Science has decided that pursuant to Section 8 of the Requirements for the Diploma in Computer Scicnce a student is not permitted to include in his programme any of the mutually exclusive subjects listed in the Table below, nor may he include a subject if he has previously includcd the content of that subject in his work for a degree or diploma whieh has already been conferred or awarded or approved for conferment or award.

1. CS-Opcratiolls Research ME487-0perations Research -- Quantitative (Mathematics III Topic U Deterministic Models Business ~ Operations Research) Analysis II

1-

2. ME404---Mathcmatical ME58IG-·Mathematical Programming Programming

-----3. CS--11lCory of EE569-Formal Languages

Computing and Automata

DlESCRlIP1rION OF SUBJECTS

GROUP 1--- CORE SUBJECTS

410136 CS "~Cmnmcrciai Programmillg ~ 1. R. Beaman

Assumed Standard of Mathematics I Topic NM or Ccmrncrcia1 Attainment LD.P.

Hours

l~xamiIWii()il

COli tent

:' lcctl'fC llcmrs pCl" wcek for 1 ';t half YC:lr

Two :1-:10[]]" P;jPCL, (i) Thcofy~at mid year (ii) Collol at end of year

Basic conccpts of file handling and fi1c m;,inlenance, il;cluc!inS fiie creation :mel

Flo'w charting; file merging and upd:tling of transactiom; lilpe block· ;1 nd bnfIcring.

118

General run types including editing, searching and soninf',. Direct access versus serial; random or ocqllcntial organisation; rC-;!!l1 tech .. niques; verifying programme accuracy; table lookup; programme documentation and use of test data.

C:0BOL as a b~!siness data proccc;sing and file organi:;ation languaBe. ExtensIve practical work in COBOL, including c;[se studies.

Texts J.c.L. Feingold, C.

References

Clifton, H. D.

Davis, G. B. & Liteeky, C. R.

DeRossi, C. J. Kapur, G. K. Laden, H. N. &

Gildersleeve, T. R. McCracken, D. D.

et al. Muraeh, M.

Sanders, D. H.

Sprowls, R. C. Stern, N. B. & R. A. Watters, .T. L.

5332H

1900 Series COBOl, lVfanual

Fundamentals of COI30L Programming (W. C. Brown)

Systems Analysis jor Business Data Processing (Business Books)

Elementary Cobol Programming (lVIcGraw-Hill)

Learning COBOL Fast (Re'iton)

Programming ill Standard COnOL (S.R.A.)

System Design for Computer Applications (Wiley)

Programming Business Compllters (Wiley)

Standard COBOL (S.R.A.)

Computers in Business (M cGrmv-H iii) Computing with COBOL (Harper & Row) Cobol Programming (Wiley)

Cobol Programming (Heinemann)

Assllmed Standard of Mathematics I A itainment

Hours

Examination

Content

I t hour~ of lectures ami practical work per week flJr the whole year

assessment and final examination

H(,lSic ~co.rnfutcr ~jclncnts and peripherals, r'~prfscntation and orgL.,Jlzq

elf_10n 01 Infonncll!ODI number systcrns and arithrnf.'ticj

iOQ;ical opcratioas, Hardware compol1cnls, processor stmcturc, addre:)si~1;-; modes and Il1stmetlOfl set, machinc-iangw:_sc subroutines, traps and mtcrrupts, use of the ,olack. macros, recursion

and re .. cntrancy, relocation, linking and loading. System software: assemblers, linkers, loaders, dumpers, interpreters, simulators, com· pilers. Lectures will be supplemented with practical assignments using the PDP .. 11 computer.

Texts Eckhousc, R. H. JI'

Referellces Chu, Y. H.

Donovan, J. J. Stone, H. S.

Minicomputer Systems Organization and Programming (PDP .. ]]) (Prentic;:;..Hall 1975)

Processor Handbook PDP·" 1 /20 (DEC)

ComjJuter Organization and Micro Programming (Prentice-IlaIl 1972)

Systems Programming (McGrawnHill 1972) Introduction to Computer Organization and

Data Structures (McGraw-JIill 1972)

Assumed Standard of Mathematics I Attainment

Hours 3 hours of lectures, tutorials and practical work per week for the 1 st half year

Examination Progrcssive assessment and final examination

Content Boolean algebra, combinational logic, logical circnits, minimization techniques, threshold logic. Data representation, binary arithmetic, codes, error checking and correcting. Sequential logic, flip-flops, state diagrams, state reduction, races and hazards. Logic subsystems: registers, adders, counters, converters, coders, etc. Basic architecture of di2ital computers.

Text Friedman, A. D.

References Hill, F. J. &

Peterson, G. R. Kohavi, Z.

Mano, M. M. Prather, R. E.

Logical Design of Digital Systems (Computer Science 1975)

Introduction to Switching Theory and Logical Design (Wiley 1968)

Switching and Finite Automata Theory (McGraw-Hill 1970)

Computer Logic Design (Prentice··Hall 1972) Introduction to Switching Theory: A Mathe·

matical Approach (Allyn & Bacon)

120

Assumed Standard of Attainment

Hours

Examination

Content

Mathematics I

2 lecture hOur3 and 1 tutori~ll hour per weck for the 1st half year

One 3·,hour paper and n possible paper on programming techniques

Structured Programming, program dl~sign. Flow charts. Decision Tahlcs, Natural Languagc formulations of algorithms. Introduction to FORTRA1'.J, ALGOL and the conversational !:lnr,uage BASIC. Use of higher level languages to solv,~ problems of a non~numericHI m'.turc. Programming tcchniques, efficient pro;;ramming, cvalL,ation of expre:> sions, sources of error. Programme development, diagnostics, testing, etc. Nature of algorithms and heuristic~;. Analysis of algorithms. Programme structure, procedurcs, subroutines, scope of variables. Recursion. Simulation, Random number eeneralors.

Text Guttmann, A. J.

References Knuth, D.


Blatt, J. M.

Day, A. C.

Kernighan, B. W. & Plauger, P. J.

Programming (lnd Algorithms (Heinemann 1977)

The Art of Computer Prograrnming Vol. I -"'- Fundarncntal Al,",orithms (1968) Vol. II - Semi-numerical Algorithms ( 1969) Vol.lll-Sorting and Searching (1973) (Addison-Wesley)

Algol Programming Manual

Introduction to Fortran IV Programming (Goodyear 1967)

Fortran Techniques: with Special Reference to NOll-numerical Applications (Cambridge D.P. 1972)

The Elements of Programming Style (McGraw-Hill 1974)

Kernighan, B. W. & Software Tools (Acldison-VVesley 1976) Plauger, P. J.

Assumed Standard of CS .. -Programming & Algorithms Attainment

121

Hours

Examination

Content

2 lecturc hours and 1 tutorial hour per week for the 2nd half year

One 2-hour paper

Introduction to data structures: lists, strings, arrays, trees, graphs, searching and sorting; list proces;;ing. Higher level programming languages: Syntax and semantics. Backus normal form. Polish notation. Declarations, storage allocation, sub .. routines and linkage. Compilation, interpretation and translation. Study and comparison of data structures in several languagcs, e.g. ALGOL 60, ALGOL 68, COBOL, FORTRAN, LISP, etc.

Text

References Berztiss, A. T.

Day, A. C.

Galler, B. A. & Perlis, A. J.

Gear, W.

Knuth, D. E.

Page, E. S. & Wilson, L. B.

Sammet, .J. E.

Nil

Data Stl'Uctures: Theory and Practice (Academic 19"/1)

Fortran Techniques: with Special Reference to NOIHlumerical Applications (Cambridgc U.P. 1972)

A View of Programming Languages (Addison .. Wesley 1970)

Computer Organization and Programming (McGraw-Hill 1969)

The Art of Computer Programming Vol. 1- Fundamental Algorithms (1968) Vol. ll- Semj .. numerical Algorithms

(1969) Vol. 111 - Sorting and Searching (1973) (Addison-Wesley)

Information Representation and Manipulation in a Computer (Cambridge V.P. 1973)

Programming Languages: History and Fundamentals (Prentice-Hall 1969)

660113 CS~"NlJmcricai Analysis ~ R. W. Gibberd

Assumed Standard of Part II Mathematics Topics C. :0, F Attainment

Hours 1 lecture hour and 1 tutorial hour per week

Examination One 2 .. hour paper

Content Solution of simultaneous linear equations by di rect and iterative methods, and a selection from the fo!lowing topics: Non-linear equations. Approximation-functions, experimental data, integrals. Random number generation. Overdetermined systems; lillear programming. Optimisation. Ordinary difIcrential equations--illitial and boundary value problems. Eigenvalues and eigenvectors of matrices.

Text

References

Forsythe, G. & Moler, C. B.

Steinberg, D. 1.

Nil

Computer Solution of Linear Algebraic Systems (Prenticc .. Hall J 967)

Computational Matrix Algebra (McGrawOoHill 1974)

Additional references to be advised

GROUP 11

Subjects in the main-strpam of Computer Science

OFFERED BY THE DEPARTMENTS OF COMMERCE

Note

Candidates who passed the subject Accounting Systems and Computer Applications or Ivlanagement Studies prior to 1974 will not be permitted to enrol in this subject.


Hours

Examination

Content

Commercial Electronic Data Processing (or Management Studies if passed in 1974)



The application of the theory of information systems to the analysis and design of computer systems. Topics inclnde, the study and analysis of existing manual and computer systems; the design of batch sequential and direct access processing systems; an introduction to the COBOL programming language; a detailed treatment of computer security management; considerations when implementing a computer system.

123

Texts Llewellyn, R. W. Scmprevivo, P. C.

Van Tassel, D.

References Adams, E. B.

Brightman, R. W.

Burch. J. O. J. & Strater, F. R. Jr

Eliason, A. L. & Kitts, K. D.

Gotlieb, G. C. & Borodin, A.

Jancura, E. G.

Johnson, R. A. ct al.

Lyon, .T. K. Martin, J.

M urdich, R. G. & Ross, J. E.

Schoderbcck, P. P. Tavis;;, 1. (cd.)

Watters, J. L. Yourdon, E.

Illformation Systems (Prentice-Hall)

Systems A nalysis: definition, process, and design (Science Research Associates)

Computer Security lVlanogcment (PrenticeHall)

Management of Information Technology -Case Studies (Petrocclli/Charter)

Information Systems for Modern Management (Macmillan)

Information Systems: Theory and Practice (Wiley)

Business Computer Systems and Applications (Science Research Associates)

,)'ocial Isslies in Computing (Academic Prcss)

Audit and Control of Computer Systems (Petrocelli/ Charter)

The Theory and lVlanagemellt of Systems (McGraw .. Hill )

All Introduction to Data Base Design ("Wiley)

Desip,n of Real-Time Computer Systems (Prentice-Hall)

Information Systems for Modern Management (Prenticc-Hall )

IVlul1agement Systems (Wiley) The Computer Impact (Prentice-Hall) COBOL Programming (Heinemann)

Design of On-Line Computer Systems (Prentice-Hall )

412601 Quantitative Busilless Allalysis II


Hours

Examination

N ·' 11

/, lecture hours per week

One 2-hour paper; progressive assessment and project

12';·

Content Quantitative methodology; BASIC programminl!,; mathCI1Eltics review; decision theory; demography and its applications; CPM/ PERT; inventory modelling; linear programming in practice; game theory; Markov analysis; queueing theory; dynamic programming; business forecasting; elements of simulation; management of quantitative analysis projects in real life.

Texts

Anderson, 1. et al. Levin, R. L &

Kirkpatrick, C. A. Pollard, A. H. et a1. Starr, M. 1(, &

Stein, 1.

References Baumol, W. J.

Hillier, F. S. & Lieberman, G. J.

Taha, H. A.

Wagner, H. M.

The'si,\' and Assignment Writing (Wiley) Quantitative Approaches to Manap,ement 3rd

edn (McGraw-Hill) Demographic Techniques (Pergamon)

The Practice oj Manap,ement Science (Prentice-H all)

Economic Theory and Operations Analysis (Pre\1ticc"J~I all)

Introduction to Operations Research (Holden Day)

Operations Research: A 11 Introduction (Macmillan)

Principles of Operations Research 2nd edn (Prentice-Hall)

'HODS Sodal bllplicatiolls of Computers ~-~ E. J. Burke

Assumed Standard oj Attainment

Hours

Examination

Content

Mathematics I or Commercial E.D.P.

2 hours per week for 2nd half year

One 2-hour paper

The spectrum of political, legal, managerial, philosophical, ethical and social issues; human variables associated with strategies of change; impact upon organisation structures; socio-tf:chnical systems; effects upon communication, privacy, public justification.

Texts } References To be <:ldvised

125

410124 §ystems Analysis and Design A ~~~ I. R. Beaman


Hours

Examination

Content

Nil

2. lecture hours per week for the 1st half year and associated practical work

One 3~hour paper

The lectures and case studies arc concerned with the ,malysis and documentation of typical compuler~based systcms, e.g. an order processing, stock recording and invoicing system. Topics covered include the role of the systems analyst; fact finding, recording, and analysis; documentation and standards; data capture and conversion; communication with users.

Texts

Wohl, G. & D'Angelico, M.

References

Chandor, A. et al.

Clifton, H. D.

Daniels, A. & Yeates, D.

Glans, T. B. et al.

Hare, Van Court

Optner, S. L.

Orilia, L. et al. Weiss, E. A.

The National Computing Centre Systems Analysis and Design Student Nutes will be supplied. Case Studies oj Business Data Processing

Systems (Irwin)

Practical Systems A nalysis (Rupert, Hart & Davis)

Systems A nalysis for Business Data Processing (Wiley)

Basic Training in Systems Analysis (Pitman)

Jl.1anagemellt Systems (Holt, Rinehart & Winston)

Systems A nalysis: A Diagnostic Approach (Harcourt, Brace & World)

Systems Analysis jor Business Management (Prentice-Hall)

Business Data Processing Systems (Wiley) Computer Usage! Applications (McGraw

Hill)

4:10125 §ystems Analysis ami Design B ~~ 1. R. Beaman

Assumed Standard oj Attainment

Hours

CS ~. Commercial Programming, Systems Analysis & Design A

2. lecture hours per week for the 2nd half year and associated practical work

J26

Lxamillation One J~hour paper

Content This subject is a development of the Systems Analysis and Design A, with the inclusion of the following topics: data transmission; real time systems; information retrieval; file processing; form design; management and the computer; file design; systems design and deter .. mination; operating systems, multi-programming.

Texts } As for Syotcms Analysis and Design A References

ELECTRICAL ENGINEERING

533213 EE341 Automatic Control ~"" see page 93.

533HZ EE34§ Sample Data and Digital Con/rol

Assumed Standard of EE341 Automatic Control Attainment

Hours

Examination

Content

3 hours of lectures, tutorials and laboratory work per week for the second half year

Progressive a~;sessment and final examination

Digital filtering and digital control systems, z-transforms, state-variable techniques, sampling and reconstruction, fast Fourier transforms.

Text

References Cadzow, J. A. &

Martens, H. R. Gold, B. & Rader, C. Kuo, B. C.

Nil

Discrete··Time and Computer Control Systems (Prentice~Hall 1970)

Digital Signal Processing (McGraw<·Hill 1969) Discrete-Data Control Syst.ems (Prentice~Hall

1970)

534113 EE425 Digital Electronics- A. Cantoni

Assllmed Standard oj EE421 Electronics Attainment

Hours 3 hours of lectures, tutorials and laboratory work per week for the 2nd half year

Examination Progressive assessment and final examination

127

Content Switching characteristics of bipolar and field elIcc! devices. De"ign of switching circuits. Characteristics of logic families. Design of bus structures. Digital signal transmission. Analog to digital and digital to analog conversion. Digital measurements. Introduction to micro-· processors and programmable logic.

Texts

References Kohonen, T. Peatman, T. B.

Nil

Digital Circuits alld Devices (Prentice-Hall)

Design oj Digital Systems (McGraw-Hill)

534134 EE447 Digital Communications~, J. B. Moore

Prerequisite

Hours

Examination

Content

Nil

3 hours of lectures and tutorials per v/eek for 2nd half year.


1. Noisy Mernoryless M-ary channels Orthogonal signalling on noisy memory]c:;s channels. Optimum receivers, the matched fillers, the correlation receiver. Shannons channel cClpaeity theorem. Introduction to coding techniques; block, algebraic and convolution codes.

2. Noisy channels with memory Optimal receiver and transmitter structures for di~;persive channels. The Viterbi algorithm. Linear and Nonlinear Adaptive Equalisers. Base band Signal Design.

Text

References Lucky, R. W. et al.

W ozencraft, J. M.

Nil

Principles oj Data Communication (McGraw-Hill)

The Principles of Communication Engineering (Wiley)

534124 EE463 Computer Opexatillg Systems - A. Cantoni


Hours

EE36! Computer Structure: Machine & Assembly Languages

Three hours per week for the fip;t f;;:\1f of Inc

year

Examination Progressive assessment and final examination

Content Views of an operating system. M ultiprogramrni!lg, intccractillg con· current proeesses, proces:J eontrol primitives. Processor management, memory management, name mall~1i3ement. Protection.

Text Shaw, A. C.

References Coffman, E. G. &

Denning, P. 1. Hansen, P. 13. Madnick, S. E. &

Donovan, T. J.


Hours

Examination

Content

The "Logical Design of Operating Systems (Prentice-Hall )

Operating Systems Theory (Prentice-Hall)

Operating Systems Principles (Prentice-Hall)

Operating Systems (McGraw-Hill)

EE36! Computer Structure: Machine & Ass·~ cmbly Languages

:I hours pc!' week for the 2nd half year


The design of assembler;;. Introduction to the theory of grammars, parsing techniques, construction of compilers, object code generation. Construction of interpreters.

Text Gries, D. Compiler Construction for Digital Computers

(Wiley) References

Aho, A. V. & Ullman, J. D.

The Theory oj Parsing, Trwldation and Compiling 2nd Vol. (Prentice-Hall)

Donovan, J. T. Systems Programming (McGraw"·Hill)

530114 lElE462 TOllic§ III Switchillg Theory

530108 EE565 Pattem Recognition

530119 lEE566 AllItomat'l alld Computing Machines

530125 EE56'7 Computer PlWcess Contl'Ol

53012J lEE!56H Advanced Computer Al'chitectun~

530122 lElE569 Formal Langnages amI Automata

129

-, not offered in 1977

MA'rJ-IEMATICS

6(;6116 CS···· ·Topic in Applied Probability M3Jthematics In Topic Y, e.g. Iufowmatiou 'll'heoI'Y see page 50

66612'j CG···TheoI'Y of Computing Mathematics III Topic TC, see page 47

660128 C§·~~MathemaHcal PlrincilJle§ Mathematics HI Topic Z, of Nnmn'ical Allalysis sec page 5 1

MECHANICAL ENGINEERING

544452 MEIlO:,l, Systems Planl1ing, Organization and Contl'Ol~·~sec page 105

544417 ME464 Mathematkal lProgl'llmming ·-~see page 105

546119 lVa~5g1G Mathematical Pl'ogl'llmming ... ~ K. L. Ritz

Assumed Standard of Part II Mathematics Topics C, D Attainment

Hours

Examination

Content

3 hours per week

To bc advised

A survey on methods for the solution of static, deterministic optimisation problems. Linear programming, the simplex algorithm and its revised form; duality theory; sensitivity analysis; decomposition algorithms; transportation and assignment problems. Linear programming in integers; cutting plane algorithms; branch-and .. bound methods; implicit enumeration algorithms for binary integer programmes. Network, scheduling and other combinatorial problcms, Introduction to the theory of convex nonlinear programmes; the Kuhn~Tucker theorem; applici1tions to quadratic programming and geometric programming, Dynamic programming methods,

Texts

Gass, S. I.

Geoffrion, A lVL (ed.)

Nemhauser, G. L.

Linear Programming 3nl cdn (McGraw-Hill Internat. Students Edn 1969)

Perspectives Optimisation (Addison-Vvcsley 1972)

Introduction to Dynamic Programming (Wiley 1966)

130

Rejerences

Bellman, R. E, & Dreyfus, S. E.

Duffin, R. J. et a!.

I-ladley, G.

Kiinzi, H. P. et a!.

Luenberger, D. G.

Salkin, H. M,

Wilde, D. J. & Beightlcr, C. S.


Geometric Programming (Vviley 1967) Lineal' Progl'wrlJllilig

Student Serics 1969) World

Nonlinear Programming (Blaisdell 1966)

Introduction to Linear and Nonlincar Programming [9'13)

Integer Programming (Addisol1 .. Wesley 1975)

Foundations oj Optimisation (Prentice-Hall 1967)

GROUP m -.~ SUBJECTS

Listed below are a number of subjects which the Board regards as suitable for Group HI. This list is not, however, intended to be exhaustive and other subjects will be considered.

OFFERED BY THE DEPARTMENTS OF CIVIL ENGINEERING

520115 C]8515

I For details consult (he Engineering Faculty Handbook,

COMMERCE

413612 Them'jes of OrganisatiOil

Assumed Standard oj Organisational Behaviour Attainment

Hours 2 lecture hours per week

Examination Two 3-houl' papers

Content

The influence of politics, power and conflict: topics include organisations and the rationalisation of work; organisational structures; bureaucracies as working communitics; the scientific management movement; Mayo and the Hawthorne cxperiments; K.urt Lewin and field theory; group membership and intergroup conniet; search for principles of management; worker participation model:;; organisational development; and propositions of organisational behaviour.

131

'texTS

Lupton, T

Poole, M,

Sofcr, Cor Mouzclis, N. p,

References Argyle, M.

Brown, W.

Management and the Social Sciences (Penguin)

Worker Participation in Industry (Rolltledge Kegan & Paul)

Organisations in Theory and Practice (Heinemann)

Organisation and Bureaucracy~~An Analysis of Modern Theories (Routledge Kegan & Paul)

The Psychology of Interpersonal Behaviour (Penguin)

Organisations (Heinemann)

Kast, F. & Rosenzweig, J. E,

Organisation and Management: A Systems Approach (McGraw~HiIl)

Katz, D, & Kahn, R. L.

The Social Psychology of Organisations (Wiley)

Kerr, C. D. et a1. Klein, L.

March, .T. G. & Simon, H. A

Margulies, N. & Raid, A. P.

Silverman, D. Woodward, J.

533107 EE3],3 533HlS EI~3Z4J,

533110 EE342 533113 .EE344 534108 EJ&:421 534126 EE423L 534115 ~~E442

534132 EE443 534'128 EE445 530100 EE516

Industrialism and Industrial Man (Pelican) New Forms of Work Organisation

(Tavistock) Organisations (Wiley)

Organisation Development: Values, Process and Technology (McGraw-Hill)

The Theory of Organisations (Heinemann) Industrial Organisation: Theory and Practice

(Oxford U.P.)

ELECTRICAL ENGINEERING

Linear EledK'onicsl Electronics lLaiJonaiory 1

Linear System Thcor'yl Com~l'nniclltiom;l

Electronici'll Electronics Laboratory1 Modem COIlh'o! ~~ Not ofIercd in 1977 Op~;miz:iltioll Tedmiqucsl Commtmicalimn Systems -"- Not offered in 1977 Computeroaided Analysis of Power Systems Not ofrered in 19T1

1 For details consult the Engineering Faculty Handbook,

MATHEMATICS

660114 C§o·~,Mathematical Logic .~ Bee Mathematics HI, 'fopic 0 pa.ge 42

660115 C§~·~Operation§ Research ~.- See Mathematics II}!, l'opic U page 48

660'H7 C§~'~PJ"Olmbmty and Shltistics See Mathematics UI, 'rOpl<: R page 45

(,60113 CS~~""Asymptotr~ IVlethods ill Amllysis [icc Mathematics IV page

660119 <C§~~Rmulom amI Rcstricteocl Walk.;; Sec Mathematics IV page

6iJ0120 C§~-.Gjigl1al Detection See lV1athema~ics IV page 660121 C§" .. -,§tocha~tk Processes ~~§ee ]\1iathemaiics IV page 660122 C§~~Cmnbil!latm'ial . De§igm; ==> See Mathematics IV page 6@123 CB~·,-Combimdorlc§ Sec IVi'atilem;,tics IV page 660124 C~-PopUJlation llJymm'lic§ ~-.~~. §ee IViathem:dic§ IV page 66~125 C§"-~Gl'aph Tb.em:;), --00 May not be offered ill 19'17

54484'1

MECHANICAL ENGINEERING

Mlt:449 RcliabiUty 1"''''m~'1j!rj lfm: IVledmnkal §yldllmll see pages 107-109

ME437 OllemtimlS Re§e:u'ch ~."~ Determi .. is!ic Models see pages j07~109 MlE48S Ollcratioll§ Rcsclm:ll ,~~~ lP'miJal:Jilisik Mo(lels sec pages 107-109

Ml~489 Research " , lln Rnfllif,tJ!y, sec pages 07-109

540101 MJ~S03G Design of E::qleriments for Engil1eedll~ Resem'clil 1 1 For details consult the Engineering Faculty Handbook,

METALLURGY

113312 Met 312 OI.timizl1irrcm ami Controll 1 Por details consult the Enp,inccring Faculty Handbook.

PHYSICS

660126 Cg~·J!nf>imment~lti(Jn Tecimiques

AssLlmed Standard of l'hy:;ics fA or !B Attainlilent

Hours

Examination

Content

Olle hour per week and a 12~hour project

Project assessment and one 2~hour paper

From the subject Electronics and Instrumentation H: Specialist Instrumentation 8 lectures Instrumentation Systems 8 lectures Measurement Devices 14 lectures

70

71 61 62 69 64 59

Texts Malmstad!, H.V. et al . Instrumentation jor Sciclltists Series (Vols 1-4)

Text with Experiments or Text only or combined volume (Benjamin 1973)

REQUIREMENTS FOR THE DIPLOMA IN MATHEMATICAL STUDIES

1. In these Requirements, unless the context or subject matter other~ wise indicates or requires, "the Faculty Board" means the Faculty Board of the Faculty of Mathematics and "the Dean" mcans the Dean of the Faculty of Mathematics.

2. An applicant for registration as a candidate for the Diploma shall: (a) have satisfied all the Requirements for admission to a degree

in the University of Newcastle or another institution approved for this purpose by the Faculty Board, OR

(b) in exceptional circumstances produce evidence of possessing such other qualifications as may be approved by the Faculty Board.

3. The Faculty Board will appoint an adviser for each candidate.

4. An applicant for registration as a candidate for the Diploma may be granted standing on conditions to be determined by the Faculty Board, provided that standing may not be granted in respect of any studies for which credit has been given for admission to a degree or for the award of another diploma.

5. In order to qualify for the Diploma, a candidate shall, in not less than three tenns in the case of a full-time student or not less than six terms in the case of a part-time student, complete a course of studies comprising 12 units of advanced work offered by the Department of Mathematics or another department offering courses with considerable mathematical content. Two units of this advanced work may be a project approved by the Faculty Board. Each unit will requirc altendancc at lectures, seminars and tutorials, reading exercises, laboratory work and examinations as may bc prescribed by the Faculty Board.

6. (a) To complete a unit qualifyinG towards the Diploma, a candidate sha 11 attend sueh lectnres, tutorials, seminars and laboratory classes, and submit such written work as the Faculty Board may require.

(b) To pass a unit, a candidate shall complete the unit and pass sueh examinations as the Faculty Board may require.

7. (a) A candidate may withdraw from a unit or units only by notifying the Secretary to the University in writing and the withdrawal shall take effect from the date of receipt of such notification in writing.

[34

(b) A candidate who after:~-the eighth Monday in First Term, in the case of a unit la~;ting only the first half-year, the sixth Monday in Second Term, in the case of a unit lasting the whole year, the secane! Monday in Third Term, in the case of it unit lasting only the second half-year,

withdraws from a unit in which he has enrolled, shall be deemed to have failed in that unit, unless granted permission by the Dean to withdraw without penalty.

8. In exceptional circumstances the Senate may, on the recommendation of the Faculty Board, relax any of the above requirements.

REQUlREMLNTS FOR THE DI'..'GREE OF MASTER OF MATHEMATICS

1. An application to register as a candidate for thc degree of Ma~;ter of Mathematics shall be made on thc prescribed form which shall be lodged with the Sccretary at least 011': full caien(!ar month before the commencement of the term in which the candidate desires to register.

2. A person may register for thc degree of Master of Mathematics if~ (a) he is a graduate or graduand of the University of Newcastle or

other approved University with Honours in the subject to be studied for that degree; or

(b) he is a graduate or gradwmd of the University of Newcastle or other approved University; or

(c) in exceptional cases he produces evidence of such academic and professional attainments as may be approved by thc Senate, on the recommendation of the Faculty Board.

3. In the case of applicants c!e5iring to register under provision 2 (b) , and (c), the Faculty Board may require the candidates to carry out such work and sit for such examinations as the Board may determine before registration ap, a candidate for the ck!lree of Master of Mathematics is confirmed. '

4. In e~cry case, before permitting an applicant to register as a e~l~dldate, the. ~'?culty Board shall be satisfied that adequate superVISIOn and faCIlities are available.

5. An applicant approved by the Faculty Board shall rcgister in ant: of the following categories :-'--

0) Student in full-time attendance at the University. (ii) Student in part~time attendance at the University.

135

6. 0) Every candidate for the degree shall be required to submit a thesis embodying the results of research carried out by him during his candidature, to take such examination and to per~ form such other work as may be prescribed by the Faculty Board. The candidate may submit also for examination any work he has published, whether or not such work is related to the thesis.

(ii) The research and other work as provided in paragraph 6 (i) shall be conducted under the direction of a supervisor ap~ pointed by the Faculty Board or under such conditions as the Faculty Board may determine.

(iii) A parHime candidate shall, except in special circumstances i. conduct the major proportion of his research in the

University; and ii. take part in research seminars within the Department in

which he is working. (iv) Every candidate shall submit annually a report on his work to

his supervisor for transmission to the Higher Degree Committee. (v) Every candidate shall submit three eopies of the thesis as

provided under paragraph 6(i). All copies of the thesis shall be in dOllble~spaced typescript, shall include a summary of approximately 200 words, and a certificate signed by the candidate to the effect that the work has not been submitted for a higher degree to any other University or institution. The ORIGINAL copy of the thesis for deposit in the Library shall be prepared and bound in a form approved by the Universityl. The other two copies of the thesis shall be bound in such manner as allows their transmission to the examiners without possibility of their disarrangement.

(vi) It shall be understood that the University retains the three copies of the thesis and is free to anow the thesis to be con·· suIted or borrowed. Subject to the provisions of the Copyright Aet (1968) the University may issue the thesis in whole or in part in photostat or microll1m or other copying medium.

7. No candidate shall be considered for the award of the degree until the lapse of "ix complete terms from the date from which the registration becomes effective, save that in the case of a candidate who has obtained the degree of Bachelor with Honours or a qualification deemed by the Faculty Board to be equivalent or who has had previous research experience, this period may, with the approval of the Faculty Board, be reduced by up to three terms.

8. For each candidate there shall be two examiners appointed by the Senate, one of whom shall be an external examiner.

13()

9. A candidate who fails to satisfy the examiners may be permitted to resubmit his thesis in an amended form. Such a resubmission must take place within twelve months from the date on which the candidate is advised of the result of the first examination. No further resubmission shall be permitted.

1 A. separate. sheet on the preparation and binding of higher degree thesis is available 011 apphcatJ011.

REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

1. The degree of Doctor of Philosophy may be awarded by the Council on the recommendation of the Senate to a candidate who has satisfied the following requirements.

2. A candidate for registration for the degree of Doctor of Philosophy sha11:--

(i) have satisfied all of the requirements for admission to the degree of master or the degree of bachelor with first or second class honours in the University of Newcastle or a degree from another University recognised by the Senate as having equivalent standing; ox'

(ii) have satisfied all of the requirements for admission to the degree of bachelor with third class honours or without honours in the University of Newcastle or a degree from another University recognised by the Senate as having equivalent standing, and have achieved by subsequent work and study a standard recognised by the Senate as equivalent to at least second class honours; or

(iii) in exceptional cases submit such other evidence of general and professional qualifications as may be approved by the Senate.

3. Th~ Senate may require a candidate, before he is permitted to regtster, to undergo such examination or carry out such work as it may prescribe.

4. A candidate for registration for a course of study leading to the degree of Ph.D. shall:- . .

0) apply on the prescribed form at least One calendar month before the commencement of the term in which he desires to register;

mull

(ii) submit with his application a certificate from the Head of Department in which he proposes to study stating that the candidate is a fit person to undertake a course of study or ~'ese~r~h leading to the Ph.D. degree and that the Department IS wIllIng to undertake the responsibility of supervising the work of the candidate.

137

5. Before being admitted to candidature, an applicant shall satisfy the Senate that he can devote sufficient time to his advanced study and research.

6. Subsequent to registration, the candidate shall pursue a course of advanced study and research for at least nine academic terms, save that any candidate who before registration was engaged upon research to the satisfaction of the Senate, may be exempted from three academic terms.

7. A candidate shall present himself for examination not later than fifteen academic terms from the date of his registration, unless special permission for an extension of time be granted by the Senate.

S. (a) The course shall be carried out in a Department of the University.

(b)

(c)

Notwithstanding the provisions of subsection (a) of this clause a candidate may be granted special permission by the Se'nate to spend a period of not more than three academic terms in research at another institution approved by the Senate. The course shall be carried out under the direction of a supervisor or supervisors appointed by the Senate-

9. Not later than three academic terms after registration, the candidate shall submit the subject of his thesis for approval by the Senate. After the subject has been approved it may not be changed except with the permission of the Senate.

10. A candidate may be required to attend a formal course of study appropriate to his work.

11. On completing his course of study evelY candidate shall submit a thesis which complies with the following requirements:~-

(i) The greater proportion of the work described must have been completed subsequent to registration for the Ph.D. degree.

(ii) It must be a distinct contribution to the knowledge of the subject.

(iii) It must be written in English or in a language approved by the Senate and reach a satisfactory standard of literary presentation.

12. The thesis shall consist of the candidate's own account of his research. In special cases work done conjointly with other persons may be accepted provided the Senate is satisfied on the candidate's part in the joint research.

13. Every candidate shall be required to submit with his thesis a short abstract of the thesis comprising not more than 300 words.

138

14. A candidate may not submit as the main content of his thesis any work or material which he has previously submitted for a University degree or other similar award.

15. The candidate shall give in writing three months' notice of his intention to submit his thesis and such notice shall be accompanied by the appropriate fee.

16. Four copies of the thesis shall be submitted together with a certificate from the supervisor that the candidate has completed the course of study prescribed in his case and that the thesis is fit for examination.

17. The thesis shall be in double-spaced typescript. The original copy for deposit in the Library shall be prepared and bound in a form approved by the University. The other three copies shall be bound in such manner as allows their transmission to the examiners without possibility of disarrangement.

18. It shall be understood that the University retains four copies of the thesis and is free to allow the thesis to be consulted or borrowed. Subject to the provisions of the Copyright Act (1968) the University may issue the thesis in whole or in part in photostat or microfilm or other copying medium.

19. The candidate may also submit as separate supporting documents any work he has published, whether or not it bears on the subject of the thesis.

20. The Senate shall appoint three examiners of whom at least two shall not be members of the teachine staff of the University_

21. The examiners may require the candidate to answer, viva voce or in writing, any questions concerning the subject of his thesis or work.

22. The result of the ex,unination shall be in accordance with the decision of a majority of the examiners.

23. A candidate permitted to re-submit his thesis for examination shall do so within a period of twelve months from the date on which he is advised of the result of the first examination.

24. In exceptional circumstances the Senate may relax any of these requirements.

REQUIREMENTS FOR THE DEGREE OF DOCTOR OF SCIENCE

1. The degree of Doctor of Science may be awarded by the Council, on the recommendation of the Senate, for an original contribution or contributions of distinguished merit adding to the knowledge or understanding of any braneh of learning with which the Faculty is concerned.

139

2. An applicant for registration for the degree of Doctor of Science shall hold a degree of the University of Newcastle or a degree from another University recognised by the Senate as being equivalent or shall have been admitted to the status of such a degree.

3. The degree shall be awarded on published 1 work although additional unpublished work may also be considered.

4. Every candidate in SUbmitting his published work and such un~ published work as he deems appropriate shall submit a short discourse describing the research embodied in his submission. The discourse shall make clear the extent of originality and the candidate's part in any collaborative work.

5. An applicant for registration for the degree shall submit in writing to the Secretary a statement of his academic qualifications together with:-(a) four copies of the work, published or unpublished, which he

desires to submit; and (b) a Statutory Declaration indicating those sections of the work, if

any, which have been previously submitted for a degree or diploma in any other University.

6. The Senate shall appoint three examiners of whom at least two shall not be members of the teaching staff of the University.

7. The examiners may require the candidate to answer, viva voce or in writing, any questions concerning his work.

8. The result of the examination shall be in accordance with the decision of a majority of the examiners.

1 In these requirements the teTIll "published work" shall mean printed in a periodical or as a pamphlet or' as a book readily available to the public. The examiners are given discretion to disregard any of the work submitted if, in their opinion, the work has not been so available for criticism.

Algebra

RESEARCH IN THE DEPARTMENT OF MATHEMATICS

Mr R. F. Berghout is pursuing some topics in ring theory and ringlike categories, making use of the theory of radicals, and is also engaged in the extension of this theory to additive categories. Associate Professor W. Brisley is working on some problems occurring in the laws defining certain varieties of groups, and the subsequent lattice of sub-varieties of given varieties.

Basic Biological Forces Dr E. R. Smith is studying the role of Van de Waals and related forces in the stabilisation of biological arrays and colloids.

140

Chemical Kinetics Dr D. L. S. McElwain is working on the mathematical modelling of non~equilibrium phenomena in gases, using the Master Equation approach.

Combinatorial Theory and Operations Research Dr R. B. Eggleton is interested in all aspects of combinatorial mathe .. matics, particularly graph theory. Professor R. W. Robinson is applying combinatorics to the counting of various structures, sueh as graphs and search trees. Dr R. J. Vaughan is interested in the application of optimisation methods to industrial production problems. Associate Professor "V. D. Wallis is carrying out researc\;t on block designs and graph theory. He is also working on rostering and scheduling problems.

Differential Geometry and Relativity Dr P. Smrz is working on generalizations of Einstein's theory of relativity using modern differential geometry ~- in particular, the theory of Lie groups and fibre bundles.

Dynamical Systems Dr J. G. Couper is working on stable and generic properties of flows and diffeomorphisms.

Environmental and Urban Studies Dr R. J. Vaughan is investigating mathematical models in urban geography. Associate Professor W. D. Wallis is working on mathematical models in urban geography and urban soeiology. Dr R. W. Gibberd is studying the art of popUlation projections and various models of urban structure and urban deVelopment. He is also interested in urban sociology, voting pattcrns and urban dcmographic models.

Fluid Mechanics Associate Professor A . .T. Guttmann is studying the problem of extrapolating regular perturbation series in fluid mechanics. Powder Mixing -the problem of powder mixing is being invcstigated. Dr W. T. F. Lau is concerned with potential flow and viscous flow problems.

Functional Analysis Associate Professor J. R. Giles is involved in determining properties of Banach spaces which can be derived from relations between the points of the space and their support functionals. In particular, he is examining differentiability properties of the norm. He is also working on the development of the theory of the numerical range of operators

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on locally convex spaces, and of clements of locally m~eonvex algebras. Dr V. Ficker and Mr C. 1. Ashman are working in measure theory, particularly in some problems on classes of null sets.

Geophysical Fluid Dynamics Dr W. Summerfield is currently studying the dynamics of estuarine systems. He is also intcrested in all ocean wave phenomena.

History of Mathematics Mr R. F. Berghout is pursuing research into the development of algebra, notably modern algebra, as well as the relations between this and classical occidental and oriental algebra. Mr Berghout, together with Mrs Frost, is working on Greek algebra. Mrs Frost is currently translating into English some of Euclid's as yet untranslated works.

information Theory Professor R. G. Keats is continuing to work in co-operation with research scientists at the Weapons Research Establishment who are active in the study of signal processing. This work involves the study of non-linear systems with stochastic inputs.

Mathematical Logic Professor R. W. Robinson is studying the structure of the recursively enumerable degrees and the degrees below 0'.

Mathematical Models of Tumour Growth Dr D. L. S. McElwain is investigating models for the growth of solid isolated tumours.

Number Theory Dr R. B. Eggleton is interested in number theory, particularly in combinatorial aspects of the subject. Dr T. K. Sheng studies the structure of humanly manageable numbers, application of dispersive and explosive linear operators, distribution of algebraic numbers in the complex plane, and functions defined on rational numbers.

Numerical Analysis and Computing Associate Professor A. J. Guttmann is interested in methods of function approximation, particularly from the viewpoint of using a linear differential equation representation. He is also interested in the analysis of theoretical and experimental data. Dr W. Summerfield is working on ways of determining the "condition" of linear systems of equations. Further, he is interested in the solution by linear marching schema of ordinary differential equations, in particular "stiff" systems. He is also investigating the finite element method of solution for partial differential equations.

Statistical Mechanics

Associate Professor A. J. Guttmann is working on the theory of cquilibrium critical phenomena. He is particularly interested in the analysis of power series expansions which are frequently used to study systems exhibiting phase transitions. Dr E. R. Smith is working on the theory of non~homogcneous systems and the theory of polar liquids.

Dr W. P. Wood is investigating the dynamical bchaviour of long chain molecules in solution.

Dr R. W. Gibberd is intercsted in most aspects of statistical mechanics. Associate Professor C. A. Croxton is working on the statistical meeh.· anics of liquids and liquid interfaces.

Statistics

A~sociate Professor W. D. Wallis is working on the theory and applie~ atlOll of Room square designs and paired comparison designs.

Transportation Problems

Dr R. J. Vaughan is continuing his work in the application of mathematics to traffic engineering, traffic accidents and transportation planning.

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COllEGE EDUCATION

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faculty of mathematics handbook, 1977...may i first welcome all those students who arc enrolled, or...

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