m.sc mathematics syl2011.pdf · m.sc mathematics [cbcs revised] (with effect from 2011-2012...

M.Sc MATHEMATICS

[CBCS Revised]

(With effect from 2011-2012 onwards)

Courses of Study

Scheme of Examinations

And Syllabi

Post Graduate Department of Mathematics

Nehru Memorial College (Autonomous)

Puthanampatti -621007

Trichy District

PG DEPARTMENT OF MATHEMATICS

NEHRU MEMORIAL COLLEGE (AUTONOMOUS)

PUTHANAMPATTI - 621007

M.Sc., PROGRAMME IN MATHEMATICS (CBCS)

(For the candidate to be admitted form the year 2011 onwards)

Semester

Courses

I

5 Core courses

II

4 Core courses

1 Core Elective course

III

3 Core courses

1 Core Elective courses

1 Open Elective course

IV

2 Core courses

2 Core Elective courses

1 Project

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NEHRU MEMORIAL COLLEGE (AUTONOMOUS), PUTHANAMPATTI-621 007

M.Sc Mathematics Course Structure under CBCS Pattern 2011

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CORE COURSES (CC)

Code Title of the Courses Lecture

Hours

Tutorial

Hours

Practical

Hours

Credit Prerequisite

(Exposure)

CC1 Linear Algebra 4 2 0 5 NIL

CC2 Real Analysis 4 2 0 5 NIL

CC3 Ordinary Differential

Equations

4 2 0 5 NIL

CC4 Integral Equations,

Calculus of variations and

Fourier Transforms

4 2 0 4 NIL

CC5 Graph Theory 4 2 0 4 NIL

CC6 Algebra 4 2 0 5 CC1

CC7 Complex Analysis 4 2 0 5 CC2

CC8 Topology 4 2 0 5 CC2

CC9 Partial Differential

Equations

4 2 0 4 CC3

CC10 Functional Analysis

4 2 0 5 CC2 & CC8

CC11 Measure and Integration 4 2 0 5 CC2 &

CC10

CC12 Fluid Dynamics 4 2 0 4 CC3 & CC9

CC13 Differential Geometry

4 2 0 5 CC2

CC14 Stochastic Process

4 2 0 5 DEC4

CC15 Classical Dynamics 4 2 0 4 CC3,CC9 &

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CC12

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CORE ELECTIVE COURSES (CEC)

Code Title of the

Courses

Lecture

Hours

Tutorial

Hours

Practical

Hours

Credit Prerequisite

(Exposure)

CEC1 Number Theory 4 2 0 4 NIL

CEC2 Optimization

Techniques

4 2 0 4 NIL

CEC3 Numerical

Analysis

4 2 0 4 NIL

CEC4 Mathematical

Probability

4 2 0 4 NIL

CEC5 Fuzzy

Mathematics

4 2 0 4 NIL

CEC6 Combinatorics 4 2 0 4 NIL

CEC7 Combinatorics 4 2 0 4 NIL

OPEN ELECTIVE COURSES (OEC)(Courses Offered by Other Department)

Code Title of the

Courses

Lecture

Hours

Tutorial

Hours

Practical

Hours

Credit Prerequisite

(Exposure)

OEC1 Cryptography 4 2 0 4 +2 Level

Mathematics

OEC2 Mathematical

Modeling and

Simulation

4 2 0 4 +2 Level

Mathematics

OEC3 Statistics 4 2 0 4 +2 Level

Mathematics

OEC4 Statistical

Methods And

Operations

4 2 0 2 +2 Level

Mathematics

Research

OEC5 Discrete

Mathematics and

Numerical

Methods

4 2 0 4 +2 Level

Mathematics

OEC6 Probability and

Statistics

4 2 0 4 +2 Level

Mathematics

OEC7 Operations

Research

4 2 0 4 +2 Level

Mathematics

OEC8 Graph and

Automata

Theory

4 2 0 4 +2 Level

Mathematics

For each courses other than the Project

Continuous Internal Assessment (CIA) - 25 Marks

End Semester Examinations (ESE) - 75 Marks

Total Marks - 100.

ESE Duration - 3 hours

For Project

2 Reviews - 40 Marks

Evaluation - 40 Marks

Viva Voce - 20 Marks

Total Marks - 100 Marks

Total Credits should not be less than 90.

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CORE COURSES (CC) (For the Candidates admitted for the academic year 2011 onwards)

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UNIT II

Determinants: Commutative Rings – Determinants Functions – Permutations and the

uniqueness of Determinants – Additional properties of Determinants.

UNIT III

Canonical Forms – Characteristic Values-Invariant Subspaces – Simultaneous

Triangulation; Simultaneous Diagonalization.

UNIT IV

Direct-sum Decompositions – Invariant Direct sums – The Primary Decomposition

Theorem.

UNIT V

Cyclic subspace and Annihilators – Cyclic Decompositions and the Rational Form – The

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REFERENCE BOOKS

1) I.N.Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi, 1975.

2) I.S.Luther & I.B.S Passi, Algebra, Vol. I Groups, (1996), Vol. II – Rings, (1999),

Narosa Publishing House.

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1. W.T. Reid. , Ordinary Differential Equations, John Wiley and Sons, New York, 1971

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UNIT I

Linear Integral Equations: Definition, Regularity Conditions – Special kind of Kernels – Eigen values and

Eigen Functions – Convolution Integral – The Inner and Scalar Product of Two Functions –Reduction to a system

of Algebraic Equation – Examples – Fredholm Alternative – Examples – An Approximate Method.

UNIT II

Method of Successive Approximations: Iterative Scheme – Examples – Volterra Integral Equation –

Examples – Some Results about the Resolvent Kernel – Classical Fredholm Theory: The method of Solution of

Fredholm - Fredholm’s First Theorem – Second Theorem – Third Theorem (Statement only).

UNIT III

Variational Problems with Fixed Boundaries: The concept of variation and its properties - Euler’s

equations – variational problems for functionals of the form – Functionals Dependent on Higher order derivatives –

Functions dependent on Functions of several Independent Variables – Variational problems in parametric Form.

UNIT IV

Variational Problems with Moving Boundaries: Functional of the form ( )2

1

( , , )

x

x

I y x F x y y dx′= ∫ -

Variational Problem with a movable Boundary for a Functional Dependent on Two functions – One sided variations

– Sufficient conditions for an extremum field of extremals : – Jacobi condition – Weirstrass Function – Legendre

condition.

UNIT V

Fourier Transform: Fourier sine and cosine transforms-Properties, convolution-solving integral

Equations-Finite Fourier transform-finite Fourier sine and cosine transform-Fourier integral theorem-parseval

Identity. Hankel transform: Definition-Inverse formula-Linearity property-Hankel transform of the derivatives of

The function-Hankel transform of differential operation.

TEXT BOOKS 1. Ram. P. Kanwal, Linear Integral Equations Theory and Technique, Academic press 1971.

2. A.S. Gupta, Calculus of Variations with Application, Prentice-Hall of India Pvt. Ltd., New Delhi, 1997.

3. A.R. Vasistha, R.K. Gupta, Integral Transforms, Krishna Prakashan Media Pvt. Ltd., India 2002.

UNIT I: Ch 1 and 2 of (1). UNIT II: Ch 3 and 4 of (1) UNIT III: Ch 1(1.1 - 1.6) Of (2)

UNIT IV: Ch 2(2.1- 2.3) &Ch 3(3.1 to 3.4) of (2) UNIT V: Ch 7 and 9 of (3)

REFERENCE BOOKS 1. F.G.Tricomi, Integral Equations, Dover Publications Inc, New York, 1897.

2. Hilde Brand, Calculus of Variations.

3. Bruce Van Brunt, Calculus of Variations, Springers, 2006.

4. L. Elsgolts, Differential equations and the calculus of variations, Mir Publishers, Moscow 1970.

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1. J. Clark and D.A.Holton, a First look at Graph Theory, Allied Publishers, New

Delhi, 1995.

2. R. Gould, Graph Theory, Benjamin/Cummings, Menlo Park, 1989.

3. A. Gibbons, Algorithmic Graph Theory, Cambridge University Press, Cambridge,

1989.

4. R.J. Wilson and Watkins, Graphs: An introductory Approach, John Wiley and

Sons, New York, 1989.

5. S.A. Choudum, a First Course in Graph Theory, MacMillan India Ltd. 1987.

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UNIT II

Ring theory: Euclidean Rings, A particular Euclidean Ring, Polynomial Rings,

Polynomials over the Rational Field, Polynomial Rings over commutative Rings.

UNIT III

Vector spaces and modules: Dual spaces, Inner product spaces, Modules.

UNIT IV

Fields: Extension Fields, Roots of polynomials, More about Roots, The Elements of

Galois’s theory.

UNIT V

Linear transformations: Characteristic Roots, Matrices, and Canonical Forms: Triangular

Form, Nilpotent Transformations, Hermitian, Unitary and Normal Transformations.

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REFERENCE BOOKS

1) Serge Lang, Algebra, Revised Third Edition, Springer Verlag, 2002.

2) Kenneth Hoffman and Ray Kunze, Linear Algebra, Second Edition ,Prentice-Hall of

India pvt.Ltd.,New Delhi,1975.

3) David S.Dummit and Richard M.Foote, Abstract Algebra, Wiley and Sons. Third

Edition, 2004.

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UNIT II

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Frvbujpot!=!Opo.mjofbs!Gjstu!psefs!QEF/!

UNIT III

Second order PDE: Genesis of second order PDE – Classification of second order PDE –

One-Dimensional wave Equation – Vibrations of an Infinite string – Vibrations of a Semi-

infinite string – Vibrations of a string of Finite length (Method of Separation of variables).

UNIT IV

Laplace’s Equation: Boundary Value Problems – Maximum and Minimum principles –

The Cauchy Problem – The Dirichlet problem for the Upper Half Plane - The Neumann Problem

for the Upper Half Plane – The Dirichlet Interior problem for a circle – The Dirichlet Exterior

problem for a circle – The Neumann problem for a circle – The Dirichlet problem for a

Rectangle – The Harnack’s Theorem – Laplace’s Equation – Green’s Function.

UNIT V

Heat Conduction Problem – Heat Conduction Infinite Rod Case – Heat conduction Finite

Rod case – Duhamel’s principle – Wave Equation – Heat Conduction Equation.


T. Amarnath, an Elementary Course in Partial Differential Equations, Narosa1997.

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VOJU!JW;!Di!3!)3/5!=!3/5/22*!!!!!VOJU!W;;;;!!!!Di!3!)3/6!=!3/7/3*/!

REFERENCE BOOKS

1. I.C.Evens, Partial Differential Equations, Graduate studies in Mathematics, vol 19,

AMS, 1998. !!!!

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UNIT II

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UNIT III

Finite Dimensional Spectral theory: Matrices – Determinants and the spectrum of an

operator – The spectral theorem – A survey of the situation.

UNIT IV General preliminaries on Banach Algebras: The definition and some examples – Regular

and singular elements – Topological divisors of zero – The spectrum – The formula for the

spectral radius – The radical and semi-simplicity.

UNIT V

The structure of commutative Banach Algebras: The Gelfand mapping – Applications of

the formula r(x) = Lim ||xn||

1/n – Involutions in Banach Algebras – The Gelfand –Neumark

theorem.


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23!!!!!VOJU!W;!Di!24!

REFERENCE BOOKS 1) Walter Rudin, Functional Analysis, TMH edition, 1964.

2) B. V. Limaye, Functional Analysis, Wiley Eastern limited, Bombay, second print,

1985.

3) K. Yosida, Functional Analysis, Springer Verlag, 1964.

4) Laurent Schwarz, Functional Analysis, Courant Institute of Mathematical sciences,

New York University, 1864. !!!!

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UNIT II

Integration of non-negative functions-the general integral, integration of series, Riemann

and Lebesgue integrals.

UNIT III

Abstract measure spaces - Measures and outer measures, completion of a measure,

measure spaces, Integration with respect to a measure.

UNIT IV

LP

spaces - convex functions, Jenson’s inequality, inequalities of Holder and Minkowski,

completeness of LP (µ).

UNIT V

Signed measure - Hahn decomposition, measurability in a product spaces, Fubini’s

theorem.


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REFERENCE BOOKS 1) M.E.Munroo addition-Measure and Integration, Wesley, Second Edition Publishing

Company, 1971.

2) H.L.Royden, Real Analysis, PHI, Third Edition, 1989.

3) R. G.Bartle, Elements of Real Analysis, John Wiley, 1976.

!!!!

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Hours/Week

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UNIT I

Kinematics of Fluids in Motion: Real Fluids and Ideal Fluids – Velocity of a fluid at a point –

Streamlines and Path lines : Steady and Unsteady flows – The Velocity Potential – The vorticity vector –

Local and Particle rates of change – The equation of continuity – Worked Examples – Acceleration of a

fluid.

UNIT II

Equations of Motion of a Fluid: Pressure at a point in a fluid at rest – Pressure at a point is a

moving fluid – Euler’s Equations of motion – Bernoulli’s equation - Discussion of the case of steady

motion under Conservative Body Forces – Some Potential theorems – Impulsive motion.

UNIT III

Some Three-dimensional Flows: Sources, sinks and doublets – Images in rigid infinite plane –

Images in solid spheres - Axisymmetric flour; Stoke’s stream function.

UNIT IV

Some Two-dimensional Flows: The Stream function – The complex potential for two

dimensional, irrotational, incompressible flow – Complex velocity potentials for standard two

dimensional flows – some worked examples – Two dimensional image systems – The Milne Thomson

circle theorem – The theorem of Blasis.

UNIT V

Viscous Flow: Stress components in a Real Fluid – Relations between Cartesian components of

stress - Translational Motion of Fluid element – The Rate of Strain Quadric and Principal Stresses – Some

Further properties of the Rate of Strain Quadric - Stress Analysis in Fluid Motion – Relations between

stress and Rate of strain – The Co-efficient of viscosity and Laminar Flow – The Navier – Stokes

Equations of Motion of a viscous Fluid-Some solvable problems in Viscous flow.

TEXT BOOK:

F. Chorlton, Text Book of Fluid Dynamics, CBS Publishers & Distributors, Delhi 1985.

UNIT I : Ch 2 (2.1 – 2.9), UNIT II: Ch 3 (3.1, 3.2, 3.4 – 3.8 & 3.11)

UNIT III: Ch 4 (4.2 – 4.5), UNIT IV: Ch 5 (5.1 – 5.9), UNIT V: Ch 8 (8.1 – 8.10)

REFERENCE BOOKS

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)Gps!uif!Dboejebuft!benjuufe!gps!uif!bdbefnjd!zfbs!3122!poxbset*)Gps!uif!Dboejebuft!benjuufe!gps!uif!bdbefnjd!zfbs!3122!poxbset*)Gps!uif!Dboejebuft!benjuufe!gps!uif!bdbefnjd!zfbs!3122!poxbset*)Gps!uif!Dboejebuft!benjuufe!gps!uif!bdbefnjd!zfbs!3122!poxbset*!!!!



22QN52722QN52722QN52722QN527!!!! DD24!DD24!DD24!DD24!!!!!Ejggfsfoujbm!Ejggfsfoujbm!Ejggfsfoujbm!Ejggfsfoujbm!

HfpnfuszHfpnfuszHfpnfuszHfpnfusz!!!!7777!!!! 5555!!!! 6666!!!!


!!!!!!!!!!!!!!Tqbdf!Dvswft;!Efgjojujpo!pg!b!Tqbdf!Dvswf!=!Bsd!mfohui!=!Ubohfou!=!opsnbm!boe!!

Cjopsnbm! =! Dvswbuvsf! boe! Upstjpo! =! Dpoubdu! cfuxffo! dvswft! boe!Tvsgbdft!=Ubohfou!Tvsgbdf!=!

Jowpmvuft! boe! Fwpmvuft! =! Jousjotjd! frvbujpot! =! Gvoebnfoubm!fyjtufodf!Uifpsfn!gps!tqbdf!dvswft!!

=!Ifmjdft/!

UNIT II

!!!!!!!!!!!Jousjotjd!Qspqfsujft!pg!b!Tvsgbdf;!!!!Efgjojujpo!pg!b!

tvsgbdf!=!Dvswft!po!b!tvsgbdf!=!Tvsgbdf!pg!sfwpmvujpo!=!

Ifmjdpjet!=!Nfusjd!=!Ejsfdujpo!Dp.fggjdjfou!=!Gbnjmjft!pg!

dvswft!=!Jtpnfusjd!dpssftqpoefodf!=!Jousjotjd!qspqfsujft//!

UNIT III

Geodesics: Geodesics – Canonical geodesic equations – Normal property of geodesics –

Existence theorems.

UNIT IV Geodesic parallels – Geodesic curvature – Gauss-Bonnet Theorem – Gaussian curvature –

Surface of constant curvature.

UNIT V

Non-Intrinsic Properties of a Surface: The second fundamental form – Principal curvature

– Lines of curvature – Developable – Developable associated with space curves and with curves

on surface – Minimal Surfaces – Ruled Surfaces. UFYU!CPPLUFYU!CPPLUFYU!CPPLUFYU!CPPL!!!! !!!!

1. T. J. Willmore, An Introduction to Differential Geometry, Oxford University Press,

17th

Impression, New Delhi 2002, Indian print.

VOJU!J;!Di!2!)2.:*!!!!!!!!VOJU!JJ;!Di!3!)2.:*!!!!!!VOJU!JJJ;!Di!3!)21.24*!!!VOJU!JW;!Di!3!)25.29*!!!VOJU!W;!!!!Di!4!)2.9*!

REFERENCE BOOKS 1. D. T. Struik Lectures on classical Foundations of Differential Geometry, Addison

Wesley, Mass 1950.

2. S. Kobayashi and K. Nornizu, Foundations of Differential Geometry, Interscience

publishers, 1963.

3. Wihelm Klingenberg, A course in Differential Geometry, Graduate Texts in

Mathematics, Springer Verlag, 1978.

4. J. A. Thorpe, Elementary topics in Differential Geometry, under graduate Texts in

Mathematics, Springer Verlag, 1979.

)Gps!uif!Dboejebuft!benjuufe!gps!uif!bdbefnjd!zfbs!3122!poxbset*)Gps!uif!Dboejebuft!benjuufe!gps!uif!bdbefnjd!zfbs!3122!poxbset*)Gps!uif!Dboejebuft!benjuufe!gps!uif!bdbefnjd!zfbs!3122!poxbset*)Gps!uif!Dboejebuft!benjuufe!gps!uif!bdbefnjd!zfbs!3122!poxbset*!!!!



22QN52822QN52822QN52822QN528!!!! DD25DD25DD25DD25!!!!Tupdibtujd!Tupdibtujd!Tupdibtujd!Tupdibtujd!

QspdfttftQspdfttftQspdfttftQspdfttft!!!!7777!!!! 5555!!!! 6666!!!!


!!!!!!!!!!!!!!Tupdibtujd! Qspdftt;! Tpnf! Opujpot!!!! ====!!!! Jouspevdujpo! .!

Tqfdjgjdbujpot!pg!Tupdibtujd!Qspdftt!=!!

Tubujpobsz! qspdftt! .!Nbslpw!Dibjot!=!Efgjojujpo!boe!fybnqmft! .

Ijhifs!usbotjujpo!qspcbcjmjujft!=!

Hfofsbmj{bujpo! pg! joefqfoefou! Cfsopvmmj! usjbmt! =! Tfrvfodf! pg!dibjo!=!efqfoefou!usjbmt/!

UNIT II !!!!!!!!!Nbslpw!Dibjot!=!Dmbttjgjdbujpot!pg!Tubuft!boe!Dibjot!=!Efufsnjobujpo!pg!ijhifs!usbotjujpo!qspcbcjmjuz!=!Tubcjmjuz!pg!b!Nbslpw!Tztufn!=!Nbslpw!dibjo!xjui!Efovnfsbcmf!Ovncfs!pg!tubuft!=!Sfevdjcmf!Dibjot/!

UNIT III Markov Processes with Discrete state space: Poisson Process and its Extensions – Poisson Process

– Poisson Process and Related Distributions – Generalization of Poisson process – Birth and Death

Process – Markov Processes with Discrete state space (Continuous time Markov Chains).

UNIT IV Renewal Processes and Theory: Renewal Process – Renewal Processes in Continuous Time –

Renewal Equation – Stopping Time – Wald’s Equation – Renewal Theorems.

UNIT V

Stochastic process in queueing and reliability – Queueing Systems: general concepts, the Queueing

model M/M/1 model non- morkovian queueing models, the model GI/M/I UFYU!CPPL;UFYU!CPPL;UFYU!CPPL;UFYU!CPPL;!!!! !!!!

1 J. Medhi, Stochastic Processes, Second edition, New Age International (P) Ltd, New Delhi.

UNIT I: Ch 2 (2.1-2.3) & Ch 3 (3.1-3.3) UNIT II: Ch 3 (3.4-3.6, 3.8, 3.9)

UNIT III: Ch 4 (4.1-4.5) UNIT IV: Ch 6 (6.1-6.5) UNIT V: Ch 10: (10.1-10.3, 10.7, 10.8.)

!!!!!!!!!!)Fydfqu!21/3/3-!21/3/4-!21/8/3/2-!21/8/4/3-!21/8/4/4-!21/8/4/5-!21/9/3*!

REFERENCE BOOKS

1. Samuel Karlin, Howard M. Taylor, A first course in Stochastic Processes , Second Edition,

Academic Press, 1981.

2. Narayan Bhat, Elements of Applied Stochastic Processes, Second edition, John wiley, 1984.

3. S.K.Srinivasan and K.Mehta, Stochastic Processes, TMH, 1976.

4. N.U.Prabhu, Stochastic Processes, Macmillan (NY), 1965.




!!!! DD26DD26DD26DD26!!!!Dmbttjdbm!Dmbttjdbm!Dmbttjdbm!Dmbttjdbm!

EzobnjdtEzobnjdtEzobnjdtEzobnjdt!!!!7777!!!! 4444!!!! 6666!!!!

!!!!

VOJU!JVOJU!JVOJU!JVOJU!J!

!!!!!!!!!!!Jouspevdupsz! dpodfqut;! Uif! nfdibojdbm! tztufn.

Hfofsbmj{fe!Dp!psejobuft!=dpotusbjout.!

Wjsuvbm!xpsl.Fofshz!boe!npnfouvn/!

VOJU!JJVOJU!JJVOJU!JJVOJU!JJ!

!!!!!!!!!!!Mbhsbohf=t!frvbujpo;!Efsjwbujpo!boe!fybnqmft.Joufhsbmt!pg!

uif!Npujpo.Tnbmm!ptdjmmbujpot/!

VOJU!JJJVOJU!JJJVOJU!JJJVOJU!JJJ!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Tqfdjbm!Bqqmjdbujpot!pg!Mbhsbohf=t!Frvbujpot;!Sbzmfjhi=t!

ejttjqbujpo!gvodujpo!jnqvmtjwf!npujpo.Hzsptdpqjd!tztufnt.

Wfmpdjuz!efqfoefou!qpufoujbmt/!

UNIT IV

Hamilton’s equations: Hamilton’s principle-Hamilton’s equation-Other Variational

principles-Phase space.

UNIT V Hamilton-Jacobi theory: Hamilton’s Principal Function- The Hamilton-Jacobi Equation-

Separablity.

TEXT BOOK

Donald T.Greenwood, Classical Dynamics, Prentice – Hall of India, New Delhi 1979.

!!!!!!!!VOJU!J;!Di!2!)2/2.2/6*!!!!!VOJU!JJ;!Di!3!)3/2.3/5*!!!!!!VOJU!JJJ;!Di!4!

)4/2-!4/3!boe!4/5*!!!!!!!!!!!

!!!!!!!!)Fydfqu4/4*!!VOJU!JW;!Di!5!)5/2.5/5*!!!!VOJU!W;!!!!Di!6!)6/2.6/4*!

SFGFSFODF!CPPLTSFGFSFODF!CPPLTSFGFSFODF!CPPLTSFGFSFODF!CPPLT!!!!

2/ I/Hpmetufjo-!Dmbttjdbm!Nfdibojdt-!Obsptb!Qvcmjtijoh!ipvtf-!

3oe!fejujpo-!Ofx!Efmij/!

3/ Obsbzbo!Diboesb!Sbob!'!Qspnpe!Tibsbe!Diboesb!Kpbh-!

Dmbttjdbm!Nfdibojdt-!UNI!2::2/!

CORE ELECTIVE COURSES(CEC)

(For the candidates admitted from the year 2011 onwards)

Code Course Title Hours/week Semester Credits

22QN32122QN32122QN32122QN321 CEC1 Number

Theory

6 2 4

UNIT I

Divisibility: Introduction-Divisibility-Primes-The Bionomical Theorem.

UNIT II

Congruence-Solutions of Congruence-The Chinese Remainder Theorem-Techniques of Numerical

Calculation-Prime Power Module-Primitive roots and Power Residue.

UNIT III

Quadratic Reciprocity and Quadratic Forms: Quadratic Residues- Quadratic Reciprocity-The

Jacobi Symbol-Binary Quadratic Forms.

UNIT IV

Some Function of Number Theory: Greatest integer Function-Arithmetic Functions –The Mobius

Inversion Formula-Recurrence Functions.

UNIT V

Some Diophantine Equations: The Equation ax+ by=c –Simultaneous Linear Equations-

Pythagorean Triangles-Assorted Examples.

TEXT BOOK

Ivan Nivan, Herbert S.Zuckerman and Hugh L.Montgomery, An Introduction to the theory of

Numbers, Fifth edition., John Wiley and Sons Inc,2009.

UNIT I: Ch 1 UNIT II: Ch 2(2.1-2.4, 2.6 &2.8) UNIT III: Ch 3(3.1-3.4)

UNIT IV: Ch 4(4.1-4.4) UNIT V: Ch 5(5.1-5.4)

REFERENCE BOOKS

1. David M.Burton, Elementary of Number theory, W.M.C Brown Publishers, Dubuque,

Lawa, 1989. .

2. William.J.Leveque, Fudamentals of Number theory, Addison-Wesley Publishing Company,

Phillipines, 1977.

3. Tom.M.Apostal-Introduction to Analytic Number theory, Narosa, New Delhi. (For the candidates admitted for the academic year 2011 onwards)

Code Course Title Hours/Week Semester Credits

22QN529c22QN529c22QN529c22QN529c CEC2 Optimization

Techniques

6 4 4

UNIT I

Integer Programming

UNIT II

Dynamics (Multistage) Programming

UNT III

Decision Theory and Games.

UNIT IV

Inventory Models

UNIT V

Non-Linear Programming algorithms

TEXT BOOK

Hamby A. Taha, Operations Research (4th End), McGraw Hill Publications, New Delhi.2002.

Unit I: Ch 8 (8.1-8.5) Unit II: Ch 9 (9.1-9.5) Unit III: Ch 11 (11.1-11.4)

Unit IV: Ch 13 (13.1-13.4) Unit V: Ch 19(19.1& 19.2)

REFERENCE BOOKS

1. O.L. Mangesarian, Non Linear Programming, TMH, New Yark.

2. Mokther S.Bazaraa and C.M. Shetty, Non Linear Programming, Theory and Algorithms,

Willy, New Yark.

3. Premkumar Gupta and D.S. Hira, Operations Research: An Introduction, S. Chand and Co.,

Ltd. New Delhi.

4. S.S.Rao, Optimization theory and Applications, Wiley Eastern Ltd, New Delhi.

!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!

(For the candidates admitted for the academic year 2011 onwards)

Code Course Title Hours/Week

Semester Credits

22QN529b22QN529b22QN529b22QN529b CEC3 Numerical

Analysis 6 4 4

UNIT I

!!!!!!!!!!Usbotdfoefoubm!boe!Qpmzopnjbm!Frvbujpot;!Sbuf!pg!dpowfshfodf!=!Jufsbujwf!Nfuipet!=!Qpmzopnjbm!Frvbujpot;!Csjehf!=!Wjtub!nfuipe-!Cbstupx=t!nfuipe-!Hsbggf=t!sppu!trvbsjoh!nfuipe/!

UNIT II

System of Linear Algebraic Equations and Eigen Value Problems: Error Analysis of

direct and iteration methods – Finding Eigen values and Eigen vectors – Jacobi and Power

methods.

UNIT III

Interpolation and Approximation: Hermit Interpolations – Piecewise and Splice

Interpolation – Vicariate Interpolation – Approximation – least square approximation.

UNIT IV

Differentiation and Integration: Numerical Differentiation – optimum choice of step –

length Extrapolation methods – Partial Differentiation – Methods based on undetermined

coefficients – Gauss Methods.

UNITV

Ordinary Differential Equations: Local truncation error – Euler, Backward Euler,

Midpoint, Taylor’s Method and second orders Runge – kutta method – stability analysis.

TEXT BOOK

M.K.Jain, S.R.K.Iyengar and R.K.Jain, “Numerical Methods for Scientific and

Engineering Computation” III Edition, Wiley Eastern Ltd., 1993.

UNIT I: Ch 2 (2.5-2.8) UNIT II: Ch 3 (3.1 - 3.5) UNIT III: Ch 4(4.5 - 4.9)

UNIT IV: Ch 5 (5.2 - 5.5 & 5.8) UNIT V: Ch 6 (6.2, 6.3 & 6.6).

REFRRENCE BOOKS

1. Kendall E. Atkinson, “An Introduction to Numerical Analysis. II Edition, John Wiley

& sons 1988.

2. M.K.Jain, Numerical Solution of Differential Equations, II Edition New Age

International Pvt Ltd 1983.

3. Samuel. D.Conte, Carl De Boor, Elementary Numerical Analysis. McGraw – Hill

International Edition., 1983.



Semester Credits

22QN52:b22QN52:b22QN52:b22QN52:b CEC4 Mathematical

Probability 6 4 4

UNIT I

Sets, Classes of Events and Random Variables: The Event – Algebra of Sets – Fields and

σ fields – Class of Events – Functions and Inverse – Functions – Random Variables – Limits of

Random Variables.

UNIT II

Probability Spaces: Definition of Probability – Some Simple Properties – Discrete

Probability Space - General Probability Space- Induced Probability Space – Other Measures.

UNIT III

Distribution Functions: Distribution function of Random Variables – Decomposition of

D.F’s - Distribution function of Vector Random Variables – Correspondence Theorem.

UNIT IV

Expectation and Moments: Definition of Expectation-Properties of Expectation –

Moments, Inequalities.

UNIT V

Characteristics Functions: Definition and Some Properties – Some Simple Problems –

Inversion Formula - Characteristics Functions and Moments-Bochner’s Theorem.

TEXT BOOK

B.Ramdas Bhat, Modern Probability Theory, II Edition, Wiley Eastern Ltd, 1988.

UNIT I: Ch 1(1.1-1.4) & Ch 2(2.1-2.3) UNIT II: Ch 3 (3.1 - 3.6) UNIT III: Ch 4(4.1 - 4.4)

UNIT IV: Ch 5 (5.1 - 5.3) UNIT V: Ch 7 (7.1-7.5)

REFERENCE BOOKS

1. Sheldon Ross, First Course in Probability, Maxwell Mac. Millar International Edition, New

York, VI Edition, 2008.

2. Geoffery Grimmell and Domeonic Welsh, Probability – An Introduction, Oxford

University Press, 1986.

3. M.Fisz, Probability Theory and Mathematical Statistics, John Wiley and Sons, New York,

1963.

4. K.L.Chung, A Course in Probability, Academic Press, New York, 1974.

))))For the candidates admitted for the academic year 2011 onwards)


22QN425b22QN425b22QN425b22QN425b CEC5 Fuzzy

Mathematics

6 3 5

UNIT I

Fuzzy sets-Basic type-Basic Concepts Fuzzy - α -cuts- Additional properties of α- cuts Extension

principle for Fuzzy sets.

UNIT II

Operations on Fuzzy sets-Types of Operations- Fuzzy complements-t-Norms-Fuzzy Unions-

Combinations of operations.

UNIT III

Fuzzy Arithmetic- Fuzzy numbers- Arithmetic Operations on intervals- Arithmetic

Operations on Fuzzy Numbers.

UNIT IV

Fuzzy relations-Binary fuzzy relations-Fuzzy equivalence relations-Fuzzy compatibility Fuzzy

relations- Fuzzy ordering relations-Fuzzy morphisms.

UNIT V

Fuzzy relation equations-General discussion- Problem partitioning-Solution method- Fuzzy

relations equations based on Sup-I Compositions-Fuzzy Relation equations based on inf-ωi compositions.

TEXT BOOK

George J.Klir and B.Yuan, Fuzzy sets and Fuzzy Logic, Prentice Hall of India New Delhi, 2004.

UNIT I: Ch 1 and Ch 2 UNIT II: Ch 3 UNIT III: Ch 4 UNIT IV: Ch 5 UNIT V: Ch 6

REFERENCE BOOK

H.J.Zimmermann, Fuzzy set Theory and its Applications, Allied Publishers Limited, New

Delhi, 1991.



22QN425c22QN425c22QN425c22QN425c CEC6 Combinatorics

6 3 4

UNIT I

Permutations and combinations-distributions of distinct objects –distributions of non distinct

objects - Stirlings formula.

UNIT II

Generating functions-generating function for combinations-Enumerators for permutations-

distributions of distinct objects into non-distinct cells-partitions of integers-the Ferrers graphs-elementary

relations

UNIT III

Recurrence relations-linear recurrence relations with constant coefficients solutions by the

technique of generating functions –special class of nonlinear difference equations- recurrence relations

with two indices.

UNIT IV

The principle of inclusion and exclusion-general formula-permutations with restriction on relative

position-derangements-the rook polynomials-permutations with forbidden positions.

UNIT V

Polya’s theory of counting-equivalence classes under a permutation group Burnside theorem-

equivalence classes of functions-weights and inventories of functions-Polya’s fundamental theorem-

generation of Polya’s theorem.

TEXT BOOK

C.L. Liu, Introduction to Combinatorial Mathematics, TMH, New Delhi.

UNIT I: Ch 1 UNIT II: Ch 2 UNIT III: Ch 3 UNIT IV: Ch 4 UNIT V: Ch 5

REFERENCE BOOKS

1. Marshall Hall.Jr., Combinatorial Theory.

2. H.J.Rayser, Combinatorial mathematics, Carus, Mathematical Monograph.No.14



22QN52:c22QN52:c22QN52:c22QN52:c CEC7 Coding

Theory

6 4 5

UNIT I

Linear Block Codes: Basic Definitions, The Generator Matrix, Description of Linear Block

codes, the parity check matrix and Dual Codes, Error Deletion and Correction over Hand-Input Channels,

Weight, Distributions of Codes and their Duals.

UNIT II

Hamming Codes and their codes, Performance of linear codes, Modifications to Linear Codes,

Best Known Linear Block Codes

UNIT III

Cyclic Codes, Rings and Polynomials: Introduction, Basic Definitions, Rings, Quotient Rings,

Ideals in Rings, Algebraic Description of Cyclic Codes, Nonsystematic Encoding and Parity Check,

Systematic Coding.

UNIT IV

Some Hardware Background, Cyclic Encoding, Syndrome Decoding.

UNIT V

Bounds on codes: The Gilbert – Varshamov Bound, The Poltkin Bound, The Griesmer Bound,

The Linear Programming and Related Bound, the MCEliece-Rodemich-Rumsey-Welsch Bound.

TEXT BOOK

Toddk.Moon, Error Correction Coding Mathematical Methods and Algorithms, Wiley Interscience

& John Wiley & Sons, INC., Publications.

UNIT I: Ch 3(3.1-3.4), UNIT II: Ch 3 (3.5-3.10), UNIT III: Ch 4 (4.1-4.8)

UNIT IV: Ch 4(4.9-4.11) UNIT V: Ch 9 (9.1-9.5).

REFERENCE BOOKS

1. S.J.Macwilliams and N.J.A. Slone, The theory of Error-Correcting Code, Amster Bam, North

Holland, 1977.

2. Raymond Hill, A First Course in Coding Theory, Clarendon Press, Oxford, 1986.

OPEN ELECTIVE COURSES (OEC)



Semester Credits

OEC1 Cryptography 6 5

UNIT I

Encryption Schemes -Symmetric and Asymmetric Cryptosystems - cryptanalysis -

Alphabets and words -Permutations, Block ciphers -Multiple Encryption.

UNIT II

Probability –conditional Probability –Birthday Paradox – Perfect Secrecy- Vernam one –

Time Pad –Random Numbers –Pseudorandom Numbers.

UNIT III

Prime Number Generation: Trial Division –Fermat Test – Carmichael Numbers – miller –

Rabin Test –Random Primes. .

UNIT IV

Factoring: Trail Division – P-1 Method –Quadratic Sieve – Analysis of the Quadratic

Sieve – Effienciency of other Factoring Algorithms.

UNIT V

Discrete Logarithms: The DL problems – Enumeration – shanks Baby Step Giant – Step

Algorithm – The Pollard P – Algorithm – the pohlig – Hellman Algorithm – Index Calculus.

TEXT BOOK

Johannes A.Buchmann, Introduction to Cryptography, second edition, Springers.

. UNIT I: Ch 3 (3.1-3.7) UNIT II: CH 4 UNIT III: Ch 7

UNIT IV: Ch 9 UNIT V: Ch 10 (10.1 -10.6)

REFERENCE BOOKS

1. William Stallings, Cryptography and Network Security, Principles and

Practices, Fourth Edition, Prentice Hall of India. .

2. H.L.Royden, Real Analysis, PHI, Third Edition, 1989.

3. RG.Bartle, Elements of Real Analysis, John Wiley, 1976.



OEC2 Mathematical

Modelling

and

Simulation

6 3 4

UNIT I

Statistical Models in Simulation: Review of Terminology. And Concepts – Useful

Statistical Model -Discrete Distributions – Continuous Distributions – Poisson Process –

Empirical Distributions.

UNIT II

Queueing Models: Characteristics of Queueing Systems –Queueing Notations –

Transient and Steady –State Behaviour of Infinite –.Long – Run Measures of Performance

Of Queueing Systems.

UNIT III

Queueing Models: Steady –State Behaviour of Infinite – populations Markovian

Models –Steady State Behaviour of Finite Population Models (M/M/C/K/K) - Networks of

Queue.

UNIT IV

Random –Number Generation: Properties of Random Numbers – Generation of

Pseudo - Random Numbers – Techniques for Generating random Numbers – Tests for random

Numbers.

UNIT V

Random –Variate Generation: Inverse Transform Technique – Direct Transformation

for the normal distribution – Convolution Method Acceptance Rejection – Rejection Technique

TEXT BOOK

Jerry Banks, john S.Carson, Barry l.Nelson, discrete – Event system Simulation, Second

edition, Prentice – Hall of India, 1998.

UNIT I: Ch 6 UNIT II: Ch 7(7.1-7.4) UNIT III: Ch 7(7.5-7.7)

UNIT IV: Ch 8 UNIT V: Ch 9

REFERENCE BOOK

Geoffrey Gordon, System Simulation, Second edition, Prentice Hall of India, New

Delhi, 1995. .

(For the candidates admitted from the academic year 2011 onwards)


OEC3 Statistics 6 3 4

UNIT I

Collection, Classification and Tabulation of data –Graphical and Diagrammatic Representation of

Data-Bar Diagrams, Pie Diagram, Histogram, Frequency Polygon, Frequency curve and Gives- Measures

of Central Tendency-Mean, Median and Mode in Series of Individual Observation, Discrete and

Continuous Series, More than Frequency, Less than Frequency, Mid value and Open End Class.

UNIT II

Measures of Dispersion- Range, Quartile Deviation, Mean Deviation about an average, Standard

Deviation and Coefficient of Variation for Individual, Discrete and Continuous type data.

UNIT III

Correlation-Different types of Correlation- Positive, Negative, Simple, Multiple, Linear and Non

Linear Correlation, Methods of Correlation- Karl Pearson’s and Spearman’s Correlation-Concurrent

Deviation Method.

UNIT IV

Regression Types and Method of Analysis, Regression Line, Regression Equations, Derivation

taken from Arithmetic Mean of X and Y, Derivation taken from Assumed Mean, Partial and Multiply

Regression Coefficients- Applications.

UNIT V

Chi-Square tests for Variance, Goodness of fit (Expected frequencies are equal or in a specified

proportion only) and independence of attributes F test for equality of two Variances, Analysis of

Variance- One way, Two Way and Latin Square design.

TEXT BOOKS

1. S.C.Gupta and V.k.Kapoor, Fundamentals of Statistics, Sultan Chand and Sons New Delhi 1994.

2. S.C.Gupta, Fundamentals of Statistics, 6th Revised and Enlarged Edition, Himalaya Publishing House.

UNIT 1 :Ch4(4.1-4.4),Ch 5(5.1-5.8) of (1) UNIT 2:Ch 6(6.4-6.9,6.12) of (1)

UNIT 3:Ch 8(8.1-8.4,8.7,8.8) of (1) UNIT 4:Ch 9(9.1-9.4) of (1) UNIT 5:Ch18( 18.1,18.2,18.4-18.6)

of (2)

REFERENCE BOOKS

1. J.E. Freund, Mathematical Statistics, Prentice Hall of India.

2. A.M. Goon, M.K. Gupta, B.Dos Gupta, Fundamentals of Statistical, Vol – I, World Press,

Calcutta, 1991.



OEC4 Statistical

Methods And

Operations

Research

6 2 4

UNIT I

Correlation and Regression-Karl-Pearson`s correlation coefficient, Partial correlation coefficient,

Multiple correlation coefficient and Regression Equation of two variables only.

UNIT II

Probability- Calculation of Probability based on Binomial, Poisson and Normal

distributions (Simple problems only).

UNIT III

Sampling-simple, systematic and Stratified random sampling Techniques- Standard error,

tests of significance- Large sample and small sample tests- Students ‘t’ distribution, Z-test for the

significance of the correlation coefficient.

UNIT IV

Chi-square tests for variance, goodness of fit (expected frequencies are equal or in a

specified proportion only) and independence of attributes F test for equality of two variances,

Analysis of variance – One way, two way and Latin Square design.

UNIT V

Linear Programming Problem – Formulation – Solution by graphical and simplex

methods of simple problems (≤ constraints only). Transportation problems – North West Corner

Rule, Least cost method, Vogel’s Approximation method.

TEXT BOOKS

1. S.P.Gupta, Statistical Methods, S.Chand and Sons.

2. Kanti Swarup, Operations Research, S.Chand and Sons.

REFERENCE BOOKS 1. P.A.Navanitham, Business Statistics and Operations Research, jai Publishers.

2. S.C.Gupta and V.K.Kapoor, Applied Statistics, Sultan Chand and Sons.



OEC5 Discrete

Mathematics

and

Numerical

Methods

6 1 4

Objectives:

Ideas of mathematical logic, concepts of set theory and Boolean algebra. To impart the

mathematical concepts and numerical methods required to computer science. To know the

fundamental ideas of mathematical logic, concepts of set theory and Boolean algebra

UNIT I Mathematical Logic : Statements and Notation - Connectivity’s - Statement Formula

and Truth Tables - Tautologies - Equivalence of Formulas - Duality Law. Disjunctive Normal

form - Conjuctive Normal form. The theory of inference - validity using truth tables - Rules of

Inference.

UNIT II

Basic concepts of Set Theory: Inclusion and Equality of sets - Power set - Operations on

Sets -Venn Diagrams - Cartesian Products. Relations and Ordering - Binary & Equivalence

relations - Partial Ordering. Functions - Composition of functions, inverse functions, Binary &

n-ary operations.

UNIT III

Lattices as partially ordered sets - Hash Diagrams - Properties of Lattices - Distributive

& Modular inequalities - Special lattices - Complete, Bounded, Complemented, & Distributive

lattices. Properties of Boolean algebra.

UNIT IV

Solution of polynomial equations: Birge - Vieta and Root squaring methods. System of

linear algebraic equations: Gauss - elimination, Gauss - Jordan, Triangularization and Partition

methods - Jacobi, Gauss-Seidal iterative methods. Eigen values by power method.

UNIT V Interpolation: Lagrange’s and Newton’s interpolation - interpolating polynomials using

finite difference. Numerical integration. Trapezoidal, Simpson’s rules and Romberg

integration

Note: Stress in on Numerical Problems in Units IV and V

TEXT BOOKS

1. J.P.Tremblay & R.Manohar, “: Discrete Mathematical Structures with Applications to

Computer Science”, McGraw-Hill International Edition, 1987. Chapters : 1-1, 1-2.1 -

1-2.13, 1-3.1 - 1-3.5, 1-4.1 - 1-4.3, 2-1, 2-3, 2-4.1 -2.4.4, 4-1, 4-2.

2. M.K.Jain, S.R.K.Iyengar & R.K.Jain, “Numerical Methods for Scientific and

Engineering Computation “, Wiley Eastern Limited, New Delhi, 1987. Chapters: 2.7,

2.8, 3.2, 3.4, 3.5, 4.2, 4.4, 5.9, 5.10. (Relevant Portions only)

REFERENCE BOOKS

1. Bernard Kolman & Robert C.Busyby, “Discrete Mathematical Structures for Computer

Science”, Prentice Hall of India, New Delhi 1987.

2. Curtis F. Gerald, “Applied Numerical Analysis “, Addison Wesley Publishing

Company, London, 1978.



OEC6 Probability

and Statistics

6 2 4

Objectives:

To learn the concepts of probability, random variables, and statistical applications

UNIT I

Probability – random events – sample spaces – axiomatic approach to probability

– conditional probability – addition and multiplication theorems – (two events – only)-

Boole’s inequality – Independent events – Baye’s theorem.

UNIT II

Random Variables – discrete and continuous random variables – probability

density function – marginal and conditional probability distribution function.

UNIT III

Mathematical Expectations – Variance – moment generating function – correlation

coefficients – regressions

UNIT IV

Discrete Distribution – Binominal, Poisson distributions – Continuous distribution

– normal and properties of normal distribution.

UNIT V

Concept of sampling – types of sampling – sampling distribution and standard

error – testing of hypothesis – tests for means and variances for large and small samples –

chi-square test and its application – tests of goodness of fit – test of independence of

attributes.

TEXT BOOKS

S.P.Gupta & V.K. Kapoor, “Fundamentals of Mathematical Statistics”, Sultan Chand &

Sons, New Delhi

REFERENCE BOOKS

1. P.R. Vittal, “Mathematical Statistics”, Margham Publications, Chennai.

2. P.N.Arora & S. Arora, “Statistics for Management”, Sultan Chand, New Delhi



OEC7 Operations

Research

6 3 4

Objectives:

To learn the Optimization techniques.

UNIT I

Linear Programming Problem: Formulation and Graphical solutions, simplex

method, Degeneracy, unbounded and infeasible solution, method of penalty, two phase

method.

UNIT II

Linear Programming (continued): Duality - Primal and Dual computations, Dual

simplex method. Transportation problem - Assignment problem - Hungarian method.

UNIT III

PERT/ CPM ; Arrow (Network) Diagram Representations , Time estimates ,

Critical path , Floats , Construction of Time Chart and Resource Leveling , Probability

and cost considerations crashing of Networks.

UNIT IV

Queuing: Queuing system, Characteristics of Queuing system, Classification of

queues, Definition of Transient and steady states, Poisson Queues, M/M/1 and M/M/C

Queuing models.

UNIT V

Inventory models: The inventory decisions - Deterministic models, EOQ, finite

and infinite delivery rates with out back ordering, EOQ problems with price breaks ,

multi item deterministic problem , Inventory problems with uncertain demand.

TEXT BOOK

Kanti Swarup, P.K.Gupta, ManMohan, “Operation Research “7th Edition, Sultan

Chand & Sons 1994.

REFERENCE BOOK Sundaresan, K.S.Ganapathy Subramanian, K. Ganesan, “Resource Management

Technique”, New Revised Edition, A.K. Publications, June 2000.



OEC8 Graph and

Automata

Theory

6 4 4

Objectives: To introduce the Graph theory and finite state automata theory

UNIT I Graph Path and Circuits: Introduction – Application of Graphs – Finite and Infinite Graphs

– Incidents and Degree – Isolated vertex, pendant vertex and null graph. Paths and Circuits

isomorphism Sub Graphs – Walks, Path and Circuits – Connected & Disconnected Graphs,

Euler’s graphs - Operations on Graphs - Hamiltonian Paths & Circuits.

UNIT II Trees and Fundamental Circuits, Matrix Representation of Graphs: Trees and fundamental

circuits: Properties of Trees Distance and Centers in a Tree - Rooted Binary Trees, Spanning

trees, Matrix representation of Graphs - Incidence Matrix – Sub Matrices of A9G) – Circuit

Matrix – Fundamental matrix - Adjacency Matrix

UNIT III Directed Graphs Graph Theoretic Algorithms and Computer Programs: Directed Graph:

Some Type of Digraphs - Trees with directed edges. Graph Algorithms and Computer Programs –

Computer Representation of a Graph - Algorithms for connectedness – Components and

Spanning Trees - Shortest path Algorithms

UNIT IV Finite Automata and Regular Expressions: Finite State Systems - Basic definitions - Non -

Deterministic Finite Automata - Finite Automata with epsilon moves - Regular Expressions

Applications of Finite Automata.

UNIT V

Context Free Grammars and Properties of Context Free Languages: Context Free

Grammars – Motivation and Introduction : Context - Free Grammars - Derivation Trees -

Chomsky Normal Form - Griebach Normal Form – Properties of Context Free Languages –The

Pumping Lemma for CFL’s.

TEXT BOOKS

1. Narsing Deo, “Graph Theory with applications to Engineering and Computer

Science”, Prentice - Hall of India Limited, New Delhi, 1995.

Unit I ch1 (1.1 to 1.5), Ch2 (2.1,2.2,2.4 to 2.7,2.9), Unit II: Ch 3(3.2,3.4,3.5,3.7), Ch7

(7.1 to 7.4 and 7.9) Unit III Ch9 (9.2,9.6) , Ch11 (11.2,11.4(A1 1.2),11.5(A16.7)

2. John E.Hopcroft & Jeffery D.Ullman, “Introduction to Automata Theory, Languages and

Computation”, Narosa Publishing House, New Delhi, 1997. UNIT I ch1 (1.1 to 1.5), Ch2 (2.1, 2.2, 2.4 to 2.7, 2.9),

UNIT II: Ch 3(3.2, 3.4, 3.5, 3.7) & Ch7 (7.1 to 7.4 and 7.9)

UNIT III Ch9 (9.2, 9.6) & Ch11 (11.2, 11.4(A1 1.2), 11.5(A16.7)

UNIT IV: Ch2 (2.1 to 2.5, 2.8), UNIT V: Ch4 (4.1 to 4.3, 4.5 to 4.6) & Ch6 (6.1)

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