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8/13/2019 Planimetrija_Zadaci

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Faculty of natural sciences, mathematics and education

PROPOSALFOR THE UNDERRADUATE STUD! PRORA""E

Mathematics

S#lit, "arch $%th, &''%

Uni(ersity of S#lit


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U N D E R R A D U A T E S T U D ! ) " A T H E " A T * + S

S T U D ! P R O R A " " E + U R R * + U L U "

Underraduate Study Proramme) "athematics

Faculty of Natural Sciences, "athematics, and EducationN- Tesle$&, &$''' S#lit, +roatia

Phone) . /0% &$ /0% $//Fa1) . /0% &$ /0% 2/$

de3anat4#mfst-hrhtt#) 55666-#mfst-hr

2
mailto:[email protected]:[email protected]


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1. Introduction

1.1. General information on the programme

The study #roramme here #ro#osed has its oriin in the current educational study ofmathematics that has 7een held continuously for more than a decade at this faculty- For many years,toether 6ith the #enetration of mathematics into more and more 7ranches of economy and science, 6eha(e 7een 6itnesses to a reat interest of reional hih school #o#ulation, as 6ell as our o6n students,for initiation of a scientific study of mathematics- A sinificant num7er of students comin from the

7road reion ra(itatin to S#lit, e(ery year enroll on such a study at the De#artment of "athematics,Uni(ersity of 8are7- 9esides to 7ein teachers of mathematics in elementary and secondary schools,mathematicians today find :o7 in 7an3s, insurance com#anies, com#uter centers, centers ofcommunication technoloies de(elo#ment, they are needed at the ma:ority of faculties, etc- Onem#loyment aency lists there are no unem#loyed mathematicians and the e1#erience throuhout the6orld sho6s that this is not only tem#orarily so, 7ut the need for mathematicians 6ill increase in thefuture-

;e #ro#ose the ne6 t6o


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1.3. Student mobility scheme

The study entirely consists of one


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2. General description

!ype of

programme

Underraduate

Programme title "athematics

Institution Proposed by De#artment of "athematics, Faculty of natural sciences,mathematics and education

Participating

institutions

Faculty of natural sciences, mathematics and education

"uration / years

#$!S $0'

%dmission

re&uirements

Secondary school com#letion satisfactorily (alued and entrancee1amination in mathematics @until the State "atriculate is esta7lished

'earningoutcomes and

competences

alid 3no6lede in 7asic areas of mathematics and ca#a7ility of a7stractreasonin and sol(in #ro7lems 7y usin mathematical tools, sufficient for

a##lication in (ariety of #rofessions or for continuation of study-

%ccess to furtherstudies

raduate study in mathematics or related raduate study 6ith #rescri7eddifference courses-

(ualification

a)arded

9achelor in mathematics

*


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3. Study+"egree programme

3.1. Programme structure )ith credits

1st Semester

$ourse

code

$ourse title !ype of course

+$ourse structure+

L.S.P

#$!S

P""''$ *ntroduction to "athematics 2%.'.2% 0P""''& *ntroduction to Ale7ra 6ith Analytic eometry 2%.'.2% 0P"*''' *ntroduction to +om#utin /'.'./' %P"*''/ Prorammin * $%.'./' 2P"*''G +om#uter La7 * '.'./' /P"S''$ Enlish Lanuae * '.2%.' &!otal, 13*-*-1/ 3/

L.S.P Lectures . Seminars . Practice

2nd Semester

$oursecode


+$ourse structure+L.S.P

#$!S

P""''/ Differential and *nteral +alculus $ 2%.'.2% IP""$'$ Linear Ale7ra 2%.'.2% IP"*''0 Prorammin ** /'.'./' %

P"*'$' +om#uter La7 ** '.'./' /P"S''& Enlish Lanuae ** '.2%.' &Electi(e Social Science and Humanities +ourseJ $%.$%.' &

!otal 13*-0/-1*/ 3/

JStudent here cannot choose second forein lanuae-

0


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#lective Social Science and umanities $ourses

SPIG

$oursecode

$ourse title !ype of course+$ourse structure+

L.S.P

#$!S

ENERAL +OURSESP"S$'$ Philoso#hy of Science $%.$%.' &P"S$'2 Lanuae +ulture $%.$%.' &P"S$'/ +roatian Society in Transition $%.$%.' &P"S$$$ Socioloy of Science $%.$%.' &P"S$&' erman Lanuae ** @Secondary Le(el './'.' &

EDU+AT*ONAL +OURSES

P"S$'% "edia in Education $%.$%.' &P"S$'0 Psycholoy of Self


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#lective Social Science and umanities $ourses

5%''

$ourse

code



#$!S

ENERAL +OURSESP"S$$I Social Ecoloy $%.$%.' &P"S$'& Rhetoric $%.$%.' &P"S$$& Loic $%.$%.' &P""/'0 9ride $%.$%.' &P"S$'G erman Lanuae * @Elementary Le(el './'.' &

EDU+AT*ONAL +OURSESP"S$'' radin and E(aluation $%.$%.' &P"S$'I Psycholoy of Self


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*th Semester

$oursecode


+$ourse structure+

L.S.P

#$!S

P""$'I Real Analysis 2%.'./' KP""&'$ ector S#aces $ /'.'./' %P""$$'P Loic /'.'./' %P""$$$ Ale7raic Structures /'.'./' %

Electi(e module $ G'.'./'or 2%.$%./'

0

!otal 16*-/-1*/

or 1/-1*-1*/

3/

#lective module 1

7Student chooses courses bringing at least #$!S8999

$ourse

code



#$!S

P""'$2 +onstructi(e "thods in eometry /'.'./' %P""$$& Set Theory /'.'./' %P"*$$$ Data Structures and Alorithms /'.'./' %

P"*$$G *ntroduction to Artificial *ntellience /'.'./' %P"P'I/ *ntroduction to eneral Physics * /'.'.' /P"*$&' Net6or3 A##lication Prorammin $%.$%.' /

JJJ Should the student ha(e in mind a raduate study, the coordinator ad(ises him5her accordinly-

-

6


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0th Semester999

$ourse

code



#$!S

P""$$2 *ntroduction to To#oloy /'.'./' GP""$$% *ntroduction to Pro7a7ility and Statistics 2%.'.2% 0P""$$G +om#le1 Analysis /'.'./' GP""''I History of "athematics /'.'.' /

Electi(e module & /'.'./' %P""$$K Final Underraduate Seminar '.$.' &!otal 10*-1-13* 3/

#lective module 2

7Student chooses one of the courses offered8999

$oursecode

$ourse title !ype ofcourse

+$oursestructure+

L.S.P

#$!S

*ntroduction to Pro:ecti(e eometry /'.'./' %Noneuclidean S#aces /'.'./' %

*ntroduction to eneral Physics ** /'.'./' %"athematical "ethods of Physics /'.'./' %Data7ases /'.'./' %

JJJ Should the student ha(e in mind a raduate study, the coordinator ad(ises him5her accordinly-

First< and second< year students ha(e riht to enrol the course ymnastics and Health +ultureM@/' school hours in total #er semester- *ts #roramme 6ill 7e #resented to students at the

7einnin of each academic year-

1/


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3.2. $ourse information

$ourse title

Ale7raic structures

$ourse code P""$$$

!ype of course Theoretical course-

'evel of course 9asic mathematics course 6ith formal mathematical lanuae-

:ear of study ***- Semester -

#$!S7umber ofcredits allocated8

% E+TSTotal E+TS score for) attendin lectures @/' hours of lectures . /' hours ofe1ercises, studyin, #re#arin #artial and final e1ams-

ame of lecturer Ph-D- o3o "andi, Senior Lecturer

'earningoutcomes andcompetences

9asic 3no6lede in theory of rou#s, rins and ale7ras, com#rehension andca#a7ility of a##lyin the 3no6lede in sol(in (ariety of #ro7lems-

Prere&uisites Linear ale7ra **-

$ourse contents Groups- rou#, su7rou#, cosets of su7rou#, normal su7rou#, Buotient rou#,mor#hisms of rou#s, direct and semidirect #roduct of rou#s, e1am#les of rou#s,rou# GL@n -ings; fields i algebras. Rin, ideals, homomor#hisms of rins, rins of

#olynomials, #rinci#al ideal domain, uniBue factori=ation domain, fields, ale7ras,associati(e ale7ras @matrices ale7ras, rou# ale7ras, Buaternion ale7ras, ;eylale7ras, Lie ale7ras-Modules."odule, su7module, Buotient module, sim#le and semisim#le module,e1am#les of modules-

ecommendedreading

"- F- Atiyah, *- - "acdonald, Introduction to Commutative Algebra, Addison

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