uČn i naČrt p redmeta course syllabus - um.si progami... · d. b. west, introduction to graph...

Predme

Course

ŠtudijStudy

Ma

Mat

Vrsta pr

Univerz

PredavLectu

60

Nosilec

Jeziki / Languag

Pogoji zštudijsk

Poznava

Vsebina

Algebra

uporabe

število

indeks;

diskretn

neenako

prostor

lastnih v

et:

title:

jski programy programm

atematika, 2

thematics, 2

redmeta / C

zitetna koda

vanja ures

SeSe

0

predmeta

ges:

za vključitevkih obvezno

anje teorije

a:

aična komb

e rodovnih

particij n

teorija P

ni matema

ost; pokritj

i ciklov, kr

vrednosti).

UČN

Diskretna m

Discrete Ma

m in stopnjme and leve

2. stopnja

2nd degree

Course type

a predmeta

eminar eminar

15

/ Lecturer:

Pred

Vaje /

v v delo oz.osti:

grafov.

inatorika: r

funkcij (Ca

naravnega

Polya; line

atiki (načr

ja s polnim

roženja in

NI NAČRT P

matematika

athematics

a el

e

a / Universi

Vaje Tutorial

30

Boštjan

davanja / Lectures:

S

Tutorial: S

za opravlja

rodovne fu

atalanova š

števila); c

earna alge

ti in Fish

mi dvodelni

prerezi; up

PREDMETA /

2

2

ŠtudijskaStudy

ty course c

Kliničnewor

n Brešar

SLOVENSKO

SLOVENSKO

anje Pr

Kn

Co

unkcije;

števila,

ciklični

bra v

herjeva

i grafi;

porabe

Al

ap

nu

in

m

co

sp

ei

/ COURSE S

a smer field

ode:

e vajek

Drugšt

O/SLOVENE

O/SLOVENE

rerequisits:

nowledge o

ontent (Syll

lgebraic co

pplications

umbers, pa

ndex; Polya

mathematics

overings wit

pace, circu

genvalues)

SYLLABUS

LAc

ge oblike tudija

S

of graph the

labus outlin

mbinatorics

of genera

rtitions of a

theory; lin

s (designs

th complet

lations and

.

Letnik cademic year

1.

1.

Samost. deloIndivid. work

195

eory.

ne):

s; generati

ating functi

a positive in

near algebr

and Fisher

e bipartite

d cuts; ap

SemesterSemester

2.

2.

o ECTS

10

ng function

ions (Catal

nteger); cyc

ra in discre

r's inequalit

graphs; cyc

pplications

r r

ns;

an

clic

ete

ty;

cle

of

Kode za popravljanje napak: osnovni pojmi;

linearne kode; konstrukcije linearnih kod;

popravljanje napak; ciklične kode; klasifikacija

cikličnih kod.

Teorija grafov: dodatna poglavja iz barvanja

grafov (dokaz Brooksovega izreka, kritični grafi,

krožna barvanja); k‐povezani grafi (dokaz

Mengerjevega izreka); omrežja in pretoki v

omrežjih; dokaz izreka Kuratowskega;

neodvisne in dominirajoče množice.

Kombinatorika delno urejenih množic: linearne

razširitve; dimenzija delne urejenosti;

Dilworthov izrek; Spernerjev izrek. Schnyderjev

izrek.

Ramseyeva teorija: število monokromatičnih trikotnikov; Ramseyev izrek; Ramseyeva števila; uporabe izreka, grafovska Ramseyeva števila.

Error‐correcting codes: basic concepts; linear

codes; constructions of linear codes; correcting

errors; cyclic codes; classification of cyclic

codes.

Graph theory: additional graph coloring topics

(proof of Brooks theorem, critical graphs,

circular colorings); k‐connected graphs (proof of

Menger's theorem); networks and flows in

networks; proof of Kuratowski theorem;

independent and dominating sets.

Combinatorics of partially ordered sets: linear

extensions; dimension of a partial order;

Dilworth's theorem; Sperner's theorem.

Schnyder's theorem.

Ramsey theory: number of monochromatic triangles; Ramsey theorem; Ramsey numbers; applications of the theorem, graph Ramsey numbers.

Temeljni literatura in viri / Readings:

N. L. Biggs, Discrete Mathematics. Second Edition. The Clarendon Press, Oxford University Press,

New York, 1989.

M. Aigner, Discrete Mathematics, American Mathematical Society, Providence RI, 2007.

R. Diestel, Graph Theory, Springer‐Verlag, Berlin Heidelberg, 2005.

M. Juvan, P. Potočnik, Teorija grafov in kombinatorika, DMFA, Ljubljana, 2000.

J. H. van Lint, R. M. Wilson, A Course in Combinatorics, Cambridge University Press, Cambridge,

2001.

D. B. West, Introduction to Graph Theory, Second Edition. Prentice Hall, Inc., Upper Saddle River, NJ, 2001.

Cilji in kompetence:

Objectives and competences:

Poglobiti zahtevnejša področja sodobne

diskretne matematike in njene uporabe:

algebraično kombinatoriko, kode za

popravljanje napak, dodatna poglavja iz teorije

grafov, kombinatoriko delno urejenih množic,

metode linearne algebre v diskretni

matematiki in Ramseyevo teorijo.

To deepen the knowledge of more demanding areas of temporary discrete mathematics and its applications: algebraic combinatorics, error‐correcting codes, additional topics from graph theory, combinatorics of partially ordered sets, tools from linear algebra in discrete mathematics, and Ramsey theory.

Predvideni študijski rezultati: Intended learning outcomes:

Znanje in razumevanje:

Razumevanje zahtevnejših principov diskretne matematike.

Poglobiti netrivialne uporabe diskretne matematike.

Povezati diskretno matematiko z drugimi matematičnimi področji.

Prenosljive/ključne spretnosti in drugi atributi:Prenos zahtevnejšega znanja metod diskretne matematike na druga področja (računalništvo, kemija, biologija, optimizacija, ...)

Knowledge and Understanding:

Be able to understand more demanding principals of discrete mathematics.

To deepen the knowledge of nontrivial applications of discrete mathematics.

To connect discrete mathematics with other fields of mathematics.

Transferable/Key Skills and other attributes: Knowledge transfer of more demanding methods of discrete mathematics into other fields (computer science, chemistry, biology, optimization, …)

Metode poučevanja in učenja:

Learning and teaching methods:

Predavanja

Seminarske vaje

Lectures

Tutorial

Načini ocenjevanja:

Assessment:

Način (pisni izpit, ustno izpraševanje, naloge, projekt)

‐ Seminarska naloga ‐ Pisni testi ‐ Ustni izpit

Vsaka izmed naštetih obveznosti mora biti opravljena s pozitivno oceno. Pozitivna ocena pri seminarski nalogi in pisnih testih sta pogoja za pristop k ustnemu izpitu.

Delež (v %) / Weight (in %)

25% 25% 50%

Type (examination, oral, coursework, project):

‐ Seminar exercise ‐ Written tests ‐ Oral exam

Each of the mentioned commitments must be assessed with a passing grade. Passing grade of the seminar and of written tests are required for taking the oral exam.

Reference nosilca / Lecturer's references: 1. BREŠAR, Boštjan, KRANER ŠUMENJAK, Tadeja. The hypergraph of [Theta]-classes and

[Theta]-graphs of partial cubes. Ars combinatoria, ISSN 0381-7032, 2014, vol. 113, str. 225-239. [COBISS.SI-ID 16824153]

2. BREŠAR, Boštjan, CHALOPIN, Jérémie, CHEPOI, Victor, GOLOGRANC, Tanja, OSAJDA, Damian. Bucolic complexes. Advances in mathematics, ISSN 0001-8708, 2013, vol. 243, str. 127-167. http://dx.doi.org/10.1016/j.aim.2013.04.009. [COBISS.SI-ID 16633177]

3. BREŠAR, Boštjan, KLAVŽAR, Sandi, KOŠMRLJ, Gašper, RALL, Douglas F. Domination game: extremal families of graphs for 3/5-conjectures. Discrete Applied Mathematics, ISSN 0166-218X. [Print ed.], 2013, vol. 161, iss. 10-11, str. 1308-1316. http://dx.doi.org/10.1016/j.dam.2013.01.025. [COBISS.SI-ID 16614745]

4. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel, TARANENKO, Andrej. On the vertex k-path cover. Discrete Applied Mathematics, ISSN 0166-218X. [Print ed.], 2013, vol. 161, iss. 13/14, str. 1943-1949. http://dx.doi.org/10.1016/j.dam.2013.02.024. [COBISS.SI-ID 19859464]

5. BREŠAR, Boštjan, KLAVŽAR, Sandi, RALL, Douglas F. Domination game played on trees and spanning subgraphs. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2013, vol. 313, iss. 8, str. 915-923. http://dx.doi.org/10.1016/j.disc.2013.01.014. [COBISS.SI-ID 16564313]

UČNI NAČRT PREDMETA / COURSE SYLLABUS

Predmet: Fraktali in dinamični sistemi

Course title: Fractals and dynamic systems

Študijski program in stopnja

Study programme and level

Študijska smer

Study field

Letnik

Academic

year

Semester

Semester

Matematika, 2. stopnja 1. ali 2. 1. ali 3.

Mathematics, 2nd

degree 1. or 2. 1. or 3.

Vrsta predmeta / Course type

Univerzitetna koda predmeta / University course code:

Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 15 15 135 7

Nosilec predmeta / Lecturer: Dušan PAGON

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE

Vaje / Tutorial: SLOVENSKO/SLOVENE

Pogoji za vključitev v delo oz. za opravljanje

študijskih obveznosti:

Prerequisits:

Linearna algebra, Algebra, Analiza 2 Linear algebra, Algebra, Analysis 2

Vsebina:

Content (Syllabus outline):

Metričen prostor, različne vrste

podprostorov, prostor fraktalov.

Afine transformacije, skrčitve, sistemi

iterirajočih funkcij.

Osnove dinamičnih sistemov, dinamika

fraktalnih množic.

Teoretično in eksperimentalno

določanje dimenzije fraktala,

Hausdorff-Bezikovičeva dimenzija.

Juliajeve množice, primeri njihove

uporabe.

A metric space, different types of

subspaces, the space of fractals.

Affine transformations, contraction

mappings, systems of iterating functions.

Introduction to dynamical systems,

dynamics on fractal sets.

The theoretical and experimental

determination of the fractal dimension,

Hausdorff-Besicovitch dimension.

Julia sets, examples of their application.


Barnsley, M. F.: Fractals Everywhere. Academic Press, Boston (1988); Second edition (1993)

Barnsley, M. F.: Superfractals. Cambridge University Press, Cambridge (2006)

Devaney, Robert: An Introduction To Chaotic Dynamical Systems, 2nd ed., Westview Press (2003)

Devaney. R. L.: Chaos, Fractals and Dynamics - Computer Experiments in Dynamics, Addison-

Wesley (1990)

Edgar, G: Classics on Fractals. Westview Press, Boulder (1992)

Falconer, K. J.: The Geometry of Fractal Sets. Cambridge University Press,

Cambridge (1985)

Lapidus, M. L., Frankenjuijsen, M. v.: Fractal Geometry, Complex Dimensions

and Zeta Functions. Springer, New York (2006)

Edgar, Gerald: Measure, Topology, and Fractal Geometry, 2nd ed., Springer, New York (2008)



Študenti se seznanijo s strukturo podprostora

fraktalov v metričnem prostoru in z osnovnimi

načini generiranja fraktalov (družine

iterirajočih preslikav). Spoznajo tudi različne

pristope k določanju dimenzije fraktala ter

dinamiko fraktalnih množic.

Students get familiar with the structure of the

subset of fractals in a metric space and with the

main ways of generating fractals (iterated

functions systems). They also study different

approaches to the fractal dimension and the

dynamics of fractal sets.

Predvideni študijski rezultati:

Intended learning outcomes:


- aktivno obvladanje strukture metričnega

prostora in prepoznavanje fraktalnih

podmnožic

- teoretično in eksperimentalno določanje

dimenzije fraktalov

- analiza dinamičnih sistemov in njihova

uporaba

Prenesljive/ključne spretnosti in drugi atributi:

- sposobnost generiranja fraktalov

- izračun dimenzije fraktalne množice

- modeliranje z dinamičnimi sistemi

-


- active knowledge of metric space structure

and the ability to recognize its fractal subsets

- theoretical and experimental ways for

finding the dimension of a fractal

- the analysis of dynamical systems and their

application

Transferable/Key Skills and other attributes:

- the abbility to generate fractals

- the calculation of fractal dimension

- modeling with dynamical systems

-



Predavanja

Seminarske vaje

Individualno delo

Lectures

Tutorial

Individual work


Assessment:

Način (pisni izpit, ustno izpraševanje,

naloge, projekt)

Seminarska naloga

Pisni izpit– praktični del

Ustni izpit – teoretični del

Delež (v %) /

Weight (in %)

20%

40%

40%

Type (examination, oral, coursework,

project):

Seminar work

Written exam – practical part

Oral exam – theoretical part

Reference nosilca / Lecturer's

references:

1. PAGON, Dušan, REPOVŠ, Dušan, ZAICEV, Mikhail. On the codimension growth of simple

color Lie superalgebras. J. Lie theory, 2012, vol. 22, no. 2, str. 465-479.

http://www.heldermann.de/JLT/JLT22/JLT222/jlt22017.htm. [COBISS.SI-ID 16070233]

2. PAGON, Dušan. Simplified square equation in the quaternion algebra. International journal of

pure and applied mathematics, 2010, vol. 61, no. 2, str. 231-240. [COBISS.SI-ID 17718024]

3. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. On chains in H-closed topological pospaces.

Order (Dordr.), 2010, vol. 27, no. 1, str. 69-81. http://dx.doi.org/10.1007/s11083-010-9140-x.

[COBISS.SI-ID 15502169]

4. GUTIK, Oleg, PAGON, Dušan, REPOVŠ, Dušan. The continuity of the inversion and the

structure of maximal subgroups in countably compact topological semigroups. Acta math. Hung.,

2009, vol. 124, no. 3, str. 201-214. http://dx.doi.org/10.1007/s10474-009-8144-8, doi:

10.1007/s10474-009-8144-8. [COBISS.SI-ID 15212121]

5. PAGON, Dušan. The dynamics of selfsimilar sets generated by multibranching trees.

International journal of computational and numerical analysis and applications, 2004, vol. 6, no.

1, str. 65-76. [COBISS.SI-ID 14037081]

http://www.heldermann.de/JLT/JLT22/JLT222/jlt22017.htm

http://cobiss.izum.si/scripts/cobiss?command=DISPLAY&base=COBIB&RID=16070233


http://dx.doi.org/10.1007/s11083-010-9140-x


http://dx.doi.org/10.1007/s10474-009-8144-8

http://dx.doi.org/10.1007/s10474-009-8144-8




Predmet: Integralske transformacije

Course title: Integral Transforms



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

30 15 30

135 7

Nosilec predmeta / Lecturer: Marko JAKOVAC

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Poznavanje matematične analize. Knowledge of mathematical analysis.

Vsebina: Content (Syllabus outline):

Klasične Fouriereve vrste. Hilbertov prostor.

Ortonormiran sistem.

Fouriereva in Laplaceova tansformacija.

Osnovne lastnosti. Inverzna formula.

Uporaba Fouriereve in Laplaceove

transformacije.

Primeri drugih integralskih transformacij:

Dvostranska Laplaceova transformacija.

Hartleyjeva transformacija. Mellinova

Classical Fourier series. Hilbert space.

Orthonormal system.

Fourier and Laplace transform. Basic properties.

Inversion formula.

Applications of Fourier and Laplace transform.

Examples of other integral transforms: Two

sided Laplace transform. Hartley transform,

Mellin transform. Weierstrass transform. Abel

transform. Hilbert transform.

transformacija. Weierstrassova transformacija.

Abelova transformacija. Hilbertova

transformacija.


E. Zakrajšek: Analiza III, DMFA Slovenije, Ljubljana, 1998

E. Zakrajšek: Analiza IV, DMFA Slovenije, Ljubljana, 1999

A. Suhadolc: Integralske transformacije, Integralske enačbe, DMFA Ljubljana, 1994.

A. Suhadolc: Metrični prostor, Hilbertov prostor, Fouriereva analiza, Laplaceova transformacija,

DMFA-založništvo, Ljubljana, 1998.

B. Zmazek: Diferencialna analiza, skripta, Maribor, 2006.

Gabrijel Tomšič, Tomaž Slivnik: Matematika IV, Založba FE in FRI, Ljubljana, 1998.



Temeljito spoznati integralske transformacije.

Poznati uporabo Fouriereve in Laplaceove

transformacije.

To know thoroughly integral transforms.

To know thoroughly about applications of

Fourier and Laplace transform.




- Razumevanje in uporaba integralskih

transformacij.


- Identifikacija, formulacija in reševanje

matematičnih in nematematičnih problemov

s pomočjo integralskih transformacij.

- Prenos znanja v zvezi z integralskimi

transformacijami na druga področja

(strojništvo, astronomija, fizika in druge)


- Be able to understand and implement

integral transforms.


- Identification, formulation and solving

mathematical and non mathematical

problems with integral transforms.

- Knowledge transfer of the concepts,

connected with integral transforms into

other fields (mechanical engineering,

astronomy, physics and others).



Predavanja

Seminarske vaje

Individualno delo

Seminarska naloga

Lectures

Tutorial

Individual work

Seminar


Assessment:

Sprotno preverjanje:

Seminarska naloga

Izpit:

Pisni izpit – problemi

Ustni izpit – teorija

Delež (v %) /

Weight (in %)

20%

40%

40%

Mid-term testing:

Seminary work

Exams:

Written exam – problems

Oral exam – theory

Vsaka izmed naštetih obveznosti mora

biti opravljena s pozitivno oceno.

Opravljene sprotne obveznosti so pogoj

za pristop k pisnemu izpitu – problemi.

Opravljen pisni izpit – problemi je

pogoj za pristop k ustnemu izpitu –

teorija.

Each of the mentioned assessments must

be assessed with a passing grade.

Passing grades of all mid-term testings

are required for taking the written exam –

problems. Passing grade of written exam

– problems is required to take the oral

exam – theory.


references:

1. JAKOVAC, Marko, TARANENKO, Andrej. On the k-path vertex cover of some graph

products. Discrete math.. [Print ed.], 2013, vol. 313, iss. 1, str. 94-

100. http://dx.doi.org/10.1016/j.disc.2012.09.010, doi:10.1016/j.disc.2012.09.010. [COBISS.SI-

ID 19464968]

2. JAKOVAC, Marko, PETERIN, Iztok. The b-chromatic index of a graph. Preprint series, 2012,

vol. 50, no. 1183, str. 1-20. http://www.imfm.si/preprinti/PDF/01183.pdf. [COBISS.SI-

ID 16517977]

3. JAKOVAC, Marko, PETERIN, Iztok. On the b-chromatic number of some graph products. Stud.

sci. math. Hung. (Print), 2012, vol. 49, no. 2, str. 156-

169. http://dx.doi.org/10.1556/SScMath.49.2012.2.1194. [COBISS.SI-ID 16321113]

4. CABELLO, Sergio, JAKOVAC, Marko. On the b-chromatic number of regular graphs. Discrete

appl. math.. [Print ed.], 2011, vol. 159, iss. 13, str. 1303-

1310. http://dx.doi.org/10.1016/j.dam.2011.04.028, doi:10.1016/j.dam.2011.04.028. [COBISS.SI-

ID 15914329]

5. JAKOVAC, Marko, KLAVŽAR, Sandi. The b-chromatic number of cubic graphs. Graphs

comb., 2010, vol. 26, no. 1, str. 107-118. http://dx.doi.org/10.1007/s00373-010-0898-9.


http://dx.doi.org/10.1016/j.disc.2012.09.010



http://www.imfm.si/preprinti/PDF/01183.pdf


http://dx.doi.org/10.1556/SScMath.49.2012.2.1194


http://dx.doi.org/10.1016/j.dam.2011.04.028



http://dx.doi.org/10.1007/s00373-010-0898-9



Predmet: Izbrana poglavja iz topologije

Course title: Selected topics from Topology



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30

135 7

Nosilec predmeta / Lecturer: Iztok BANIČ

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Poznavanje splošne topologije. Knowledge of general topology.


Vsebina predmeta se prilagaja aktualnim

potrebam in razvoju.

1. Poglavja iz splošne topologije:

- Evklidski prostor. Evklidska topologija.

- Uryshnonova lema. Tietzejev

razširitveni izrek.

- Mnogoterost. Notranja točka. Robna

točka. Notranjost. Rob mnogoterosti.

Sklenjena mnogoterost.

- Kompaktne mnogoterosti. Povezane

The contents of this subject is adjusted to the

current needs and development.

1. Topics from general topology:

- Euclidean space. Euclidean topology.

- Urysohn lemma. Tietze extension

theorem.

- Manifold. Internal point. Boundary

point. Interior. Boundary of a manifold.

Closed manifold.

- Compact manifold. Connected manifold.

mnogoterosti.

- Osnovne lastnosti mnogoterosti.

Konstrukcije.

- Klasifikacija sklenjenih 2-mnogoterosti.

2. Poglavja iz teorije kontinuumov

- Kontinuumi. Zgledi kontinuumov.

Vgnezdeni preseki. Verige.

- Osnovne lastnosti.

- Kompozanti.

- Posebni primeri kontinuumov.

Knasterjev kontinuum, psevdolok,

pahljače, grafi.

- Hiperprostori. Konvergenca množic.

- Inverzna zaporedja. Inverzne limite.

- Basic properties of manifolds.

Constructons.

- Classification of closed 2-manifolds.

2. Topics from continuum theory

- Continua. Examples of continua. Nested

intersections. Chains.

- Basic properties

- Composants.

- Special examples. Knaster continuum,

pseudoarc, fans, graphs.

- Hyperspaces. Convergence of sets.

- Inverse sequences. Inverse limits.


J.R.Munkres: Topology: a first course,Englewood Cliffs, NJ, Prentice-Hall, 1975

E.H.Spanier: Algebraic topology, New York (etc.), McGraw-Hill, 1966

S.Lipschutz: Schaum's outline of theory and problems of general topology, New York (etc.),

McGraw-Hill,

1965

P.Pavešić, A.Vavpetič: Rešene naloge iz topologije, Ljubljana, Društvo matematikov, fizikov in

astronomov

Slovenije, 1997

M.Cencelj, D.Repovš: Topologija, Ljubljana, Pedagoška fakulteta, 2001

J. Mrčun: Topologija. Izbrana poglavja iz matematike in računalništva 44, Društvo matematikov,

fizikov in astronomov - založništvo, Ljubljana, 2008

S .B. Nadler: Continuum theory: an introduction, Marcel Dekker, New York, 1992

A. Illanes, S. B. Nadler: Hyperspaces. Fundamentals and recent advances, Marcel Dekker, Inc.,

New York, 1999

J. Vrabec: Metrični prostori. Ljubljana: DMFA, 1993.



Temeljito spoznati klasične izreke evklidskih

prostorov.

Temeljito spoznati topološke mnogoterosti,

njihove lastnosti in konstrukcije.

To know thoroughly classical theorems of

Euclidean spaces.

To know thoroughly topological manifolds, their

properties and constructions.

Temeljito spoznati kontinuume in njihove

lastnosti.

Temeljito spoznati inverzna zaporedja in

inverzne limite kontinuumov.

To know thoroughly about continua and their

properties.

To know thoroughly about inverse sequences

and inverse limits of continua.




Študent razume in zna uporabiti klasične izreke

evklidskih prostorov.

Študent obvlada osnovne koncepte topoloških

mnogoterosti. Zaveda se pomena odprtih

množic v mnogoterosti in njihovih lastnosti.

Razumevanje in uporaba osnovnih lastnosti

kontinuumov.

Razumevanje in uporaba konstrukcijskih metod

za konstrukcijo novih primerov kontinuumov.


Prenos znanja obravnavanih metod na

druga področja, predvsem na področja

analize, kompleksne analize, teorije grafov,

geometrije in topologije.


To understand basic concepts of classical

theorems of Euclidean spaces and know their

applications.

To understand basic concepts of topological

manifolds. To be aware of the importance of

open sets in manifolds and their properties.

Be able to understand and implement basic

properties of continua.

Be able to understand and implement

construction methods for constructions of new

examples of continua.


Knowledge transfer of treated methods into

other fields, to analysis, complex analysis,

graph theory, geometry and topology.



Predavanja

Seminarske vaje

Individualno delo

Lectures

Tutorial

Individual work


Assessment:


naloge, projekt)

Izpit:





50% 50%


project):

Exam:



Each of the mentioned assessments

must be assessed with a passing grade.

Opravljen pisni izpit – problemi je pogoj

za pristop k ustnemu izpitu – teorija.

Pisni izpit – problemi se lahko nadomesti z enim testom (sprotne obveznosti).

Passing grade of written exam –

problems is required to take the oral

exam – theory.

Written exam – problems can be repalced with one mid-term test.


references:

1. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš, SOVIČ, Tina.

Ważewski's universal dendrite as an inverse limit with one set-valued bonding function. Preprint

series, 2012, vol. 50, št. 1169, str. 1-33. http://www.imfm.si/preprinti/PDF/01169.pdf.


2. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Paths through

inverse limits. Topol. appl.. [Print ed.], 2011, vol. 158, iss. 9, str. 1099-1112.

http://dx.doi.org/10.1016/j.topol.2011.03.001. [COBISS.SI-ID 18474504]

3. BANIČ, Iztok, ŽEROVNIK, Janez. Wide diameter of Cartesian graph bundles. Discrete math..

[Print ed.], str. 1697-1701. http://dx.doi.org/10.1016/j.disc.2009.11.024, doi:

10.1016/j.disc.2009.11.024. [COBISS.SI-ID 17543176]

tipologija 1.08 -> 1.01

4. BANIČ, Iztok, ČREPNJAK, Matevž, MERHAR, Matej, MILUTINOVIĆ, Uroš. Limits of



5. BANIČ, Iztok, ERVEŠ, Rija, ŽEROVNIK, Janez. Edge, vertex and mixed fault diameters. Adv.

appl. math., 2009, vol. 43, iss. 3, str. 231-238. http://dx.doi.org/10.1016/j.aam.2009.01.005, doi:

10.1016/j.aam.2009.01.005. [COBISS.SI-ID 13396502]



http://dx.doi.org/10.1016/j.topol.2011.03.001







http://dx.doi.org/10.1016/j.aam.2009.01.005




Predmet: Aktuarska matematika

Course title: Actuarial mathematics



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester

Matematika, 2. stopnja

1. ali 2. 2. ali 4.

Mathematics, 2nd

degree

1. or 2. 2. ali 4.



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

60

45

195 10


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


1. Matematične podlage

2.Verjetnostni modeli življenja

3.Kapitalska zavarovanja

4.Rekurzijske formule

5.Neto premije, komutacijske funkcije

6.Neto premijske rezerve

7.Tehnični dobiček

8.Stroški in bruto premije

9.Matematična bruto rezerva

10. Modeli izločanja

11. Zavarovanje na več življenj

12. Analiza portfelja

1. Mathematical basis

2. Probability models

3. General life insurance

4. Recursion formulae

5. Net premiums, commutational functions

6. Net premium reserves

7. Technical gain

8. Expense loadings

9. Premium reserves

10. Multiple decrements

11. Multiple life insurance

12. Portfolio analysis

13. Pozavarovanje

14. Specifična zavarovanja

13. Reinsurance

14. Specific insurances


1. Gerber H.U..1996. Matematika življenskih zavarovanj. DMFA Ljubljana, Zavarovalnica

Triglav.

2. Bowers N.L., Gerber H.U., Hickman J.C., Jones D.A., Nesbitt C.J:. 1986. Actuarial

Mathematics. Itasca, USA..

3. Gerber H.U..1996. Life Insurance Mathematics. Springer. Berlin, New York.



Namen predmeta je posredovati temeljna

teoretična in praktična znanja potrebna pri

kvantitativnem in kvalitativnem obravnavanju

nalog in procesov s področja aktuarske

matematike in zavarovalniškega poslovanja.

Prav tako je namen predmeta dati osnovo za

spremljanje sodobne literature in nadaljnje

strokovno izpopolnjevanje.

The objective is to provide fundamental

theoretical knowledge and practical skills

of actuarial mathematics and insurance

business.

The objective is also to enable the students

for additional learning and individual study of

new methods.



Poglobljeno znanje in razumevanje temeljnih

vsebin in orodij potrebnih za strokovno

korektno vodenje poslov s področja

aktuarskega dela.


Sposobnost samostojnega praktičnega in

teoretičnega dela. Zmožnost nadaljnega študija.


Fundamental theoretical knowledge and

practical skills of actuarial work.


Capabilitiy of understanding and application of

knowledge in praxis. Ability of additional

learning and individual study of new methods.



Predavanja, tehnične demonstracije,

aktivne vaje, seminarske vaje

Lectures, technical demonstration,

active work, tutorial


Assessment:


Seminarska naloga

Izpit:


Pisni izpit – teorija

Delež (v %) /

Weight (in %)

20%

40%

40%

Mid-term testing:

Seminary work

Exams:


Written exam – theory




za pristop k pisnemu izpitu – problemi.


pogoj za pristop k pisnemu izpitu –

teorija.

Pisni izpit – problemi se lahko

nadomesti z dvema delnima testoma

(sprotne obveznosti).




are required for taking the written exam –

problems. Passing grade of written exam

– problems is required to take the written

exam – theory.

Written exam – problems can be replaced

with two mid-term tests.


references:

1. JAKOVAC, Marko. The k-path vertex cover of rooted product graphs. Discrete applied

mathematics, ISSN 0166-218X. [Print ed.], 2015, vol. 187, str. 111-119, doi:

10.1016/j.dam.2015.02.018. [COBISS.SI-ID 21355272]

2. JAKOVAC, Marko. A 2-parametric generalization of Sierpiński gasket graphs. Ars

combinatoria, ISSN 0381-7032, 2014, vol. 116, str. 395-405. [COBISS.SI-ID 17053529]

3. YERO, Ismael G., JAKOVAC, Marko, KUZIAK, Dorota, TARANENKO, Andrej. The partition

dimension of strong product graphs and Cartesian product graphs. Discrete Mathematics, ISSN

0012-365X. [Print ed.], 2014, vol. 331, str. 43-52. http://dx.doi.org/10.1016/j.disc.2014.04.026.


4. BREŠAR, Boštjan, JAKOVAC, Marko, KATRENIČ, Ján, SEMANIŠIN, Gabriel,

TARANENKO, Andrej. On the vertex k-path cover. Discrete applied mathematics, ISSN 0166-

218X. [Print ed.], 2013, vol. 161, iss. 13/14, str. 1943-1949.

http://dx.doi.org/10.1016/j.dam.2013.02.024. [COBISS.SI-ID 19859464]


products. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2013, vol. 313, iss. 1, str. 94-100.

http://dx.doi.org/10.1016/j.disc.2012.09.010, doi: 10.1016/j.disc.2012.09.010. [COBISS.SI-ID

19464968]












Predmet: Numerična analiza

Course title: Numerical Analysis



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


1. ali 2. 2. ali 4.

Mathematics, 2nd

degree

1. or 2. 2. ali 4.



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

60

30 15 195 10

Nosilec predmeta / Lecturer: Valerij ROMANOVSKIJ

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Poznavanje matematične analize. Knowledge of mathematical analysis.


1. Analize numeričnega računanja.

2. Reševanje nelinearnih enačb: Reševanje

sistemov nelinearnih enačb.

3. Diferenčne operatorji in diferenčne enačbe.

4. Sistemi linearnih enačb. Iterativne metode.

5. Problem lastnih vrednosti: Schurov in

Gershgorinov izrek. Simetrični in

nesimetrični problem lastnih vrednosti.

6. Navadne diferencialne enačbe: Lastnosti

rešitev in stabilnost rešitev. Picardova

1. Analysis of numerical computing.

2. Nonlinear equations solving: Systems of

nonlinear equations.

3. Difference equations and difference

operators.

4. Systems of linear equations. Iterative

methods.

5. Eigenvalues computation problem: Schur's

and Gershgorin's theorems. Symmetric and

non-symmetric eigenvalue problem.

metoda. Metode Runge-Kutta. Večkoračne

metode. Robni problem. Sistemi

diferencialnih enačb.

7. Numerično odvajanje:Richardsonova

ekstrapolacija.

8. Polinomske sistemi: Groebnerjeva baza.

Raznoterost polinomskega ideala in njene

lastnosti. Razcep raznoterosti.

9. Parcialne diferencialne enačbe.

6. Ordinary differential equations: Properties

of solutions and stability of solutions.

Runge-Kutta methods. Multi-step methods.

Boundary-value problems. Systems of

differential equations.

7. Numeric derivation: Richardson's

extrapolation.

8. Polynomial systems: Groebner basis, Variety

of polynomial ideal and its properties.

Decomposition of varieties. Modular

methods.

9. Partial differential equations.


Z. Bohte, Numerično reševanje nelinearnih enačb, DMFA Slovenije, Ljubljana, 1993.

Z. Bohte, Numerično reševanje sistemov linearnih enačb, DMFA Slovenije, Ljubljana, 1994.

D. Kincaid, W. Cheney: Numerical Analysis, Brooks/Cole, Pacific Grove, 1996.

E. Zakrajšek, Uvod v numerične metode, druga izdaja, DMFA Slovenije, Ljubljana, 2000.

V. G. Romanovski and Douglas S. Shafer, The Center and Cyclicity Problems. A Computational

Algebra Approach, Boston-Basel-Berlin: Birkhauser, 2009.

G. Teschl, Ordinary Differential Equations and Dynamical Systems. Providence: American

Mathematical Society, 2012.



Poglobiti znanje iz zahtevnejših konceptov in

rezultatov s področja numerične analize –

simbolnega računanja in numeričnih metod.

To deepen the knowledge of more demanding

concepts and results from numerical analysis –

symbolic mathematics and numerical methods.




Poglobiti znanje iz zahtevnejših

numeričnih metode in njihovih

uporabnih vrednosti.

Prepoznati praktične probleme in

njihovo modeliranje z orodji numerične

matematike.


Prenos znanja numeričnih metod na

druga področja (računalništvo,

statistika, optimizacija, ...)


To deepen the knowledge of more

demanding numerical methods and their

applications.

To recognize practical problems and

their modeling with numerical

mathematics tools.


Knowledge transfer of numerical

methods into other fields (computer

science, statistics, optimization, …)



Predavanja Lectures

Seminarske vaje

Izdelava seminarske naloge

Tutorial

Seminar (project) work


Assessment:


naloge, projekt)

Opravljena seminarska naloga


Pisni izpit – teoretija

Pisni izpit - problemi se lahko


(sprotni obveznosti)

Pisni izpit - teorja se lahko nadomesti z

dvema delnima testoma (sprotni

obveznosti)



Delež (v %) /

Weight (in %)

10%

50%

40%


project):

Completed seminar (project)

work




by two parital tests (mid-term testing)

Written exam – theory can be replaced


Each of the mentioned commitments



references:

1. ROMANOVSKI, Valery, SHAFER, Douglas. The center and cyclicity problems : a

computational algebra approach. Basel: Birkhäuser, 2009. XV; 330 str. ISBN 978-0-8176-4726-1.


2. ROMANOVSKI, Valery, PREŠERN, Mateja. An approach to solving systems of polynomials

via modular arithmetics with applications. Journal of Computational and Applied Mathematics,

ISSN 0377-0427. [Print ed.], 2011, vol. 236, iss. 2, str. 196-208. doi: 10.1016/j.cam.2011.06.018.


3. PAUSCH, Marina, GROSSMANN, Florian, ECKHARDT, Bruno, ROMANOVSKI, Valery.

Groebner basis methods for stationary solutions of a low-dimensional model for a shear flow.

Journal of nonlinear science, ISSN 0938-8974. [Print ed.], 2014, vol. 24, iss. 5, str. 935-948, doi:

10.1007/s00332-014-9208-7. [COBISS.SI-ID 20920584]

4. MAHDI, Adam, ROMANOVSKI, Valery, SHAFER, Douglas. Stability and periodic

oscillations in the Moon-Rand systems. Nonlinear analysis: real world applications, ISSN 1468-

1218, 2013, vol. 14, iss. 1, str. 294-313. [COBISS.SI-ID 19482120]

5. BOULIER, F., HAN, M., LEMAIRE, F., ROMANOVSKI,V. Qualitative investigation of a gene

model using computer algebra algorithms. Programming and computer software, ISSN 0361-7688,

2015, vol. 41, no. 2, str. 105-111, doi: 10.1134/S0361768815020048. [COBISS.SI-ID 21355784]


http://dx.doi.org/10.1016/j.cam.2011.06.018


http://dx.doi.org/10.1007/s00332-014-9208-7



http://dx.doi.org/10.1134/S0361768815020048



Predmet: Teorija mere

Course title: Measure theory



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester

Matematika, 2. stopnja Modul F1 1. ali 2. 1. ali 3.

Mathematics, 2nd

degree Module F1 1. or 2. 1. or 3.



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

60

45

165 9

Nosilec predmeta / Lecturer: Valerij Romanovskij

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Osnovni pojmi teorije mere: Algebra, σ-

algebra, Borelova σ-algebra na Rn. Mere in

osnovne lastnosti mer. Merljivi prostori.

Pozitivne mere. Zunanje mere.

Lebesqueova mera na Rn.

Funkcije in integrali: Merljive funkcije.

Stopničaste funkcije. Integral stopničaste

funkcije. Integral merljive funkcije. Izrek o

monotoni konvergenci. Fatoujeva lema in

Lebesqueov izrek o dominantni

konvergenci. Povezanost Riemannovega in

Lebesqueovega integrala.

Basic concepts of measure theory: Algebra,

σ-algebra, Borel σ-algebra on Rn. Measure

and its basic properties. Measurable spaces.

Positive measures. Outer measures.

Lebesque measure on Rn.

Functions and integrals: Measurable

functions. Simple measurable functions. The

integral of a simple measurable function.

The integral of a measurable function. The

monotone convergence theorem. Fatou’s

lemma and Lebesque’s dominated

convergence theorem. Relationships between

Konvergenca: Zaporedja merljivih funkcij

in konvergenca. Konvergenca skoraj

povsod. Norma in normirani Lp-prostori.

Neenakosti (Hölder, Minkowski). Dualni

prostori.

Predznačne in kompleksne mere:

Predznačne mere in Hahnov razcepni izrek.

Kompleksne mere in Radon-Nikodymov

izrek. Funkcije z omejeno varianco.

Produktne mere: Merjenje in integriranje po

produktnih prostorih (Fubinijev izrek).

Odvajanje: Odvodi mer. Odvodi funkcij.

Rieszov izrek o reprezentaciji pozitivnih

linearnih funkcionalov na C(X).

Lebesgue-Stieltjesov integral.

Riemann’s and Lebesque’s integral.

Convergence: Sequences of measurable

functions and convergence. Convergence

almost everywhere. Norm and normed Lp-

spaces. Inequalities (Hölder, Minkowski).

Dual spaces.

Signed and complex measures: Signed

measures and the Hahn decomposition

theorem. Complex measures and the Radon-

Nikodym theorem. Functions of bounded

variation.

Product measures: Measures and integrals on

product spaces (Fubini’s theorem).

Differentiation: Differentiation of measures.

Differentiation of functions.

The Riesz representation theorem on

positive linear functionals on C(X).

Lebesgue-Stieltjes integral


1. M. Capinski, E. Kopp: Measure, integral and probability, Springer-Verlag London, 2004.

2. D. L. Cohn: Measure theory, Birkhäuser, 1994.

3. R. Drnovšek: Rešene naloge iz teorije mere, DMFA, 2001.

4. M. Hladnik: Naloge in primeri iz funkcionalne analize in teorije mere, DMFA, 1985.

5. W. Rudin: Real and complex analysis, 3th edition, Mc-Graw-Hill, 1986.

6. H. Sohrab, Basic real analysis, Birkhauser Boston, 2003.

7. I. Vidav, Višja matematika II, DZS, Ljubljana, 1975.



Glavni cilj predmeta je proučiti temeljne

koncepte in rezultate teorije mere. The main goal of the course is to study the

fundamental concepts and results of measure

theory.




merljivi prostori, merljive funkcije,

abstraktno integriranje, izreki o

konvergenci, Lp-prostori, produktne mere,

odvodi mer.


Poznavanje osnov teorije mere je

podlaga za študij različnih matematičnih

področij (funkcionalne analize,

verjetnosti, parcialnih diferencialnih

enačb itd.).


Measurable spaces, measurable functions,

abstract integration, convergence theorems,

Lp-spaces, product measures, differentiation

of measures.


Knowing the fundamentals of measure

theory is a prerequisite for studying various

mathematical areas (functional analysis,

probability, partial differential equations

etc.).



Predavanja

Teoretične vaje

Lectures

Theoretical exercises


Assessment:


naloge, projekt)








obveznosti)



Delež (v %) /

Weight (in %)

50%

50%


project):










references:

1. CHEN, Xingwu, GINÉ, Jaume, ROMANOVSKI, Valery, SHAFER, Douglas. The 1: -q resonant

center problem for certain cubic Lotka-Volterra systems. Appl. math. comput.. [Print ed.], Aug.

2012, vol. 218, iss. 32, str. 11620-11633. http://dx.doi.org/10.1016/j.amc.2012.05.045, doi:

10.1016/j.amc.2012.05.045. [COBISS.SI-ID 19321352]

2. BASOV, Vladimir V., ROMANOVSKI, Valery. Linearization of two-dimensional systems of

ODEs without conditions on small denominators. Appl. math. lett.. [Print ed.], 2012, vol. 25, iss. 2,

str. 99-103. http://dx.doi.org/10.1016/j.aml.2011.06.029, doi: 10.1016/j.aml.2011.06.029.


3. LEVANDOVSKYY, Viktor, PFISTER, Gerhard, ROMANOVSKI, Valery. Evaluating cyclicity

of cubic systems with algorithms of computational algebra. Commun. pure appl. anal., 2012, vol.

11, no. 5, str. 2023-2035, doi: 10.3934/cpaa.2012.11.2023. [COBISS.SI-ID 19075080]

4. WENTAO, Huang, CHEN, Xingwu, ROMANOVSKI, Valery. Linear centers with perturbations

of degree 2d + 5. Int. j. bifurc. chaos appl. sci. eng., 2012, vol. 22, no. 1, str. [1250007-1 -

1250007-12]. http://www.ejournals.wspc.com.sg/ijbc/22/2201/S0218127412500071.html, doi:

10.1142/S0218127412500071. [COBISS.SI-ID 69213185]

5. HAN, Maoan, ROMANOVSKI, Valery. Isochronicity and normal forms of polynomial systems

of ODEs. J. symb. comput., Oct. 2012, vol. 47, iss. 10, str. 1163-1174.

http://dx.doi.org/10.1016/j.jsc.2011.12.039, doi: 10.1016/j.jsc.2011.12.039. [COBISS.SI-ID

19324168]

http://dx.doi.org/10.1016/j.amc.2012.05.045



http://dx.doi.org/10.1016/j.aml.2011.06.029



http://dx.doi.org/10.3934/cpaa.2012.11.2023


http://www.ejournals.wspc.com.sg/ijbc/22/2201/S0218127412500071.html

http://dx.doi.org/10.1142/S0218127412500071


http://dx.doi.org/10.1016/j.jsc.2011.12.039




Predmet: Kompleksna analiza

Course title: Complex Analysis



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30

135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Poznavanje analize in kompleksnih števil. Knowledge of analysis and complex numbers.


Funkcije kompleksne spremenljivke.

Elementarne funkcije v kompleksnem: linearne

funkcije, ulomljene linearne funkcije. Potenčne

vrste v kompleksnem. Elementarne funkcije,

definirane s potenčnimi vrstami. Logaritem in

ciklometrične funkcije.

Holomorfne funkcije. Cauchy – Riemannov

izrek. Konformnost holomorfnih funkcij.

Integral funkcije kompleksne spremenljivke.

Cauchyjev izrek in Cauchyjeve formule.

Functions of complex variable. Elementary

functions: linear function, Möbius functions.

Power series. Elementary functions defined by

power series. Logarithm and cyclometric

functions.

Holomorphic functions. Cauchy – Riemann

theorem. Conformality of holomorphic

mappings.

Complex line integrals. Cauchy integral theorem

and Cauchy formula. Liouville theorem. Power

Liouvilleov izrek. Taylorjeva vrsta.

Laurentova vrsta. Klasifikacija izoliranih

singularnih točk. Mali Piccardov izrek. Izrek o

residuih. Uporaba pri računanju realnih

integralov.

Laplaceova in Fourierova transformacija.

Uporaba.

series representation.

Laurent series. Classification of isolated

singularity. Behaviour of holomorphic function

near isolated singularity. Little Piccard

Theorem. Residui theorem. Applications to the

calculations of definite integrals and sums.

Laplace and Fourier transforms. Applications.


S. G. Krantz: Handbook of Complex Variables, Birkhäuser, Boston, 1999.

J.B.Conway: Functions of One Complex Variable I, 2nd edition, Springer, New York, 1995.

L. Ahlfors: Complex Analysis, 3rd edition, McGraw-Hill, New york, 1979.



Študent poglobi znanje iz osnov teorije funkcij

kompleksne spremenljivke ter poglobi znanje

iz uporabnih aspektov te teorije, predvsem v

povezavi s preslikovanji območij, pri računanju

določenih integralov, seštevanju vrst ter

reševanju diferencialnih enačb.

Deepening the knowledge of concepts from the

theory of functions of one complex variable. To

deepen the knowledge of possible applications

of this theory, specialy in connection with

transformations of the regions, calculating

definite integrals and sums and solving





Študent razume pojem holomorfne funkcije

pozna osnovne s tem povezane rezultate,

posebej tiste, ki se nanašajo na integracijo

in na integralsko reprezentacijo ter

reprezentacijo s potenčno vrsto.

Študent razume koncept preslikovanja

območij z uporabo ulomljenih linearnih in

drugih preprostejših elementarnih funkcij v

kompleksnem.

Študent razume pojem izolirane singularne

funkcije in pozna uporabno vrednost izreka

o residuumih.

Študent razume koncepta Laplaceove in

Fourierove transformacije in pozna njune

možnosti uporabe.


Ilustracija dejstva, da nam teorija, navidez

oddaljene od realnosti, lahko ponudi mnoge

praktično uporabne rezultate.

Dojemanje transformacij kot opcije za

pretvorbo matematične situacije v drugo


To understand the concept of holomorphic

function and to know the basic results,

specialy those about line integrals and about

the integral and the power series

representation of holomorphic functions.

To understend the concept of transforming

plane regions using Möbius transformations

and other basic elementary functions.

To understand the concept of isolated

singularity and to be aware of the

importance of the residui theorem.

To understand the concepts of Laplace and

Fourier tranformations and to be aware of

their possible applications.


An illustration of the fact, that a more

abstract theory can give us many nice results

with useful practical applications.

Understanding the concept of

transformations as tools to convert a certain

situacijo, ki je udobnejša za obravnavo. mathematical situation into a more

convenient one.



Predavanja

Seminarske vaje

Lectures

Tutorial


Assessment:

Izpit:







teorija.




Delež (v %) /

Weight (in %)

50%

50%

Exams:







exam – theory.




references:


TARANENKO, Andrej. On the vertex k-path cover. Discrete Applied Mathematics, ISSN 0166-






19464968]

3. JAKOVAC, Marko, PETERIN, Iztok. On the b-chromatic number of some graph products.

Studia scientiarum mathematicarum Hungarica, ISSN 0081-6906, 2012, vol. 49, no. 2, str. 156-










Applied Mathematics, ISSN 0166-218X. [Print ed.], 2011, vol. 159, iss. 13, str. 1303-1310.

http://dx.doi.org/10.1016/j.dam.2011.04.028, doi: 10.1016/j.dam.2011.04.028. [COBISS.SI-ID

15914329]

5. JAKOVAC, Marko, KLAVŽAR, Sandi. The b-chromatic number of cubic graphs. Graphs and

combinatorics, ISSN 0911-0119, 2010, vol. 26, no. 1, str. 107-118.

http://dx.doi.org/10.1007/s00373-010-0898-9. [COBISS.SI-ID 15522905]




http://dx.doi.org/10.1007/s00373-010-0898-9



Predmet: Algebrska topologija

Course title: Algebraic Topology



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 30 135 7

Nosilec predmeta / Lecturer: Uroš MILUTINOVIĆ

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Poznavanje algeberskih struktur in topologije. Knowledge of algebraic structures and

topology..


Kategorije in funktorji. Izomorfizmi.

Homotopija, homotopska kategorija topoloških

prostorov.

Funktor fundamentalne grupe. Krovni prostori.

Primeri uporabe.

Simplicialni kompleksi in poliedri. Funktor

simplicialne homologije. Eulerjeva

karakteristika, Bettijeva števila. Osnove

homološke algebre. Druge homološke teorije.

Categories and functors. Isomorphisms.

Homotopy, homotopy theory of topological

spaces.

The fundamental group functor. Covering

spaces. Examples.

Simplical complexes and polyhedra. The

simplical homology functor. Euler characteristic,

Betti numbers. Fundamentals of homological

algebra. Other homology theories.




M.Cencelj: Simplicialni kompleksi in simplicialna homologija, Ljubljana, Pedagoška fakulteta,

1996



Obvladati osnovne tehnike dela s funktorji

algebrske topologije. Students learn how to use the basic techniques

of work with algebraic topology functors.




Uporaba kategorij in funktorjev.

Sposobnost uporabe osnovnih tehnik

dela s konkretnimi funktorji algebrske

topologije.


Algebrska topologija je področje, ki

povezuje algebro in topologijo. Je

močan aparat, ki se ga da uporabiti pri

reševanju zelo različnih problemov.


The use of categories and functors.

Be able to use the basic techniques of

work with specific algebraic topology

functors.


Algebraic topology connects algebra and

topology. It is a powerful apparatus that

can be used in solving of many different

problems



Predavanja

Seminarske vaje

Lectures

Tutorial

Načini ocenjevanja: Assessment:


naloge, projekt)

Izpit:





Pozitivna ocena pri pisnem izpitu -

problemi je pogoj za pristop k ustnemu

izpitu – teorija.


nadomesti z dvema delnima testoma (ki

sta sprotni obveznosti).

Delež (v %) /

Weight (in %)

50%

50%


project):

Exams:





Passing grade of the written exam –

problems is required for taking the oral

exam – theory.


by two mid-term tests.


references:



series, 2012, vol. 50, št. 1169, str. 1-33. http://www.imfm.si/preprinti/PDF/01169.pdf. [COBISS.SI-

ID 16194137]







4. KLAVŽAR, Sandi, MILUTINOVIĆ, Uroš, PETR, Ciril. Stern polynomials. Adv. appl. math.,

2007, vol. 39, iss. 1, str. 86-95. http://dx.doi.org/10.1016/j.aam.2006.01.003. [COBISS.SI-ID

14276441]

5. IVANŠIĆ, Ivan, MILUTINOVIĆ, Uroš. Closed embeddings into Lipscomb's universal space.

Glas. mat., 2007, vol. 42, no. 1, str. 95-108. [COBISS.SI-ID 14338393]











Predmet: Analitični pristopi v geometriji

Course title: Analytical approaches in geometry



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


1. ali 2. 1. ali 3.

Mathematics, 2nd

degree

1. or 2. 1. or 3.



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30

135 7

Nosilec predmeta / Lecturer: Bojan HVALA

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Analitična geometrija v kartezičnih

koordinatah. Premice, stožnice. Uporaba v

konkretnih primerih v geometriji. Eulerjeve

stožnice.

Analitična geometrija v trilinearnih

koordinatah. Premice, stožnice. Projektivna

ravnina. Uporaba v konkretnih primerih v

geometriji. Eulerjeva premica, Kiepertova

hiperbola. Kubične krivulje trikotnika.

Kompleksna števila v geometriji. Potrebni

in zadostni pogoji za podobnost trikotnikov

z danimi oglišči. Pogoji za to, da so tri

Analytic geometry in Cartesian coordinates.

Lines, conics. Examples of use in geometry.

Euler's conics.

Analytical geometry in trilinear coordinates.

Lines, conics. Projective plane. Examples of

use in geometry. Euler line, Kieper

hyperbola. Cubics associated with a triangle.

Complex numbers in geometry. Necessary

and sufficient conditions for similarity of

triangles with given vertices. Conditions that

three given points are the vertices of an

equilateral triangle. Napoleon and

točke oglišča enakostraničnega trikotnika.

Napoleonov, Thebaultov izrek, Napoleon –

Barlottijev izrek. Kolinearnost in

koncikličnost. Ptolomejev izrek. Cliffordovi

izreki.

Thebaultov theorem. Napoleon – Barlotti

theorem. Colinearity and concyclity.

Ptolemey theorem. Clifford theorems.


B. Spain: Analytical conics, Dover Publications, Mineola, New York, 2007.

O. Botema, R. Erne, R. Hartshorne: Topics in elementary geometry, Springer, New York, 2008

Liang-shin Hahn: Complex numbers & geometry, MAA, Washington, 1994



Cilj predmeta je na konkretnih primerih

ravninske geometrije ponoviti in utrditi

analitično geometrijo v kartezičnih

koordinatah.

Predstavitev alternativnih trilinearnih koordinat

ima dvojen namen:

predstaviti sredstvo, ki je včasih bistveno

udobnejše, včasih pa celo zapletenejše od

znanih sredstev;

prestaviti teorijo, ki bo za študente podobno

nova, kot bo klasična analitična geometrija

nova za njihove bodoče dijake.

Cilj zaključnega poglavja je seznaniti študente

s kompleksnimi števili kot močnim orodjem v

ravninski geometriji.

The aim of this course is (through the work on

concrete cases of planar geometry) to

repeat and consolidate the students knowledge

on analytic geometry in Cartesian coordinates.

We introduce an alternative trilinear coordinates

in order to present a new mean, sometimes

substantially more comfortable and sometimes

even more complex than the known ones. This

chapter also brings a completely new method for

work with circles and lines to the future

teachers, which will make them understand

better the situation of their future students being

for the first time acquainted with the usual

methods.

The objective of this course is also to acquaint

students with complex numbers as a powerful

tool in the planar geometry.




Po zaključku tega predmeta bo študent utrdil

znanje klasične analitične geometrije in

pridobil občutek za prednosti alternativnih

metod, kot sta uporaba trilinearnih koordinat in

kompleksnih števil v ravninski geometriji.


Zavest o dejstvu, da investicija v izgradnjo

močnejšega matematičnega orodja prinaša

prednosti v fazi uporabe.


On completion of this course the student will

consolidate his knowledge on classical analitic

geometry and get an insight in the advantages of

the use of trilinear coordinates and complex

numbers in the plane geometry.


Awareness of the fact that investment in

building a more powerful mathematical tools

brings advantages during the application.



Predavanja Lectures

Teoretične vaje

Individualno delo

Theoretical excersises

Individual work


Assessment:

Izpit:


Ustni izpit




pogoj za pristop k ustnemu izpitu.

Delež (v %) /

Weight (in %)

50%

50%

Exams:


Oral exam





exam.


references:

1. HVALA, Bojan. Diophantine Steiner triples. Math. Gaz., March 2011, vol. 95, no. 532, str. 31-

39. [COBISS.SI-ID 18256648]

2. HVALA, Bojan. Diophantine Steiner triples and Pythagorean-type triangles. Forum geom.,

2010, vol. 10, str. 93-97. http://forumgeom.fau.edu/FG2010volume10/FG201010.pdf. [COBISS.SI-

ID 15669337]

3. HVALA, Bojan. Modernizing mathematics education in Slovenia : a teacher friendly approach.

V: LAMANAUSKAS, Vincentas (ur.). Challenges of science, mathematics and technology teacher

education in Slovenia, (Problems of education in the 21st century, vol. 14). Siauliai: Scientific

Methodological Center Scientia Educologica, 2009, str. 34-43. [COBISS.SI-ID 17351944]

4. HVALA, Bojan. Generalized Lie derivations in prime rings. Taiwan. j. math., dec. 2007, vol. 11,

iss. 5, str. 1425-1430. [COBISS.SI-ID 15969288]

5. BREŠAR, Matej, HVALA, Bojan. On additive maps of prime rings. II. Publ. math. (Debr.),

1999, letn. 54, št. 1/2, str. 39-54. [COBISS.SI-ID 8598617]


http://forumgeom.fau.edu/FG2010volume10/FG201010.pdf






Predmet: Osnove teorije mere

Course title: Basic measure theory



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30

135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:






Lebesgueova mera na Rn.





Lebesgueov izrek o dominantni


Lebesgueovega integrala.





Lebesgue measure on Rn.






lemma and Lebesgue’s dominated






prostori.






Riemann’s and Lebesgue’s integral.





Dual spaces.





variation.















theory.







odvodi mer.


Poznavanje osnov teorije mere je podlaga za

študij različnih matematičnih področij

(funkcionalne analize, verjetnosti, parcialnih

diferencialnih enačb itd.).





of measures.


Knowing the fundamentals of measure theory is

a prerequisite for studying various mathematical

areas (functional analysis, probability, partial

differential equations etc.).



Predavanja

Teoretične vaje

Lectures



Assessment:

Način (pisni izpit, ustno izpraševanje, Delež (v %) / Type (examination, oral, coursework,

naloge, projekt)








obveznosti)



Weight (in %)

50%

50%

project):










references:




10.1016/j.amc.2012.05.045. [COBISS.SI-ID 19321352]











10.1142/S0218127412500071. [COBISS.SI-ID 69213185]




19324168]










http://dx.doi.org/10.1142/S0218127412500071










Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30

135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

















functions.



mappings.







integralov.


Uporaba.






































kompleksnem.



o residuumih.



možnosti uporabe.





























convenient one.



Predavanja

Seminarske vaje

Lectures

Tutorial


Assessment:

Izpit:







teorija.




Delež (v %) /

Weight (in %)

50%

50%

Exams:







exam – theory.




references:








19464968]














15914329]







http://dx.doi.org/10.1007/s00373-010-0898-9



Predmet: Teorija grup

Course title: Group Theory



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 30 135 7


Jeziki /

Languages:

Predavanja / Lectures: SLOVENSKO/SLOVENE


Pogoji za vključitev v delo oz. za

opravljanje študijskih obveznosti:

Prerequisits:

Ne. None.


Simetrične grupe. Konjugirani elementi in

podgrupe. Delovanje grupe na množico.

Linearne grupe: osnovne lastnosti in primeri.

Izreki Sylowa. Podajanje grupe z generatorji

in relacijami. Direktni produkt grup. Abelove

grupe.

Enostavne grupe. Komutant grupe, rešljivost

končnih p-grup in grupe zgornje trikotnih

matrik.

Upodobitve grup: osnovni pojmi in primeri.

Symetric groups. Conjugated elements and

subgroups. The action of a group on a set. Linear

groups: main properties and examples.

Sylow's theorems. Definition of a group by

generators and relations. Direct product of groups.

Abelian groups.

Simple groups. Derived group, solvability of finite

p-groups and the group of upper triangular

matrices.

Representations of groups: concepts and examples.


W. Y. Gilbert, W. K. Nicholson, Modern Algebra with Applications, Wiley, Chichester 2004

S. Lang, Undergraduate Algebra, Springer, 2005

J. F. Humphreys, A Course in Group Theory, Oxford University Press, 1997

I. Vidav, Algebra, DMFA, Ljubljana 1980



Študentje poglobijo znanje osnove teorije grup

in njihovih upodobitev. Students deepen the knowledge of the concepts

of the theory of groups and their representations.




Razumevanje osnov teorije grup in

njihovih upodobitev.

Poznavanje osnovnih značilnosti in

tipičnih primerov grup.


Pridobljena znanja prispevajo k

razumevanju ostalih predmetov s

področja algebre, geometrije in

topologije.


To understand the main concepts of

groups and their representations.

To recognize the typical properties and

main examples of groups.


The obtained knowledge contributes to

better understanding of other subjects in

fields of algebra, geometry and topology.



Predavanja

Seminarske vaje

Lectures

Tutorial


Assessment:


naloge, projekt)

Pisni izpit – praktični del


Pisni izpit – praktični del se lahko


(sprotni obveznosti).

Delež (v %) /

Weight (in %)

50%

50%


project):



Written exam – practical part can be

replaced by two partial tests (mid-term

testing).


references:















10.1007/s10474-009-8144-8. [COBISS.SI-ID 15212121]



1, str. 65-76. [COBISS.SI-ID 14037081]

http://dx.doi.org/10.1007/s11083-010-9140-x


http://dx.doi.org/10.1007/s10474-009-8144-8

http://dx.doi.org/10.1007/s10474-009-8144-8




Predmet: Zgodovina matematike

Course title: History of Mathematics



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

75

135 7

Nosilec predmeta / Lecturer: Daniel EREMITA

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Metodologija zgodovine matematike,

zgodovinski viri.

Glavni centri in obdobja razvoja matematike:

mezopotamska matematika, egipčanska

matematika, starogrška in helenistična

matematika, kitajska matematika, indijska

matematika, japonska matematika, matematika

indijanskih civilizacij, arabska matematika,

matematika renesanse, matematika XV., XVI.,

Methodology of the history of mathematics,

historical sources.

The main centers and periods of mathematical

development: Mesopotamian mathematics,

Egyptian mathematics, Ancient Greek and

Hellenistic mathematics, Chinese mathematics,

Hindu mathematics, Japanese mathematics,

mathematics of indigenous cultures of the

Americas, Arabic mathematics, Renaissance

mathematics, mathematics of XV., XVI., XVII.,

XVII., XVIII., XIX. in XX. stoletja.

Razvoj glavnih področij matematike:

geometrije, aritmetike, algebre, teorije števil,

analize, matematične logike, teorije množic,

topologije, teorije grafov, teorije verjetnosti,

statistike, računalništva, metodike matematike,

zgodovine matematike idr. Razvoj osnovnih

matematičnih pojmov.

Pomembni matematiki in njihov prispevek k

razvoju matematike. Slovenski matematiki.

Zgodovina matematike kot del splošne

zgodovine. Filozofski, sociološki, psihološki,

lingvistični in podobni aspekti matematike.

Matematika in druge znanosti.

XVIII., XIX. and XX. centuries.

The development of the major areas of

mathematics: geometry, arithmetic, algebra,

number theory, analysis, mathematical logic, set

theory, topology, graph theory, probability

theory, statistics, computer science,

methodology of mathematics, history of

mathematics, etc. The development of the

fundamental mathematical notions.

Important mathematicians and their contribution

to mathematics. Slovenian mathematicians.

A history of mathematics as a part of a general

history. Philosophical, sociological,

psychological, linguistic and similar aspects of

mathematics. Mathematics and other sciences.


A History of Mathematics. New York: J. Wiley & Sons, 1989.

A History of Mathematics, An Introduction. Reading (Mass.) [etc.] : Addison-

Wesley, 1998

A History of Mathematicad Notation. New York: Dover Publications, Inc., 1993.

Geometry and Algebra in Ancient Civilizations. Berlin: Springer Verlag,

1983.

Kratka zgodovina matematike. Ljubljana: Državna založba Slovenije, 1978.



Spoznati zgodovinski razvoj matematike,

razvoj njenih osnovnih področij in razvoj

osnovnih matematičnih pojmov. Seznaniti se s

pomembnimi matematiki in njihovimi

prispevki k razvoju matematike.

To obtain knowledge of the historical

development of mathematics, the development

of its major areas, and the development of the

fundamental mathematical notions. To get

acquainted with the important mathematicians

and their contribution to mathematics.




zgodovinski razvoj matematike, razvoj

njenih osnovnih področij in razvoj osnovnih

matematičnih pojmov

pomembni matematiki in njihovi prispevki

k razvoju matematike



historical development of mathematics,

the development of its major areas, and

the development of the fundamental

mathematical notions

important mathematicians and their

contribution to mathematics

prenos znanja zgodovine matematike na vse

matematične predmete in na nekatera druga

področja (fizika, astronomija, mehanika,

računalništvo, filozofija, zgodovina, …).


knowledge transfer of history of

mathematics to all mathematical courses and

also to other areas (physics, astronomy,

mechanics, computer science, philosophy,

history, …).



Predavanja

Individualno delo

Lectures

Individual work


Assessment:

Seminarska naloga

Ustni izpit



Opravljena seminarska naloga je pogoj

za pristop k izpitu.

Delež (v %) /

Weight (in %)

20%

80%

Seminar assignment

Oral exam



Passing grade of the seminar assignment

is required to take the exam.


references:

1. EREMITA, Daniel. Functional identities of degree 2 in triangular rings revisited. Linear and Multilinear Algebra, ISSN 0308-1087, 2015, vol. 63, iss. 3, str. 534-553. http://dx.doi.org/10.1080/03081087.2013.877012. [COBISS.SI-ID 17044057] 2. EREMITA, Daniel, GOGIĆ, Ilja, ILIŠEVIĆ, Dijana. Generalized skew derivations implemented by elementary operators. Algebras and representation theory, ISSN 1386-923X, 2014, vol. 17, iss. 3, str. 983-996. http://dx.doi.org/10.1007/s10468-013-9429-8. [COBISS.SI-ID 17043545] 3. EREMITA, Daniel. Functional identities of degree 2 in triangular rings. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2013, vol. 438, iss 1, str. 584-597. http://dx.doi.org/10.1016/j.laa.2012.07.028. [COBISS.SI-ID 16528217] 4. EREMITA, Daniel, ILIŠEVIĆ, Dijana. On (anti-)multiplicative generalized derivations. Glasnik matematički. Serija 3, ISSN 0017-095X, 2012, vol. 47, no. 1, str. 105-118. http://dx.doi.org/10.3336/gm.47.1.08. [COBISS.SI-ID 16341849] 5. BENKOVIČ, Dominik, EREMITA, Daniel. Multiplicative Lie n-derivations of triangular rings. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2012, vol. 436, iss

http://dx.doi.org/10.1080/03081087.2013.877012


http://dx.doi.org/10.1007/s10468-013-9429-8


http://dx.doi.org/10.1016/j.laa.2012.07.028


http://dx.doi.org/10.3336/gm.47.1.08


11, str. 4223-4240. http://dx.doi.org/10.1016/j.laa.2012.01.022. [COBISS.SI-ID 16278361]

http://dx.doi.org/10.1016/j.laa.2012.01.022







Študijska smer

Study field

Letnik

Academic

year

Semester

Semester

Matematika, 2. stopnja Modul R1 1. ali 2. 1. ali 3.

Mathematics, 2nd

degree Module R1 1. or 2. 1. or 3.



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 30 135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


topology..




prostorov.


Primeri uporabe.







spaces.


spaces. Examples.


simplical homology functor. Euler

characteristic, Betti numbers. Fundamentals of

homological algebra. Other homology theories.





1996












topologije.










functors.





problems



Predavanja

Seminarske vaje

Lectures

Tutorial



naloge, projekt)

Izpit:







izpitu – teorija.




Delež (v %) /

Weight (in %)

50%

50%


project):

Exams:







exam – theory.




references:




ID 16194137]









14276441]

















Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 30 135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Ne. None.

Vsebina:




Linearne grupe: osnovne lastnosti in primeri.


in relacijami. Direktni produkt grup. Abelove

grupe.



matrik.







Abelian groups.


p-groups and the group of upper triangular

matrices.










in njihovih upodobitev. Students deepen the knowledge of the basic

concepts of the theory of groups and their

representations.












topologije.












Predavanja

Seminarske vaje

Lectures

Tutorial


Assessment:


naloge, projekt)




nadomesti z dvema delnima testoma (sprotni

obveznosti).

Delež (v %) /

Weight (in %)

50%

50%


project):




replaced by two partial tests (mid-

term testing).

Reference nosilca / Lecturer's references:














10.1007/s10474-009-8144-8. [COBISS.SI-ID 15212121]



1, str. 65-76. [COBISS.SI-ID 14037081]


http://dx.doi.org/10.1007/s11083-010-9140-x


http://dx.doi.org/10.1007/s10474-009-8144-8

http://dx.doi.org/10.1007/s10474-009-8144-8








Študijska smer

Study field

Letnik

Academic

year

Semester

Semester

Matematika, 2. stopnja Modul S1 1. ali 2. 1. ali 3.

Mathematics, 2nd

degree Module S1 1. or 2. 1. or 3.



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 30 135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


topology..




prostorov.


Primeri uporabe.







spaces.


spaces. Examples.


simplical homology functor. Euler characteristic,

Betti numbers. Fundamentals of homological

algebra. Other homology theories.





1996












topologije.










functors.





problems



Predavanja

Seminarske vaje

Lectures

Tutorial



naloge, projekt)

Izpit:







izpitu – teorija.




Delež (v %) /

Weight (in %)

50%

50%


project):

Exams:







exam – theory.




references:




ID 16194137]









14276441]













Predmet: Teorija mere

Course title: Measure theory



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

60

45

165 9


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:






Lebesqueova mera na Rn.





Lebesqueov izrek o dominantni


Lebesqueovega integrala.





Lebesque measure on Rn.






lemma and Lebesque’s dominated






prostori.





Produktne mere: Merjenje in integriranje po

produktnih prostorih (Fubinijev izrek).

Odvajanje: Odvodi mer. Odvodi funkcij.

Rieszov izrek o reprezentaciji pozitivnih

linearnih funkcionalov na C(X).


Riemann’s and Lebesque’s integral.





Dual spaces.





variation.

Product measures: Measures and integrals on

product spaces (Fubini’s theorem).

Differentiation: Differentiation of measures.

Differentiation of functions.

The Riesz representation theorem on

positive linear functionals on C(X).















theory.







odvodi mer.


Poznavanje osnov teorije mere je

podlaga za študij različnih matematičnih

področij (funkcionalne analize,

verjetnosti, parcialnih diferencialnih

enačb itd.).





of measures.


Knowing the fundamentals of measure

theory is a prerequisite for studying various

mathematical areas (functional analysis,

probability, partial differential equations

etc.).



Predavanja

Teoretične vaje

Lectures



Assessment:


naloge, projekt)








obveznosti)



Delež (v %) /

Weight (in %)

50%

50%


project):










references:




10.1016/j.amc.2012.05.045. [COBISS.SI-ID 19321352]











10.1142/S0218127412500071. [COBISS.SI-ID 69213185]




19324168]










http://dx.doi.org/10.1142/S0218127412500071










Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30

135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

















functions.



mappings.







integralov.


Uporaba.






































kompleksnem.



o residuumih.



možnosti uporabe.





























convenient one.



Predavanja

Seminarske vaje

Lectures

Tutorial


Assessment:

Izpit:







teorija.




Delež (v %) /

Weight (in %)

50%

50%

Exams:







exam – theory.




references:








19464968]














15914329]







http://dx.doi.org/10.1007/s00373-010-0898-9







Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 30 135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Ne. None.




Linearne grupe: glavne lastnosti in primeri.


in relacijami. Direktni produkt grup.

Abelove grupe.



matrik.







Abelian groups.


p-groups and the group of upper triangular matrices.










in njihovih upodobitev. Students deepen the knowledge of the basic

concepts of the theory of groups and their

representations.












topologije.












Predavanja

Seminarske vaje

Lectures

Tutorial


Assessment:


naloge, projekt)




nadomesti z dvema delnima testoma (sprotni

obveznosti).

Delež (v %) /

Weight (in %)

50%

50%


project):




replaced by two partial tests (mid-

term testing).















10.1007/s10474-009-8144-8. [COBISS.SI-ID 15212121]



1, str. 65-76. [COBISS.SI-ID 14037081]


http://dx.doi.org/10.1007/s11083-010-9140-x


http://dx.doi.org/10.1007/s10474-009-8144-8

http://dx.doi.org/10.1007/s10474-009-8144-8



Predme

Course

ŠtudijStudy

Ma

Mat

Vrsta pr

Univerz

PredavLectu

45

Nosilec

Jeziki / Languag

Pogoji zštudijsk

Jih ni.

Vsebina

FinančnČasovnaVrednotUvod v Strošek InvesticOcena dStrukturNavadnDolgoroFinancir

et:

title:

jski programy programm

atematika, 2

thematics, 2

redmeta / C

zitetna koda

vanja ures

SeSe

5

predmeta

ges:

za vključitevkih obvezno

a:

na funkcija va vrednost dtenje finančobvladovankapitala

cijske odločidenarnega tra kapitala i lastniški kočni dolžnišranje z zaku

UČN

Uvod v pos

Introductio

m in stopnjme and leve

2. stopnja

2nd degree

Course type

a predmeta

eminar eminar

/ Lecturer:

Pred

Vaje /

v v delo oz.osti:

v podjetju denarja čnih instrumnje tveganj

itve toka

apital in poki instrumeupom

NI NAČRT P

lovne finan

n to corpor

a el

e

a / Universi

Vaje Tutorial

30

Prof. d

davanja / Lectures:

P

Tutorial: D

za opravlja

mentov

litika dividenti

PREDMETA /

ce za matem

rate finance

ŠtudijskaStudy

ty course c

Kliničnewor

dr. Timotej

Prof. ddr. Ti

Doc. dr. Fra

anje Pr

Th

Co

end

FiTiVaInCoInFoCaEqLoLe

/ COURSE S

matike

e for mathe

a smer field

ode:

e vajek

Drugšt

Jagrič, CRM

imotej Jagr

njo Mlinari

rerequisits:

here are no

ontent (Syll

nancial funme value oaluation of ntroduction ost of capitanvestment dorecasting capital structquity financong‐term deeasing

SYLLABUS

maticians

LAc

1

1

ge oblike tudija

S

M

ič, CRM

č

ne.

labus outlin

ction in a cof money financial insto risk manal decisions cash flows ture cing and divebt

Letnik cademic year

1. ali 2.

1. or 2.

Samost. deloIndivid. work

135

ne):

ompany

struments nagement

vidend polic

SemesterSemester

1. ali 3.

1. or 3.

o ECTS

7

y

r r

Upravljanje obratnega kapitala Upravljanje s terjatvami do kupcev in zalogami

Working capital management Accounts receivable and inventory management


Berk, A., Lončarski, I., Zajc, P. in drugi, (2007). Poslovne finance, Ljubljana: Ekonomska fakulteta.ZRFRS. 2003. Slovenski poslovnofinančni standardi – Kodeks poslovnofinančnih načel. Ljubljana. (dostopno na www.si‐revizija.si). ZFPPIPP‐NUPB št. 14.(uvodni členi finančne vsebine). Tuji vir: Keown, A.J., Martin, J.D, Petty, J.W. 2014. Foundations of Finance. (primerna tudi starejša izdaja).



Študenti pri tem predmetu: Spoznajo teoretično ogrodje poslovnih financ in njihovo vlogo v procesu vodenja podjetja ter prepoznavajo ključne notranje in zunanje vire informacij za sprejemanje finančnih odločitev. in osvojijo osnove dobre prakse za apliciranje teh znanj. Pridobijo sposobnost uporabe teoretičnega znanja za reševanje praktičnih izzivov s pomočjo dela na raznolikih in razumljivih primerih v realističnih okoliščinah. Osvojijo standard dobre prakse in teorije, ki jim omogoča preudarno sprejemanje poslovno‐finančnih odločitev.

In this course students: recognize the theoretical framework of corporate finance and its role in a company management process and they are capable to recognize key internal and external information sources for financial decision making; earn the capability to use theoretical knowledgefor solving practical issues by working on various examples in understandable but realistic circumstances; acquire a standard of best practice and theory which enables them to find a solid ground for prudent financial decisions.



Znanje in razumevanje: Študenti: pridobijo znanje na področju osnov poslovnih financ; se naučijo strukturirati in razložiti fenomene na poslovno‐finančnem področju; pridobi praktične izkušnje na področju finančnega upravljanja in vodenja podjetij.

Knowledge and understanding: Students: acquire knowledge in the area of corporate finance fundamentals; are able to structure and explain phenomena in the field of finance in a company; receive practical experience in the field of corporate financial management.



klasična predavanja AV predstavitve obravnava primerov

common lectures AV presentations case studies



Assessment:

Način (pisni izpit, ustno izpraševanje, naloge, projekt) Pisni izpit ali 2 kolokvija. 100%

Type (examination, oral, coursework, project): Written examtion or 2 colloquiums.


ZDOLŠEK, Daniel, JAGRIČ, Timotej, ODAR, Marjan. Identification of auditor´s report qualifications : an empirical analysis for Slovenia. Ekonomska istraživanja, ISSN 1331‐677X, 2015, vol. 28, no. 1, str. 994‐1005. http://www.tandfonline.com/doi/pdf/10.1080/1331677X.2015.1101960, doi: 10.1080/1331677X.2015.1101960. [COBISS.SI‐ID 12136476], [JCR, SNIP, WoS do 8. 2. 2016: št. citatov (TC): 0, čistih citatov (CI): 0, Scopus do 5. 9. 2016: št. citatov (TC): 0, čistih citatov (CI): 0] BRICELJ, Bor, STRAŠEK, Sebastjan, JAGRIČ, Timotej. Financial crisis and the liquidity effect on market risk. The business review, Cambridge, ISSN 1553‐5827, 2014, vol. 22, no. 1, str. 127‐133. [COBISS.SI‐ID 11727900] TREFALT, Polona, JAGRIČ, Timotej. Kreditno tveganje in finančne omejitve slovenskih podjetij. IB revija, ISSN 1318‐2803. [Slovenska tiskana izd.], 2014, letn. 48, št. 1, str. 29‐42, ilustr. http://www.umar.gov.si/fileadmin/user_upload/publikacije/ib/2014/IB01‐14splet.pdf#page=31. [COBISS.SI‐ID 11715356] LEŠNIK, Tomaž, KRAČUN, Davorin, JAGRIČ, Timotej. Tax compliance and corporate income tax ‐ the case of Slovenia. Lex localis, ISSN 1581‐5374, Oct. 2014, vol. 12, no. 4, str. 793‐811, doi: 10.4335/12.4.793‐811(2014). [COBISS.SI‐ID 11815964], [JCR, SNIP, WoS do 2. 9. 2015: št. citatov (TC): 1, čistih citatov (CI): 1, Scopus do 2. 9. 2015: št. citatov (TC): 1, čistih citatov (CI): 1] ZDOLŠEK, Daniel, JAGRIČ, Timotej. Audit opinion identification using accounting ratios : experience of United Kingdom and Ireland. Aktual´ni problemi ekonomìki, ISSN 1993‐6788, 2011, no. 1 (115), str. 285‐310, graf. prikazi, tabele. [COBISS.SI‐ID 10625564], [JCR, SNIP, WoS do 5. 6. 2015: št. citatov (TC): 1, čistih citatov (CI): 1, Scopus do 14. 10. 2015: št. citatov (TC): 2, čistih citatov (CI): 2]


Predmet: Borzni trendi in strategije

Course title: Stock Market Trends and Strategies



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30

135 7

Nosilec predmeta / Lecturer: Sebastjan STRAŠEK

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Poslovni ciklus

Investicijski trgi in transakcije

Pozicioniranje sektorjev v borznem trendu

Splošni indikatorji trgov in strategije

Psihološki tržni indikatorji

Mednarodne povezave borznih trendov

Fundamentalna analiza

Tehnična analiza

Borzne krize in modeli reševanja

Business cycle

Investment markets and transactions

Positioning of sectors in market trend

General market indicators and strategies

Psychological market indicators

International links between market trends

Fundamental analysis

Stock market crises and models of resolving


Strašek, S. in Jagrič, T. Borzni trendi in strategije (načrtovana izdaja v letu 2007).

Gitman L., Joehnk, M. 1996. Fundamentals of Investing. Harper&Collins Publishers.

Teweles, R., Bradley, E. 2003. The Stock Market. John Wiley&Sons, Co.



Predmet omogoča poglabljanje znanj s

področja delovanja kapitalskih trgov.

Predmet obravnava povezavo med

poslovnim ciklusom in borznimi trendi,

makroekonomske in mikroekonomske

implikacije sprememb fundamentalnih

spremenljivk, osnove tehnične in

fundamentalne analize, značilnosti

potencialnih borznih strategij ter

obnašanje akterjev v različnih fazah

borznega in poslovnega ciklusa.

The aim of the course is to deepen the

knowledge on the stock market

functioning. The course researches the

links between business cycle and the

stock trends, macroeconomic and

microeconomic implications of the

changes in fundamentals, the basics of

technical and fundamental analysis, the

characteristics of potential stock market

strategies and behavior of players in

different phases of stock market and

business cycle.




- znanje o merodajnih informacijah za

poslovno odločanje in tržne strategij;

- zmožnost analiziranja borznih trendov

in individualnih delnic;

- razumevanje gospodarskih posledic

sprememb v makro in mikro okolju na

pozicioniranje delnic.


- sposobnost analize in sinteze;

- sposobnost uporabe znanja v praksi;

- samostojno delo;

- ustna in pisna komunikacija;

- reševanje problemov;

- sposobnost prilagajanja novim

razmeram.


- knowledge about relevant information

- for business decisions and market

strategies;

- capability to analyze stock market trends

and individual stocks;

- comprehension of economic

consequences of changes in macro and

micro environment on stocks

positioning.


- capability for analysis and synthesis;

- capacity for applying knowledge in

practice;

- autonomous work;

- oral and written communication;

- problem solving;

- capacity to adapt to new situations.



Pri predmetu so uporabljene sledeče metode

poučevanja in učenja:

predavanja (predavatelj bo podal študentom

vsebino ključnih teorij in tehnik);

vodene vaje v računalniški učilnici (primeri

modeliranja in razprava o domačih nalogah);

individualne konzultacije s predavateljem;

samostojno delo v računalniški učilnici, s

posebnim poudarkom na uporabi interneta

The following methods and forms of study are

used in the course:

lectures (lecturer will provide students with

knowledge of the fundamental theories and

techniques);

guided classes in computer room (sample

modeling is done and the main problems of

home assignments are discussed);

teachers' consultations;

(izdelava domačih nalog z uporabo Excela,

delo z ekonomskimi bazami podatkov, učna

gradiva na internetu, spletne predstavitve);

samostojni študij gradiva.

self study in computer room, in particular with

the Internet (making home assignments using

Excel, work with economic data bases, study

guides on the Internet, looking through sets of

lecture slides);

self study with literature.


Assessment:


naloge, projekt)

Pisni izpit

Seminarska naloga



Delež (v %) /

Weight (in %)

80%

20%


project):

Written exam

Seminar paper




references:

1. STRAŠEK, Sebastjan, MUNDA, Gal. Beating the market in less developed financial

exchange. Aktual. probl. ekon., 2012, no. 1 (127), str. 425-433. [COBISS.SI-

ID 10971420]

2. MUNDA, Gal, STRAŠEK, Sebastjan. Use of the TRP ratio in selected countries =

Uporaba TRP indikatorjev v izbranih državah. Naše gospod., 2011, letn. 57, št. 1/2, str.

55-60. [COBISS.SI-ID 10578716]

3. JAGRIČ, Timotej, MARKOVIČ-HRIBERNIK, Tanja, STRAŠEK, Sebastjan,

JAGRIČ, Vita. The power of market mood - Evidence from an emerging market. Econ.

model.. [Print ed.], 2010, vol. 27, iss. 5, str. [959]-967,

doi: 10.1016/j.econmod.2010.05.005. [COBISS.SI-ID 10310428]

4. STRAŠEK, Sebastjan, ŠPES, Nataša. Pojasnjevalna moč modelov finančnih

kriz. Organizacija (Kranj), jul./avg. 2010, letn. 43, št. 4, str. A 119-A 128. [COBISS.SI-

ID 10298908]

5. STRAŠEK, Sebastjan, JAGRIČ, Timotej. Policy failures and current crisis. Rev.

econ. (Sibiu), 2010, vol. 50, no. 3, str. 456-462. [COBISS.SI-ID 10432284]



http://dx.doi.org/10.1016/j.econmod.2010.05.005





Predmet: Diferencialne enačbe

Course title: Differential equations



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


1. 2.

Mathematics, 2nd

degree

1. 2.



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

60

45

195 10

Nosilec predmeta / Lecturer: Blaž ZMAZEK

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Poznavanje odvodov in integralov. Knowledge of differentials and integrals.


1. Osnovni pojmi: Konstrukcija NDE,

grafično reševanje, enačbe z ločljivima

spremenljivkama.

2. Navadne diferencialne enačbe: Osnovni tipi

NDE, parametrično reševanje, singularni

integrali, uporaba v geometriji in fiziki.

3. Eksistenčni izreki: Lokalni in globalni

eksistenčni izrek za NDE, odvisnost rešitve

od parametra, splošna enačba prvega reda.

4. Linearne diferencialne enačbe: Sistemi

linearnih diferencialnih enačb, Liouvilleva

1. Basics: Construction of ODE, graphical

solutions, equations with separable variables.

2. Ordinary differential equations: Basic types

of ODE, parametric solving, singular

integrals, applications in geometry and

physics.

3. Existence theorems: Local and global

existence theorems for ODE, solution

dependence of parameter, ODE of first

order.

4. Linear differential equations: Systems of

formula, linearna diferencialna enačba reda

n, LDE z realnimi in konstantnimi

koeficienti, Euler-Cauchyjeva enačba.

5. Variacijski račun: Naloge variacijskega

računa, osnovni izrek variacijskega računa,

Euler-Lagrangeva enačba, posplošitve,

dinamični robni pogoji, izoperimetrični

problem, Lagrangeva naloga.

6. Diferencialne enačbe v kompleksnem:

Rešitev v okolici regularne točke,

homogena linearna enačba, pravilne

singularne točke, Frobeniusova metoda.

7. Trigonometrične vrste in transformacije:

Fourierova vrsta, Fourierova

transformacija, diskretna Fourireova

transformacija.

8. Besselova diferencialna enačba: Rešitve

Besselove DE, integralske representacije.

linear differential equations, Liouvill's

formula, linear differential equation of n-th

order, LDE with real and constant

coefficients, Euler-Cauchy equation.

5. Calculus of variations: Calculus of variations

tasks, fundamental theorem of calculus of

variations, Euler-Lagrange equation,

generalizations, dynamic boundary

conditions, isoperimetric problem, Lagrange

task.

6. Differential equations in complex: Solutions

in regular point surroundings, homogeneous

linear equation, proper singular point,

Frobenius's method.

7. Trigonometric series and transformations:

Fourier series, Fourier transformation,

discrete Fourier transform

8. Bessel differential equation: Solutions of

Bessel DE, integral representations.


E. Zakrajšek, Analiza III, DMFA Slovenije, Ljubljana, 1998.

F. Križanič, Navadne diferencialne enačbe in variacijski račun, DZS, Ljubljana 1974.

W. Kaplan, Advanced Calculusi, Fourth Edition. Addisson-Wesley Publishing Company, Redwood

City, California, 1991.



Temeljito poglobiti znanje iz navadnih

diferencialnih enačbe, integralske

transformacije in variacijski račun.

To deepen the knowledge of ordinary

differential equations, integral transformations

and calculus of variations.




Poznavanje in razumevanje

diferencialnih enačb in metod za

njihovo reševanje.

Razumevanje in uporaba integralskih

transformacij in variacijskega računa.


Pridobljena znanja so podlaga za mnogo

predmetov v nadaljevanju študija.


Knowledge and understanding of

differential equations and methods of

their solution.

Be able to understand and implement

integral transformations and calculus of

variations.


The obtained knowledge is a basis for

many of the later subjects.



Predavanja

Seminarske vaje

Lectures

Tutorial


Assessment:

Način (pisni izpit, ustno izpraševanje, Delež (v %) / Type (examination, oral, coursework,

naloge, projekt)

Pisni test – praktični del

Izpit (ustni) – teoretični del



Pozitivna ocena pri pisnem testu je

pogoj za pristop k izpitu.

Weight (in %)

50%

50%

project):

Written test – practical part

Exam (oral) – theoretical part



Passing grade of the written test is

required for taking the exam.


references:

1. PRNAVER, Katja, ZMAZEK, Blaž. On total chromatic number of direct product graphs. J.

appl. math. comput. (Internet), 2010, issue 1-2, vol. 33, str. 449-457.

http://dx.doi.org/10.1007/s12190-009-0296-8, doi: 10.1007/s12190-009-0296-8. [COBISS.SI-ID

17523720]

2. ZMAZEK, Blaž, ŽEROVNIK, Janez. The Hosoya-Wiener polynomial of weighted trees. Croat.

chem. acta, 2007, vol. 80, 1, str. 75-80. [COBISS.SI-ID 11338518]

3. ZMAZEK, Blaž, ŽEROVNIK, Janez. Weak reconstruction of strong product graphs. Discrete

math.. [Print ed.], 2007, vol. 307, iss. 3-5, str. 641-649.

http://dx.doi.org/10.1016/j.disc.2006.07.013. [COBISS.SI-ID 14184025]

4. ZMAZEK, Blaž, ŽEROVNIK, Janez. On domination numbers of graph bundles. J. Appl. Math.

Comput., Int. J., 2006, vol. 22, no. 1/2, str. 39-48. [COBISS.SI-ID 10636822]

5. ZMAZEK, Blaž, ŽEROVNIK, Janez. On generalization of the Hosoya-Wiener polynomial.

MATCH Commun. Math. Comput. Chem. (Krag.), 2006, vol. 55, no. 2, str. 359-362. [COBISS.SI-

ID 13990745]

http://dx.doi.org/10.1007/s12190-009-0296-8

http://dx.doi.org/10.1007/s12190-009-0296-8








Predmet: Temelji finančnega inženiringa

Course title: Foundations of financial engineering



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30

135 7

Nosilec predmeta / Lecturer: Miklavž MASTINŠEK

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


1.Matematične osnove

2.Izvedeni finančni instrumenti

3.Tveganje in varnost

4.Opcije

5.Vrednotenje opcij, hedging

6.Binomski model

7.Black-Scholesov

8.Delta, gamma, sigma

9.Monte-Carlo metoda

10.Vodenje portfelja

11.Realne opcije

1.Mathematical tools

2.Financial derivatives

3.Risk and security

5.Option valuation, hedging

6.Binomial model

7.Black-Scholes model

8.The greeks

9.Monte-Carlo method

10.Portfolio management

11.Real options


1. Hull J., »Options, Futures and other Derivative Securities«, New Jersey, Prentice Hall Int.,

1996.

2. Wilmott P.« Paul Wilmott on Quantitative Finance«, John Wiley, (2000).

3. Cuthbertson K., »Financial engineering: derivatives and risk management«, Wiley,

(2001)






nalog in procesov s področja finančnega

inženiringa. Prav tako je namen predmeta dati

osnovo za spremljanje sodobne literature in

nadaljnje strokovno izpopolnjevanje.



of financial engineering.



new methods.





korektno vodenje poslov s področja finančnega

inženiringa.



teoretičnega dela. Zmožnost nadaljnega študija

novih kvantitativnih

metod finančnega inženiringa.



practical skills of financial engineering.









Written examination

Seminary work


Assessment:


naloge, projekt)

Pisni izpit

seminarska naloga

Delež (v %) /

Weight (in %)

80%

20%


project):

Written exam

Semynar


references:

1. MASTINŠEK, Miklavž. Charm-adjusted delta and delta gamma hedging. J. deriv., 2012, vol.

19, no. 3, str. 69-76, doi: 10.3905/jod.2012.19.3.069. [COBISS.SI-ID 10970908]

2. MASTINŠEK, Miklavž. Financial derivatives trading and delta hedging = Trgovanje z

izvedenimi finančnimi instrumenti ter delta hedging. Naše gospod., 2011, letn. 57, št. 3/4, str. 10-

http://dx.doi.org/10.3905/jod.2012.19.3.069


15. [COBISS.SI-ID 10733084]

3. MASTINŠEK, Miklavž. Descrete-time delta hedging and the Black-Scholes model with

transaction costs. Math. methods oper. res. (Heidelb.). [Print ed.], 2006, vol. 64, iss. 2, str. [227]-

236, doi: 10.1007/s00186-006-0086-0. [COBISS.SI-ID 8939292]

4. MASTINŠEK, Miklavž. Identifiability for a partial functional differential equation. Acta sci.

math. (Szeged), 2003, vol. 69, str. 121-130. [COBISS.SI-ID 7029276]

5. MASTINŠEK, Miklavž. Norm continuity for a functional differential equation with fractional

power. International journal of pure and applied mathematics, 2003, vol. 5, no. 1, str. 49-56.



http://dx.doi.org/10.1007/s00186-006-0086-0





Predmet: Osnove programiranja v diskretni matematiki

Course title: Basic programming in discrete mathematics



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30 135 7

Nosilec predmeta / Lecturer: Aleksander VESEL

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:



potrebam in razvoju. Poglobili bomo znanje iz

uporabe računalnika pri reševanju

matematičnih problemov, predvsem s področja

diskretne matematike.

- Relacije in algoritmi nad relacijami

- Boolova algebra

- Prirejanja v grafih


current needs and development. We will deepen

the knowledge of using a computer to solve

mathematical problems, mainly from discrete

mathematics.

- relations and algorithms on relations

- Bool algebra

- matchings in graphs


B. Vilfan, Osnovni algoritmi, ISBN 961-6209-13-2, Založba FER in FRI, 2. izd., 2002.

Kenneth H. Rosen, Discrete Mathematics and Its Applications, ISBN 007-2880-08-2, McGraw-

Hill, 6th ed., 2007.

Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Introduction to

Algorithms, ISBN 026-2032-93-7, The MIT Press, 2nd ed., 2001.



Z uporabo modernega, predmetno usmerjenega

programskega jezika, poglobiti znanje iz

pristopov, podatkovnih struktur in algoritmov

pri reševanju matematičnih problemov.

With the usage of modern object oriented

programming language, to deepen the

knowledge of the basic approaches, data

structures and algorithms for solving

mathematical problems.




podatkovne strukture matematičnih

modelov

razumevanje, implementacija in

uporaba pomembnejših algoritmov


uporaba matematičnih pojmov v

programskih aplikacijah

uporaba ustreznih podatkovnih struktur

pri implementaciji matematičnih

algoritmov

pridobljena znanja se prenašajo na

druge z računalništvom povezane

predmete


data structures of mathematical models

understanding, implementation and

usage of important algorithms


the usage of mathematical notions in

applications

the usage of appropriate data structures

while implementing mathematical

algorithms

the obtained knowledge is transferable

to the other computer science oriented

subjects



Predavanja

Računalniške vaje

Lectures

Computer exercises


Assessment:


Projekt

Pisni testi – teorija (3 do 5 pisnih testov

na semester)

Izpit:






Delež (v %) /

Weight (in %)

40%

40%

20%

Mid-term testing:

Project

Written tests – theory (from 3 to 5

written tests during the semester)

Exams:

Written exam - problems




are required for taking the exam.


references:

1. VESEL, Aleksander. Fibonacci dimension of the resonance graphs of catacondensed benzenoid

graphs. Discrete appl. math.. [Print ed.], 2013, str. 1-11, doi: 10.1016/j.dam.2013.03.019.

2. SHAO, Zehui, VESEL, Aleksander. A note on the chromatic number of the square of the

Cartesian product of two cycles. Discrete math.. [Print ed.], 2013, vol. 313, iss. 9, str. 999-1001.

3. KORŽE, Danilo, VESEL, Aleksander. A note on the independence number of strong products of

odd cycles. Ars comb., 2012, vol. 106, str. 473-481. [COBISS.SI-ID 16138006]

4. TARANENKO, Andrej, VESEL, Aleksander. 1-factors and characterization of reducible faces

of plane elementary bipartite graphs. Discuss. Math., Graph Theory, 2012, vol. 32, no. 2, str. 289-

297, doi: 10.7151/dmgt.1607. [COBISS.SI-ID 19104264]

5. SALEM, Khaled, KLAVŽAR, Sandi, VESEL, Aleksander, ŽIGERT, Petra. The Clar formulas

of a benzenoid system and the resonance graph. Discrete appl. math.. [Print ed.], 2009, vol. 157,

iss. 11, str. 2565-2569. http://dx.doi.org/10.1016/j.dam.2009.02.016. [COBISS.SI-ID 15142489



http://dx.doi.org/10.7151/dmgt.1607





Predmet: Programiranje v diskretni matematiki

Course title: Programming in discrete mathematics



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 15 45 165 9

Nosilec predmeta / Lecturer: Andrej Taranenko

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:








- Boolova algebra






mathematics.


- Bool algebra























modelov








algoritmov



predmete







applications



algorithms



subjects



Predavanja, seminar

Računalniške vaje

Lectures, seminary

Computer exercises


Assessment:


Seminarska naloga

Projekt


na semester)

Delež (v %) /

Weight (in %)

20%

20%

40%

Mid-term testing:

Seminary work

Project



Izpit:






20%

Exams:







references:


TARANENKO, Andrej. On the vertex k-path cover. Discrete appl. math.. [Print ed.], 2013, vol.

161, iss. 13/14, str. 1943-1949, doi: 10.1016/j.dam.2013.02.024. [COBISS.SI-ID19859464]


products. Discrete math.. [Print ed.], 2013, vol. 313, iss. 1, str. 94-100.

http://dx.doi.org/10.1016/j.disc.2012.09.010, doi: 10.1016/j.disc.2012.09.010. [COBISS.SI-

ID19464968]




4. TARANENKO, Andrej, ŽIGERT PLETERŠEK, Petra. Resonant sets of benzenoid graphs and

hypercubes of their resonance graphs. MATCH Commun. Math. Comput. Chem. (Krag.), 2012, vol.

68, no. 1, str. 65-77.http://www.pmf.kg.ac.rs/match/content68n1.htm. [COBISS.SI-ID 16051990]

5. KLAVŽAR, Sandi, SALEM, Khaled, TARANENKO, Andrej. Maximum cardinality resonant

sets and maximal alternating sets of hexagonal systems. Comput. math. appl. (1987). [Print ed.],

2010, vol. 59, no. 1, str. 506-513.http://dx.doi.org/10.1016/j.camwa.2009.06.011. [COBISS.SI-

ID 15383641]








http://www.pmf.kg.ac.rs/match/content68n1.htm


http://dx.doi.org/10.1016/j.camwa.2009.06.011



Predmet: Ekonometrija

Course title: Econometrics



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

60

45

165 9

Nosilec predmeta / Lecturer: Timotej JAGRIČ

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


- Uvod (Uvod v ekonometrijo, Ponovitev

statistike);

- Multipli regresijski model (Uvod, Ocena

parametrov, Lastnosti, Testiranje hipotez,

Mere primernosti, linearne transformacije,

napovedovanje);

- Neizpolnjevanje predpostavk (Specifikacija

modela, Normalna porazdelitev,

Multikolinearnost, Heteroskedastičnost,

Avtokorelacija);

-Introduction (Introduction to Econometrics,

Statistics Review);

-The Multiple Regression Model (Introduction,

Estimating the Parameters, Properties,

Hypothesis Testing, Goodness of Fit, linear

transformations, forecasting);

-Violations of Assumptions (Model

Specification, Multicollinearity,

Heteroskedasticity, Serial Correlation);

- Dummy variables;

- Slamnate spremenljivke;

- Odložene spremenljivke;

- Simultani sistemi;

LOGIT modeli.

- Lagged variables;

- Simultaneous systems;

- LOGIT models.


N. Gujarati (2003). Basic Econometrics – Fourth Edition. McGraw-Hill, New York.

W. H. Green (2003). Econometric Analysis – Fifth Edition. Prentice Hall, New Jersey.

G. S. Maddala (2003). Introduction to Econometrics – Third Edition. John Wiley & Sons, New

York.



Študentje naj bi dobili znanja in spretnosti, ki

so potrebna za ekonometrično analizo. V

okviru predmeta se bodo študentje učili

tradicionalne ekonometrične metode. Razumeli

bodo bistvene razlike med časovnimi vrstami in

presečnimi podatki. Študentje bodo dobili

spretnosti, ki so potrebne za oblikovanje in

razvoj enostavnih in multiplih regresijskih

modelov. Obravnavane metode bodo razumeli

do te mere, da jih lahko uporabijo na realnih

ekonomskih bazah podatkov z uporabo

sodobnih ekonometričnih programov.

The students will get the knowledge and skills of

econometric analysis. In the course the students

will learn traditional econometric methods. They

will understand differences between the time

series and cross sections data. The students will

get the skills of construction and development of

simple and multiple regression models. The

students will be able to apply methods on real

economic data bases with modern econometric

software.




- poznavanje osnovnih matričnih operacij in

njihova aplikacija v linearnih regresijskih

modelih;

- razumevanje predpostavk, na katerih

temeljijo linearni regresijski modeli;

- razumevanje posledic odstopanja modela

od teh predpostavk;

- poznavanje principov statističnega

testiranja;

- poznavanje uporabe računalniških

programov za ocenjevanje in testiranje

ekonometričnih modelov;

- interpretacija in komentiranje rezultatov;

- sposobnost prebiranja literature s področja

kvantitativnih ekonomskih analiz, ki

temeljijo na ekonometriji.


- sposobnost analize in sinteze;


- Use of basic matrix operations and their

application to the linear regression model;

- understand the assumptions of the linear

regression model

- awareness of the implications for the model

departures from assumptions;

- understand statistical testing principles;

- use software in the estimation and testing of

econometric models;

- interpret and discuss results;

- be able to understand quantitative econ.

literature that uses econometric methods.


- capability for analysis and synthesis;

- capacity for applying knowledge in practice;

- autonomous work;

- oral and written communication;

- problem solving;

- sposobnost uporabe znanja v praksi;

- samostojno delo;

- ustna in pisna komunikacija;

- reševanje problemov;

- sposobnost prilagajanja novim razmeram;

- raziskovalne sposobnosti;

- sposobnost generiranja novih idej.

- capacity to adapt to new situations;

- research skills;

- capacity for generating new ideas.



predavanja (predavatelj bo podal študentom

vsebino ključnih teorij in tehnik);

vodene vaje v računalniški učilnici (primeri

modeliranja in razprava o domačih

nalogah);

individualne konzultacije s predavateljem;

samostojno delo v računalniški učilnici, s

posebnim poudarkom na uporabi interneta

(izdelava domačih nalog z uporabo

računalnika, delo z ekonomskimi bazami

podatkov, učna gradiva na internetu, spletne

predstavitve predavanj iz ekonometrije);

samostojni študij gradiva

lectures (lecturer will provide students with

knowledge of the fundamental theories and

techniques);

guided classes in computer room (sample

modeling is done and the main problems of

home assignments are discussed);

teachers' consultations;

self study in computer room, in particular

with the Internet (making home assignments

using PC, work with economic data bases,

study guides on the Internet, looking through

sets of slides in Econometrics);

self study with literature


Assessment:


naloge, projekt)

- seminarska naloga

- pisni izpit

Delež (v %) /

Weight (in %)

50%

50%


project):

- seminar work

- written examination


references:

1. ŽUNKO, Matjaž, JAGRIČ, Timotej. Raven razkrivanja z metodo tvegane vrednosti v slovenskih

poslovnih bankah. Banč. vestn., apr. 2012, letn. 61, št. 4, str. 42-46. [COBISS.SI-ID 10994460]

2. ZDOLŠEK, Daniel, JAGRIČ, Timotej. Audit opinion identification using accounting ratios :

experience of United Kingdom and Ireland. Aktual. probl. ekon., 2011, no. 1 (115), str. 285-310,

graf. prikazi, tabele. [COBISS.SI-ID 10625564]

3. BEKŐ, Jani, JAGRIČ, Timotej. Demand models for direct mail and periodicals delivery services

: results for a transition economy. Appl. econ., apr. 2011, vol. 43, no. 9, str. 1125-1138, doi:

10.1080/00036840802600244. [COBISS.SI-ID 10071324]

4. JAGRIČ, Vita, JAGRIČ, Timotej. Primerjalna presoja bančnih bonitetnih modelov za

prebivalstvo = A comparative assessment of credit risk models for bank retail portfolio. Banč.



http://dx.doi.org/10.1080/00036840802600244


vestn., jan.-feb. 2011, letn. 60, št. 1/2, str. 48-52. [COBISS.SI-ID 10593052]

5. JAGRIČ, Timotej, JAGRIČ, Vita. A comparison of growing cell structures neural networks and

linear scoring models in the retail credit environment : a case of a small EU and EMU member

country. East. Europ. econ., nov-dec 2011, vol. 49, no. 6, str. 74-96, doi: 10.2753/EEE0012-

8775490605. [COBISS.SI-ID 10975772]


http://dx.doi.org/10.2753/EEE0012-8775490605



Fakulteta za naravoslovje in matematiko

Oddelek za matematiko in računalništvo


Predmet: Kombinatorična optimizacija

Course title: Combinatorial optimization



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester

Matematika Modul F2 1 ali 2 1 ali 3

Mathematics Module F2 1 or 2 1 or 3



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 30 135 7

Nosilec predmeta / Lecturer: Janez Žerovnik

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Jih ni. None.

Vsebina:


Obvezna vsebina, ki pri študentih vzpostavi

temeljni nabor znanj s področja kombinatorične

optimizacije:

Večkriterijska linearna optimizacija.

Ciljno programiranje. Celoštevilsko

programiranje.

Problem nahrbtnika in njegove različice.

Pretoki v omrežjih. Ford-Fulkersonov

algoritem.

Problem maksimalnega prirejanja.

Problem maksimalnega prereza.

Mandatory content, that familiarizes the students

with fundamentals of operations research and

mathematical programs:

Multicriteria linear optimization. Goal

programming. Integer programming.

Knapsack problems and its variants.

Network flows. Ford-Fulkerson’s algorithm.

Maximum matching problem.

Maximum cut problem.

Transport problem. Chinese postman

problem.

Transportni problem. Problem kitajskega

poštarja. Problem trgovskega potnika.

Aproksimacijski algoritmi.

Hevristike in metahevristike. Lokalna

optimizacija. Tabu search. Simulirano

ohlajanje. Genetski algoritmi.

Nevronske mreže. Samo-organizirajoče

se mreže.

V okviru vsebine študentje izberejo zahtevnejši

problem, s katerimi se poglobljeno ukvarjajo

pri seminarski nalogi. Problem je povezan z

njihovo bodočo kariero (praktični problemi iz

gospodarstva, teoretični problemi iz teorije

matematičnega programiranja in pripadajočih

numeričnih algoritmov). Preostala predavanja

se prilagodijo problemom, ki so jih izbrali

študentje, in obsegajo vsebine z naslednjega

seznama:

Optimalni portfelj celoštevilskih lotov in

celoštevilsko programiranje.

Problem delovnega razporeda.

Problem urnika.

Problem razporejanja nalog enega in več

strojev.

Problem optimizacije zalog.

Problemi rezanja in pakiranja.

Travelling salesman problem.

Approximation algorithms.

Heuristics and metaheuristics. Local

optimization. Tabu search. Simulated

annealing. Genetic aglorithms. Neural nets.

Self-organized maps.

Within the coursework, the students select

smaller problems whose result are coursework

reports. The problems are related to their future

career (practical problems from industry and

business, theoretical problems from the areas of

optimization, algorithms, modelling). The

content of the remaining lectures is selected

according to these projects from the following

list:

Optimal portfolio of integer lots and integer

programming.

Employee timetabling problem.

School timetabling problems.

Scheduling tasks of one or several

processors.

Stock optimization.

Cutting and packing problems.


J.Žerovnik: Osnove teorije grafov in diskretne optimizacije, (druga izdaja), Fakulteta za

strojništvo, Maribor 2005.

R. Wilson, M. Watkins, Uvod v teorijo grafov, DMFA, Ljubljana 1997.

B. Robič: Aproksimacijski algoritmi, Založba FRI, Ljubljana 2002.

E. Zakrajšek: Matematično modeliranje, DMFA, Ljubljana 2004.

B. Korte, J. Vygen: Combinatorial Optimization, Theory and Algorithms, Springer, Berlin 2000.

D. Cvetković, V. Kovačević-Vujčić: Kombinatorna optimizacija, DOPIS Beograd 1996.

S. Zlobec, J. Petrić: Nelinearno programiranje, Naučna knjiga, Beograd 1989.

E. Kreyszig: Advanced Engineering Mathematics, (seventh edition), Wiley, New York 1993.



Usvojiti proces matematičnega modeliranja na

diskretnih optimizacijskih problemih.

Razviti kompetenco samostojnega apliciranja

matematičnih metod na probleme iz finančne

optimizacije, ekonomije, ter širše iz

gospodarstva.

Spoznati tehnološka orodja, s katerimi se

srečujemo pri reševanju optimizacijskih

Familiarize the students with the process of

mathematical modelling of continuous

optimization problems.

Develop competent skills of independent

application of mathematical methods to the

problems from financial optimization,

economics, and broader from industry.

Familiarize the students with technological tools

problemov in problemov matematičnega

modeliranja.

that assist solving optimization problems and

problems related to mathematical modelling.




Razumevanje zahtevnejših principov

kombinatorične optimizacije.

Poglobi znanje iz sodobnih metod za

reševanje problemov kombinatorične

optimizacije.

Poglobiti znanje iz diskretnih modelov

in drugih zahtevnih aplikacij

kombinatorične optimizacije v finančni

matematiki, optimiranju virov, in širše


Direktne aplikacije v finančni matematiki,

ekonomiji, poslovnih vedah, inžinirstvu,

fiziki in številnih drugih družboslovnih in

naravoslovnih vedah.

Suvereno obvladovanje procesa

matematičnega modeliranja in uporabe

tehnik kombinatorične optimizacije v

problemih s področja finančne

optimizacije, ekonomije in širše.


To be able to understand advanced principles

of combinatorial optimization.

To deepen the knowledge of modern

methods for solving combinatorial


To deepen the knowledge of details of

discrete models and other advanced

applications of combinatorial optimization in

financial optimization, resource

optimization, and wider.


Direct applications in finacial mathematics,

economy, business, engineering, physics,

and numerous other social and natural

sciences.

Competent mastering of the process of

mathematical modelling and applications of

the techniques of combinatorial optimization

in problems from financial optimization,

economics, and wider.



Pri predavanjih študentje spoznajo snov

predmeta.

V okviru seminarskih vaj študentje

razumevanje snovi utrjujejo na večjem

projektu, povezanem z njihovo bodočo

kariero. Razporejeni so v večje skupine, ki

po metodah problemskega učenja

obravnavajo izbrani problem od zbiranja

podatkov, preko razvoja modela, izbora in

prilagajanja ustreznih tehnoloških rešitev do

razmisleka o implementaciji rešitve.

Koncept poučevanja je podrobneje

predstavljen kot ciljni aplikativni predmet.

At the lectures, the students are familiarized

with the course content.

At the tutorials, the student deepen their

understanding of the material by working on

an extensive problem related to their future

career. They are organized in larger groups

who research the choosen problem guided by

methodologies of problem-based learning.

Within solving the problem, they experience

all the stages from requirements and data

gathering, model development, selecting and

adapting technological solutions to

discussing various aspects of implementation

of the results.


Assessment:


naloge, projekt)

Seminarska naloga

Ustni izpit



Pozitivna ocena pri seminarski nalogi je


Delež (v %) /

Weight (in %)

80%,

20%


project):

Coursework report

Oral exam



Passing grade of the seminar exercise is



references:

1. ŠPARL, Petra, WITKOWSKI, Rafeł, ŽEROVNIK, Janez. 1-local 7/5-competitive algorithm for

multicoloring hexagonal graphs. Algorithmica, in press, doi: 10.1007/s00453-011-9562-x.


2. ERVEŠ, Rija, ŽEROVNIK, Janez. Mixed fault diameter of Cartesian graph bundles. Discrete

appl. math.. [Print ed.], Available online 10. December 2011, doi: 10.1016/j.dam.2011.11.020.


3. SAU WALLS, Ignasi, ŠPARL, Petra, ŽEROVNIK, Janez. Simpler multicoloring of triangle-free

hexagonal graphs. Discrete math.. [Print ed.], str. 181-187.



4. ŠPARL, Petra, WITKOWSKI, Rafał, ŽEROVNIK, Janez. A linear time algorithm for 7-

[3]coloring triangle-free hexagonal graphs. Inf. process. lett.. [Print ed.], 2012, vol. 112, iss. 14-15,

str. 567-571. http://dx.doi.org/10.1016/j.ipl.2012.02.008. [COBISS.SI-ID 7018003]

5. HRASTNIK LADINEK, Irena, ŽEROVNIK, Janez. Cyclic bundle Hamiltonicity. Int. j. comput.

math., 2012, vol. 89, iss. 2, str. 129-136, doi: 10.1080/00207160.2011.638375. [COBISS.SI-ID

15651862]

http://dx.doi.org/10.1007/s00453-011-9562-x






http://dx.doi.org/10.1016/j.ipl.2012.02.008


http://dx.doi.org/10.1080/00207160.2011.638375



Predmet: Funkcionalna analiza

Course title: Functional analysis



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

60

45

195 10

Nosilec predmeta / Lecturer: Matej BREŠAR

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Poznavanje linearne algebre in analize. Knowledge of linear algebra and analysis.


Banachovi prostori: vektorski in normirani

prostori, polnost, primeri; podprostori in

kvocientni prostori; končno-razsežni normirani

prostori, kompaktne množice; Banachove

algebre, spekter.

Linearni operatorji in funkcionali: omejeni in

neomejeni linearni operatorji; kompaktni

operatorji; izreki o enakomerni omejenosti,

odprti preslikavi in zaprtem grafu; dual, Hahn-

Banachov izrek, refleksivni prostori.

Banach spaces: vector spaces and normed

spaces, completness, examples; subspaces and

quotient spaces; finite dimensional normed

spaces, compact sets; Banach algebras,

spectrum.

Linear operators and functionals: bounded and

unbounded linear operators; compact operators;

uniform boundedness principle, open mapping

theorem, closed graph theorem; dual, Hahn-

Banach theorem, reflexive spaces.

Hilbertovi prostori: osnovni pojmi in primeri;

ortogonalnost, Rieszov izrek; ortonormirane

množice; adjungirani operatorji.

Hilbert spaces: basic concepts and examples;

orthogonality, Riesz theorem; orthonormal

bases, adjoint operators.


B. Brown, A. Page, Elements of functional analysis, Van Nostrand, 1970.

M. Hladnik, Naloge in primeri iz funkcionalne analize in teorije mere, DMFA, 1985.

B. P. Rynne, M. A. Youngson, Linear functional analysis, Springer, 2000.

J. Vrabec, Metrični prostori, DMFA, 1993.



Poglobi znanje temeljnih konceptov in

rezultatov funkcionalne analize.

Deepening the knowledge of fundamental

concepts and results of functional analysis.




Banachovih prostorov

Hilbertovih prostorov

Teorije operatorjev


Pridobljeno znanje je podlaga tako za

teoretično kot uporabno analizo na višji ravni.


Banach spaces

Hilbert spaces

Operator theory


The obtained knowledge is a basis for both

theoretical and applied analysis on an advanced

level.



Predavanja

Seminarske vaje

Lectures

Tutorial


Assessment:


naloge, projekt)

Pisni izpit

Delež (v %) /

Weight (in %)

100%


project):

Written exam


references:

1. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, ŠPENKO, Špela. Lie superautomorphisms

on associative algebras, II. Algebr. represent. theory, 2012, vol. 15, no 3, str. 507-525.


http://dx.doi.org/10.1007/s10468-010-9254-2


2. BIERWIRTH, Hannes, BREŠAR, Matej, GRAŠIČ, Mateja. On maps determined by zero

products. Commun. Algebra, 2012, vol. 40, no. 6, str. 2081-2090.

http://dx.doi.org/10.1080/00927872.2011.570833. [COBISS.SI-ID 16315481]

3. BREŠAR, Matej, MAGAJNA, Bojan, ŠPENKO, Špela. Identifying derivations through the

spectra of their values. Integr. equ. oper. theory, 2012, vol. 73, no. 3, str. 395-411.


4. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, KOCHETOV, Mikhail. Group gradings on

finitary simple Lie algebras. Int. j. algebra comput., 2012, vol. 22, no. 5, 1250046 (46 str.).

http://dx.doi.org/10.1142/S0218196712500464. [COBISS.SI-ID 16339545]

5. ALAMINOS, J., BREŠAR, Matej, ŠEMRL, Peter, VILLENA, A. R. A note on spectrum-

preserving maps. J. math. anal. appl., 2012, vol. 387, iss. 2, str. 595-603.

http://dx.doi.org/10.1016/j.jmaa.2011.09.024. [COBISS.SI-ID 16067673]

http://dx.doi.org/10.1080/00927872.2011.570833


http://dx.doi.org/10.1007/s00020-012-1975-7


http://dx.doi.org/10.1142/S0218196712500464


http://dx.doi.org/10.1016/j.jmaa.2011.09.024


UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Izbrana poglavja iz algebre Course title: Selected topics from algebra

Študijski program in stopnja Study programme and level

Študijska smer Study field

Letnik Academic

year

Semester Semester

Matematika 2. stopnja 1. ali 2. 1. ali 3.

Mathematics 2nd degree 1. or 2. 1. or 3.

Vrsta predmeta / Course type Univerzitetna koda predmeta / University course code:

Predavanja Lectures

Seminar Seminar

Sem. vaje Tutorial

Lab. vaje Laboratory

work

Teren. vaje Field work

Samost. delo Individ.

work ECTS

45 30 135 7

Nosilec predmeta / Lecturer: Matej BREŠAR Jeziki / Languages:

Predavanja / Lectures:

SLOVENSKO/SLOVENE


Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:

Prerequisits:

Poznavanje teorije grup. Knowledge of group theory.

Vsebina:


Kategorije: osnovni pojmi in primeri. Kolobarji: osnovni pojmi in primeri; glavni kolobarji, faktorizacija; posebni razredi kolobarjev. Moduli: osnovni pojmi in primeri; posebni razredi modulov. Polja: končne razširitve, algebraične razširitve; razpadna polja, algebraično zaprta polja; konstruktibilna števila; osnove Galoisjeve teorije.

Categories: basic concepts and examples. Rings: basic concepts and examples; principal ideal domains, factorization; special classes of rings. Modules: basic concepts and examples; special classes of modules. Fields: finite extensions, algebraic extensions; splitting fields, algebraically closed fields; constructible numbers; fundamentals of Galois theory.

Temeljni literatura in viri / Readings: W. Y. Gilbert, W. K. Nicholson, Modern algebra with applications, Chichester: Wiley, 2004. I. N. Herstein, Topics in algebra, Xerox, 1975. T. W. Hungerford, Algebra, Springer-Verlag, 1980. S. Lang, Undergraduate algebra, Springer, 2005. I. Vidav, Algebra, DMFA, 1980.



Poglobiti znanje nekaterih osnovnih področij abstraktne algebre.

Deepening the knowledge of some fundamental areas of abstract algebra..




• Teorije kolobarjev in modulov • Teorije polj


• Ring and module theory • Field theory


• Algebraične strukture so pojavljajo na vseh matematičnih področjih, zato mora biti profesionalni matematik z njimi poglobi znanje.


• Algebraic structures appear in all mathematical areas, and therefore their knowledge is necessary for every professional mathematician.



• Predavanja • Seminarske vaje

• Lectures • Tutorial



Assessment:

Pisni izpit

100%

Written exam

Reference nosilca / Lecturer's references: 1. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, ŠPENKO, Špela. Lie superautomorphisms on associative algebras, II. Algebr. represent. theory, 2012, vol. 15, no 3, str. 507-525. http://dx.doi.org/10.1007/s10468-010-9254-2. [COBISS.SI-ID 16299353]

2. BIERWIRTH, Hannes, BREŠAR, Matej, GRAŠIČ, Mateja. On maps determined by zero products. Commun. Algebra, 2012, vol. 40, no. 6, str. 2081-2090. http://dx.doi.org/10.1080/00927872.2011.570833. [COBISS.SI-ID 16315481]

3. ALAMINOS, J., BREŠAR, Matej, ŠEMRL, Peter, VILLENA, A. R. A note on spectrum-preserving maps. J. math. anal. appl., 2012, vol. 387, iss. 2, str. 595-603. http://dx.doi.org/10.1016/j.jmaa.2011.09.024. [COBISS.SI-ID 16067673]

4. BREŠAR, Matej, ŠPENKO, Špela. Determining elements in Banach algebras through spectral properties. J. math. anal. appl., 2012, vol. 393, iss. 1, str. 144-150. http://dx.doi.org/10.1016/j.jmaa.2012.03.058. [COBISS.SI-ID 16287833]

5. BREŠAR, Matej. Multiplication algebra and maps determined by zero products. Linear multilinear algebra, str. 763-768. http://dx.doi.org/10.1080/03081087.2011.564580. [COBISS.SI-ID 16310105]

http://dx.doi.org/10.1007/s10468-010-9254-2


http://dx.doi.org/10.1080/00927872.2011.570833






http://dx.doi.org/10.1080/03081087.2011.564580









Študijska smer

Study field

Letnik

Academic

year

Semester

Semester

Matematika 1 ali 2 1 ali 3

Mathematics 1 or 2 1 or 3



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 30 135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Jih ni. None.

Vsebina:




optimizacije:



programiranje.



algoritem.













problem.








se mreže.










seznama:




Problem urnika.


strojev.

















list:


programming.




processors.

Stock optimization.



















gospodarstva.












modeliranja.










optimizacije.






























sciences.









predmeta.

























of the results.


Assessment:


naloge, projekt)

Seminarska naloga

Ustni izpit





Delež (v %) /

Weight (in %)

80%,

20%


project):

Coursework report

Oral exam






references:
















15651862]

http://dx.doi.org/10.1007/s00453-011-9562-x








http://dx.doi.org/10.1080/00207160.2011.638375



Predmet: Magistrsko delo in magistrski izpit

Course title: Master Work and Master Exam



Letnik Academic

year

Semester Semester

Matematika, 2. stopnja 2. 4.

Mathematics, 2nd

degree 2. 4.



Predavanja Lectures

Seminar Seminar

Sem. vaje Tutorial


work



work ECTS

600 20

Nosilec predmeta / Lecturer: Izbrani mentor / Chosen Mentor

Jeziki / Languages:


/

Vaje / Tutorial: /

Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:

Prerequisits:

Opravljeni vsi predmeti na drugi stopnji študijskega programa Matematika

All subjects finished on the second degree of the study programme Mathematics

Vsebina:


Študent se nauči osnovna področja matematike

in svoje znanje zagovarja na magistrskem

izpitu.

Študent se nauči snov, ki mu jo poda mentor, in

napiše magistrsko delo ter ga predstavi na

zagovoru magistrskega dela.

Student learns the basic fields of general

mathematics and defends his knowledge in the

master exam.

Student learn a subject given by a mentor and

writes his master work and presents it at the

defence of the master work.

Temeljni literatura in viri / Readings: Študijski vir poda mentor / Textbooks are given by a mentor.



Uspešno zagovarjati magistrsko delo in opraviti

magistrski izpit Successfully finish master work and master

exam.




- pomembnih konceptov matematike: Analiza

in Algebra.

Knowledge and understanding:

- important koncepts of mathematics: Analysis,

Algebra.



Samostojno delo Individual work



Assessment:

- magistrski izpit

- magistrsko delo

50%

50%

- master exam

- master work



Predmet: Matematične osnove računalniških omrežij

Course title: Mathematical Foundations of Computer Networks



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30 135 7

Nosilec predmeta / Lecturer: Andrej TARANENKO

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Matematične osnove in teorija računalniških

omrežij: terija grafov, usmerjevalni postopki,

dodeljevanje frekvenc.

Omrežni račun.

Omrežno upravljanje in varnost.

Kriptografija in varnost v omrežjih: uporaba

teorije števil, klasični kriptografski algoritmi,

kriptografija z javnimi ključi, digitalni podpisi.

Petrijeve mreže in uporaba pri analizi

računalniških omrežij.

Modeliranje omrežnega prometa.

Mathematical principles and theory of computer

networks: graph theory, routing algorithms,

frequency assignment.

Network calculus.

Network menagement and security.

Cryptography and network security: number

theory, clasical encription algorithms, public-

key cryptography, digital signatures.

Application of Petri Nets to

Communication Networks.

Network traffic modeling.

Medomrežno povezovanje in zaščita: varnostni

zid.

Inter-network communications and security:

firewall.


T. Vidmar: Računalniška omrežja in storitve, Atlantis, 1997.

A. Kumar, D. Manjunath, and J. Kuri: Communication Networking: An Analytical Approach,

Elsevier, 2004.

James D. McCabe: Practical Computer Network Analysis and Design. Morgan Kaufmann

Publishers, 1998.

William Stallings: Cryptography and Network Security: Princpiles and Practice. Prentice Hall,

2003.

J. Billington, M. Diaz, G. Rozenberg: Application of Petri Nets to Communication Networks.

Springer, 1999.

Thomas G. Robertazzi: Computer Networks and Systems. Springer-Verlag, 2000.

W. Mao: Modern cryptography : theory and practice, Upper Saddle River, Prentice-Hall, 2004.



Poglobiti znanje iz matematičnih osnove,

teorije in temeljnih koncepte računalniških

omrežij. Nadgraditi znanja pridobljena pri

drugih predmetih (diskretne matematiki,

algoritmih,...) za potrebe računalniških omrežij.

Deepen the knowledge of mathematical theory

and fundamental concepts of computer

networks. Upgrade the knowledge obtained with

other subjects (algorithms, discrete mathematics,

...) for computer networks.




• Razumeti matematične principe in

teorijo

• Poglobiti znanje iz algoritmov za

usmerjanje ter algoritmov za dodeljevanje

frekvenc.

• Poglobiti znanje iz osnov varnosti in

zaščite podatkov v računalniških omrežjih


• Pridobljena znanja se prenašajo na

druge z računalništvom povezane predmete.


• To understand mathematical principles

and theory

• To deepen the knowledge of routing

algorithms and frequency assignment

algorithms.

• To deepen the knowledge of basics of

network security

• To understand secure data transmission

methods


• The obtained knowledge is transferable

to the other computer science oriented subjects.



Predavanja

Računalniške vaje

Lectures

Computer exercises


Assessment:



na semester)

Izpit:






Delež (v %) /

Weight (in %)

50%

50%

Mid-term testing:



Exams:







references:







ID19464968]










ID 15383641]













Predmet: Multivariatne statistične metode

Course title: Multivariate statistics methods



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30 135 7

Nosilec predmeta / Lecturer: Dominik BENKOVIČ

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Poznavanje splošne (osnovne) statistike. Knowledge of general (basic) statistics.


• Uvod v multivariatno analizo: Osnove

statistične analize podatkov. Variančno-

kovariančna matrika in korelacijska matrika.

Standardiziranje podatkov. Grafična

predstavitev multivariatnih podatkov.

• Razvrščanje v skupine: Proces

razvrščanja v skupine. Mera podobnosti in

različnosti. Optimizacija in kriterijske funkcije.

Hierarhične metode (minimalna, maksimalna,

Wardova,...) in nehierarhične metode (metoda

voditeljev). Dendrogram. Določanje števila

• Introduction to multivariate analysis:

Basic statistical data analysis. Variance-

covariance matrix and correlation matrix. Data

standardization. Graphical representation of

multivariate data.

• Clustering: Clustering process. Measure

of similarity and dissimilarity. Optimization and

criteria functions. Hierarchical methods

(minimal, maximal, Ward's) and non-

hierarchical methods (k-means clustering).

Dendrogram. Choosing the number of clusters.

skupin. Grafična predstavitev večrazsežnih

podatkov.

• Metoda glavnih komponent:

Večrazsežnost podatkov. Korelacijska matrika.

Komunalitete in pojasnjena varianca.

Določanje števila glavnih komponent.

• Faktorska analiza: Manifestne in

latentne spremenljivke. Splošni faktorski model

in ocenjevanje. Metode faktorske analize

(metoda glavnih osi, metoda največjega

verjetja). Pravokotne in poševne rotacije.

• Diskriminantna analiza: Predpostavke.

Diskriminantni kriterij. Pravila uvrščanja enot v

skupine. Diskriminantna funkcija in

klasifikacijska tabela. Pomen napovednih

spremenljivk in centroidov.

• Kanonična korelacijska analiza:

Kanonične rešitve. Kanonične in strukturne

uteži.

Graphical representation of high-dimensional

data.).

• Principal component analysis: High-

dimensional data space. Correlation matrix.

Comunalities and explained variance. Choosing

the number of principal components.

• Factor analysis: Manifest and latent

variables. Factor model and estimation. General

factor model and estimation. Factor analysis

methods (principal axis factoring and maximum

likelihood). Orthogonal and oblique rotations.

• Discriminant analysis: Assumptions.

Discriminant kriteria. Classification rules.

Discriminant function and classification table.

Importance of manifest variables and centroids.

• Canonical correlation analysis:

Canonical solutions. Canonical and structure

loadings.


1.Dillon W.R. in Goldstein M.: Multivariate Analysis, Wiley, New York, 1984.

2.Mardia K.V., Kent J.T. in Billy J.m.: Multivariate Analysis, Academic Press, London, 1979.

3.Sharman S.: Applied multivariate tecniques, Wiley, New York, 1996.

4.Ferligoj A.: Razvrščanje v skupine, Metodološki zvezki, 4, FSPN, Ljubljana, 1989.

5.Omladič V.: Uporaba linearne algebre v statistiki, Metodološki zvezki, 13, FDV, Ljubljana,

1997.



Glavni cilj predmeta je proučiti

najpomembnejše koncepte, metode in rezultate

multivariatne analize.

The main goal of the course is to study the

fundamental concepts, methods and results of

multivariate analysis.




• Razumevanje in poznavanje osnovnih

pojmov multivariatne analize.

• Razumevanje, izvajanje in interpretacija

različnih metod multivariatne analize.

• Obvladanje ustrezne programske

opreme za namene statističnega raziskovanja.


• Prenos znanja iz statistike na različna

strokovna in znanstvena področja, kjer se

uporabljajo metode multivariatne analize.


• Understanding and knowledge of the

basic concepts of multivariate analysis.

• Understanding, correct application and

interpretation of different methods of

multivariate analysis.

• Knowledge of using an appropriate

software for statistical research.


• Knowledge transfer of statistical methods

into different areas dealing with multivariate

analysis methods.



• Predavanja

• Laboratorijske vaje

• Projekt

• Lectures

• Laboratory exercises

• Project


Assessment:


naloge, projekt)

- Pisni test – praktični del

- Izpit (ustni) – teoretični del

- Projekt

- Vsaka izmed naštetih obveznosti

mora biti opravljena s pozitivno

oceno.

- Pozitivna ocena pri pisnem testu je


Delež (v %) /

Weight (in %)

50%

30%

20%


project):

- Written test – practical part

- Exam (oral) – theoretical part

- Project

- Each of the mentioned commitments

must be assessed with a passing

grade.

- Passing grade of the written test is



references:

1. BENKOVIČ, Dominik, EREMITA, Daniel. Multiplicative Lie n-derivations of triangular rings.

Linear algebra appl.. [Print ed.], 2012, vol. 436, iss 11, str. 4223-4240.

http://dx.doi.org/10.1016/j.laa.2012.01.022. [COBISS.SI-ID 16278361]

2. BENKOVIČ, Dominik, ŠIROVNIK, Nejc. Jordan derivations of unital algebras with

idempotents. Linear algebra appl.. [Print ed.], 2012, vol. 437, iss. 9, str. 2271-2284.

http://dx.doi.org/10.1016/j.laa.2012.06.009. [COBISS.SI-ID 16410201]

3. BENKOVIČ, Dominik. Lie triple derivations on triangular matrices. Algebra colloq., 2011, vol.

18, spec. iss. 1, str. 819-826. http://www.worldscinet.com/ac/18/preserved-

docs/18spec01/S1005386711000708.pdf. [COBISS.SI-ID 16204377]

4. LI, Yanbo, BENKOVIČ, Dominik. Jordan generalized derivations on triangular algebras.

Linear multilinear algebra, 2011, vol. 59, no. 8, str. 841-849.


5. BENKOVIČ, Dominik. Generalized Lie derivations on triangular algebras. Linear algebra

appl.. [Print ed.], 2011, vol. 434, iss 6, str. 1532-1544. [COBISS.SI-ID 15863897]


Predmet: Napredni algoritmi

Course title: Advanced algorithms



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30 135 7

Nosilec predmeta / Lecturer: Aleksander Vesel

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Razreda NP in P. Primeri NP-polni polnih

problemov. Problemi kombinatorične

optimizacije.

Algoritmi urejanja in njihova zahtevnost.

Iskanje niza v besedilu. Klasični algoritmi:

Boyer-Mooreov algoritem, Knuth-Morris-

Prattov algoritem. Priponska drevesa:

Ukkonenov algoritem in Weinerjev algoritem.

Neeksaktno iskanje niza.

Aproksimacijski algoritmi. Lokalno iskanje.

Classes NP and P. NP-complete problems.

Combinatorial optimization problems.

Sorting algorithms in their complexity.

String matching. Classical methods: Boyer-

Moore algorithm, Knuth-Morris-Pratt algorithm.

Suffix trees: Ukkonen's algorithm, Weiner's

algoritem. Inexact matching.

Approximation algorithms. Local search.

Fundamentals of heuristics and metaheuristics

methods.

Osnove hevrističnih in metahevrističnih

algoritmov.

Zahtevnejša analiza algoritmov. Metoda

amortiziranih stroškov.

Advanced algorithm analysis. Amortized

analysis.


M. A. Weiss, Data Structures and Algorithm Analysis in C++, Addison-Wesley, 2007.

C.H. Papadimitriou, K. Steiglitz, Combinatorial Optimization - Algorithms and Complexity,

Prentice-Hall, 1998.

M. Dorigo, T. Stutzle, Ant colony optimization, MIT Press, 2004.

D. Gusfield, Algorithms on strings, trees and sequences, Cambridge University Press, 1999.

M. Mitchell, An introduction to genetic algorithms, MIT Press, 2002.



Poglobiti znanje iz izbranih algoritmov, tehnik

zahtevnejših analiz algoritmov in osnov teorije

NP-polnosti. Poglobiti znanje iz načinov

reševanja težkih (grafovskih) problemov.

Predstaviti algoritme iskanja niza.

To deepen the knowledge of selected

algorithms, techniques for advanced algorithm

analysis and the principles of NP-completeness

theory. To deepen the knowledge of skills for

solving hard (graph) problems. To present string

matching algorithms.




- Poglobiti znanje iz osnovnih in zahtevnejših

grafovskih algoritmov.

- Prepoznati težke probleme.

- Razumeti pomen aproksimacijskih

algoritmov.

- Poglobiti znanje iz različnih vrst

hevrističnih in metahevrističnih tehnik.

- Razumevanje zahtevnejših postopkov

analize algoritmov.


- Prenos znanja algoritmičnih tehnik na druga

področja (diskretna matematika, biologija,

ekonomija, ...).


To deepen the knowledge of elementary

and advanced graph algorithms

To recognize hard problems.

To understand the importance of

approximation algorithms.

To deepen the knowledge of a variety of

heuristics and metaheuristics techniques.

To understand techniques for advanced

algorithm analysis


- Knowledge transfer of algorithmic

techniques into other fields (discrete

mathematics, computer science, biology,

economics, …).



Predavanja

Računalniške vaje

Lectures

Computer exercises


Assessment:


Projekt


na semester)

Izpit:






Delež (v %) /

Weight (in %)

40%

40%

20%

Mid-term testing:

Project



Exams:







references:












iss. 11, str. 2565-2569. http://dx.doi.org/10.1016/j.dam.2009.02.016. [COBISS.SI-ID 15142489]







UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Operacijske raziskave z matematičnim programiranjem Course title: Operations research with mathematical programming



Letnik Academic

year

Semester Semester

Matematika 2. stopnja 1. ali 2. 1. ali 3. Mathematics 2nd degree 1. or 2. 1. or 3.


Predavanja Lectures

Seminar Seminar

Sem. vaje Tutorial


work



work ECTS

45 30 135 7 Nosilec predmeta / Lecturer: Drago Bokal Jeziki / Languages:


SLOVENSKO/SLOVENE

Vaje / Tutorial: SLOVENSKO/SLOVENE Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:

Prerequisits:

Poznavanje enostavnih algoritmov. Poznavanje osnov linearne algebre in vektorske analize. Predmet matematično modeliranje.

Knowledge of simple algorithms. Knowledge of basic linear algebra and calculus. Predmet matematično modeliranje.

Vsebina:


Obvezna vsebina, ki pri študentih vzpostavi temeljni nabor znanj s področja operacijskih raziskav in matematičnih programov:

• Nevezani ekstrem, Newtonova metoda. • Vezani ekstrem. Lagrangeovi

multiplikatoriji. Potrebni in zadostni pogoji za nastop vezanega lokalnega ekstrema. Wolfe-ov dual konveksnega programa.

• Kvadratično programiranje. Lagrangeovske metode in metoda aktivne množice. Programi z linearnimi vezmi. Cikcakanje.

• Nelinearno programiranje. Kazenska in odbojna funkcija. Langrange-Newtonova methoda (SQP).

• Stožčasto programiranje. Lorentzov in semidefinitni stožec. Stožčasto kvadratično programiranje.

• Semidefinitno programiranje. Aplikacije v kombinatorični optimizaciji.

• Metoda notranje točke za linearno in konveksno programiranje. Dokaz obstoja centralne poti. Primarno-dualna metoda sledenja centralni poti.

V okviru vsebine študentje izberejo zahtevnejši problem, s katerimi se poglobljeno ukvarjajo pri seminarski nalogi. Problem je povezan z njihovo bodočo kariero (praktični problemi iz gospodarstva, teoretični problemi iz teorije matematičnega programiranja in pripadajočih numeričnih algoritmov). Preostala predavanja se prilagodijo problemom, ki so jih izbrali študentje, in obsegajo vsebine z naslednjega seznama:

• Robustna optimizacija po metodi cene robustnosti.

• Imunizacija portfelja in stohastično programiranje.

• Stohastično nelinearno programiranje (diskretna in zvezna slučajna spremenljivka). Dekompozicija.

• Aplikacijie semidefinitnega programiranja: kvadratični problem prirejanja, problem trgovskega potnika, problem maksimalnega prereza grafa.

• Aplikaciji stohastičnega programiranja: Markowitzevi modeli optimizacije portfelja, modeli večfaznega stohastičnega načrtovanja.

• Modeli največjega verjetja, metoda najmanjših kvadratov, umerjanje modelov na znane podatke, inverzni problemi, druge podatkovne analize.

• Optimizacijski matematični modeli s področja kontrolnih sistemov, obdelave signalov.

• Metoda podpornih vektorjev. • Druge vsebine s področja operacijskih

raziskav in matematičnega modeliranja, povezane s študentskimi projekti.

Mandatory content, that familiarizes the students with fundamentals of operations research and mathematical programs:

• Unconstrained optimization. Newton's method.

• Constrained optimization. Lagrange multipliers. Necessery and sufficient conditions for a constrained local optimum. Dual of a convex program.

• Quadratic programming. Lagrange methods and active set methods. Programs with linear constraints. Zigzagging.

• Nonlinear programming. Penalty and barrier functions. Lagrange-Newton method. Sequential Quadratic Programming.

• Conic programming. Lorentz and semidefinite cone. Conic quadratic programming.

• Semidefinite programming. Applications in combinatorial optimization.

• Interior point methods for linear and convex programming. Existence of the central path. Primal-dual methods of following the central path.

Within the coursework, the students select smaller problems whose result are coursework reports. The problems are related to their future career (practical problems from industry and business, theoretical problems from the areas of optimization, algorithms, modelling). The content of the remaining lectures is selected according to these projects from the following list:

• Price of robustness robust optimization method.

• Portfolio immunization using stohastic programming.

• Stohastic nonlinear programming (discrete and continuous stohastic variables). Decomposition.

• Applications of semidefinite programming: quadratic assignment problem, travelling salesman problem, max cut problem.

• Applications of stohastic programming: Markowitz models of portfolio optimization, multiperiod stohastic planning models.

• Maximum likelihood models, least squares method, parameter fitting for given data.

• Optimization mathematical models from control theory and signal processing.

• Support Vector Machine. • Other content from the domain of operations

research and mathematical programming, related to students' problems.

Within their coursework and exercisces, the students familiarize themselves with software for mathematical modelling, either commercial (Excel, Lindo, Matlab) or freely avaliable open source

V okviru seminarskih nalog se študentje srečajo tudi s programsko opremo za matematično modeliranje. komercialno (Excel, Lindo, Matlab) oz. prostodostopno in odprtokodno (SciLab, NEOS, R).

(SciLab, Neos, R).

Temeljni literatura in viri / Readings: R. Rardin. Optimization in Operations Research. Prentice Hall, Inc., Upper Saddle River, New Jersey, 2000. J. Curwin, R. Slater. Quantitive Methods for Business Decisions. Third Edition. Chapman & Hall, London, 1991. S. A. Zenios, Financial Optimization. Cambridge University Press, Cambridge, 1993. R. Fletcher, Practical Methods of Optimization. Second Edition. Wiley, Chichester, 2001. A. Ben-Tal, A. Nemirowski: Lectures on modern convex optimization. H. Milton Stewart School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, 2012. C. Huang, R. H. Litzenberger. Foundations for Finacial Economics. Prentice Hall, Inc., Upper Saddle River, New Jersey, 1988. P. Kall, S. W. Wallace. Stochastic Programming. Wiley, Chichester, 1994. L. Neralić, Uvod u matematičko programiranje 1. Udžbenici Sveučilišta u Zagrebu, Zagreb, 2001. R. Rardin. Optimization in Operations Research. Prentice Hall, Inc., Upper Saddle River, New Jersey, 2000. J. Renegar. A Mathematical View of Interior-Point Methods in Convex Optimization. MPS-SIAM Series on Optimization. SIAM, Philadelphia, 2001. S. A. Zenios, Financial Optimization. Cambridge University Press, Cambridge, 1993. Cilji in kompetence:


Usvojiti proces matematičnega modeliranja na zveznih optimizacijskih problemih. Razviti kompetenco samostojnega apliciranja matematičnih metod na probleme iz finančne optimizacije, ekonomije, ter širše iz gospodarstva. Spoznati tehnološka orodja, s katerimi se srečujemo pri reševanju optimizacijskih problemov in problemov matematičnega modeliranja.

Familiarize the students with the process of mathematical modelling of continuous optimization problems. Develop competent skills of independent application of mathematical methods to the problems from financial optimization, economics, and broader from industry. Familiarize the students with technological tools that assist solving optimization problems and problems related to mathematical modelling.



Znanje in razumevanje: • Razumevanje zahtevnejših principov matematičnega

programiranja. • Poglobi znanje iz sodobnih numeričnih metod za

reševanje matematičnih programov. • Poglobiti znanje iz Markowitzevih modelov in

drugih zahtevnih aplikacij matematičnega programiranja v finančni optimizaciji in širše.

Prenesljive/ključne spretnosti in drugi atributi: • Direktne aplikacije v finančni matematiki,

Knowledge and Understanding: • To be able to understand advanced principles of

mathematical programming. • To deepen the knowledge of modern numerical

methods for solving mathematical programs. • To deepen the knowledge of details of Markowitz

models and other advanced applications of mathematical programming, financial optimization and wider.


ekonomiji, poslovnih vedah, inžinirstvu, fiziki in številnih drugih družboslovnih in naravoslovnih vedah.

• Suvereno obvladovanje procesa matematičnega modeliranja in uporabe tehnik matematičnega progamiranja v problemih s področja finančne optimizacije, ekonomije in širše.

• Direct applications in finacial mathematics, economy, business, engineering, physics, and numerous other social and natural sciences.

• Competent mastering of the process of mathematical modelling and applications od its techniques in problems from financial optimization, economics, and wider.



• Pri predavanjih študentje spoznajo snov predmeta. • V okviru seminarskih vaj študentje razumevanje

snovi utrjujejo na večjem projektu, povezanem z njihovo bodočo kariero. Razporejeni so v večje skupine, ki po metodah problemskega učenja obravnavajo izbrani problem od zbiranja podatkov, preko razvoja modela, izbora in prilagajanja ustreznih tehnoloških rešitev do razmisleka o implementaciji rešitve. Koncept poučevanja je podrobneje predstavljen kot ciljni aplikativni predmet.

• At the lectures, the students are familiarized with the

course content. • At the tutorials, the student deepen their

understanding of the material by working on an extensive problem related to their future career. They are organized in larger groups who research the choosen problem guided by methodologies of problem-based learning. Within solving the problem, they experience all the stages from requirements and data gathering, model development, selecting and adapting technological solutions to discussing various aspects of implementation of the results.


Assessment:

Način (pisni izpit, ustno izpraševanje, naloge, projekt) Seminarska naloga Ustni izpit Vsaka izmed naštetih obveznosti mora biti opravljena s pozitivno oceno. Pozitivna ocena pri seminarski nalogi je pogoj za pristop k izpitu.

Delež (v %) / Weight (in %) 80% 20%

Type (examination, oral, coursework, project): Coursework report Oral exam Each of the mentioned commitments must be assessed with a passing grade. Passing grade of the seminar exercise is required for taking the exam.


1. BOKAL, Drago, BREŠAR, Boštjan, JEREBIC, Janja. A generalization of Hungarian method and Hall's theorem with applications in wireless sensor networks. Discrete appl. math.. [Print ed.], 2012, vol. 160, iss. 4-5, str. 460-470. http://dx.doi.org/10.1016/j.dam.2011.11.007. [COBISS.SI-ID 16191577]

2. BOKAL, Drago, DEVOS, Matt, KLAVŽAR, Sandi, MIMOTO, Aki, MOOERS, Arne Ø.



Computing quadratic entropy in evolutionary trees. Comput. math. appl. (1987). [Print ed.], 2011, vol. 62, no. 10, str. 3821-3828. http://dx.doi.org/10.1016/j.camwa.2011.09.030. [COBISS.SI-ID 16059481]

3. ŽUNKO, Matjaž, BOKAL, Drago, JAGRIČ, Timotej. Testiranje modelov VaR v izjemnih okoliščinah. IB rev. (Ljubl., Tisk. izd.). [Tiskana izd.], 2011, letn. 45, št. 3, str. 57-67, tabele, graf. prikazi. [COBISS.SI-ID 10777884]

4. BOKAL, Drago, CZABARKA, Éva, SZÉKELY, László, VRT'O, Imrich. General lower bounds for the minor crossing number of graphs. Discrete comput. geom., 2010, vol. 44, no. 2, str. 463-483. http://dx.doi.org/10.1007/s00454-010-9245-4. [COBISS.SI-ID 15636057]

5. BEAUDOU, Laurent, BOKAL, Drago. On the sharpness of some results relating cuts and crossing numbers. Electron. j. comb. (On line). [Online ed.], 2010, vol. 17, no. 1, r96 (8 str.). http://www.combinatorics.org/Volume_17/PDF/v17i1r96.pdf. [COBISS.SI-ID 15638361]




http://dx.doi.org/10.1007/s00454-010-9245-4


http://www.combinatorics.org/Volume_17/PDF/v17i1r96.pdf


UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Osnove ekonometrije Course title: Basic econometrics



Letnik Academic

year

Semester Semester

Matematika 2. stopnja 1. ali 2. 1. ali 3.

Mathematics 2nd degree 1. or 2. 1. or 3.


Predavanja Lectures

Seminar Seminar

Sem. vaje Tutorial


work



work ECTS

45 30 135 7 Nosilec predmeta / Lecturer: Timotej JAGRIČ Jeziki / Languages:


SLOVENSKO/SLOVENE

Vaje / Tutorial: SLOVENSKO/SLOVENE Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:

Prerequisits:

Jih ni. Jih ni.

Vsebina:


- Uvod (Uvod v ekonometrijo, Ponovitev statistike);

- Multipli regresijski model (Uvod, Ocena parametrov, Lastnosti, Testiranje hipotez, Mere primernosti, linearne transformacije, napovedovanje);

- Neizpolnjevanje predpostavk (Specifikacija modela, Normalna porazdelitev, Multikolinearnost, Heteroskedastičnost, Avtokorelacija);

Slamnate spremenljivke.

-Introduction (Introduction to Econometrics, Statistics Review); -The Multiple Regression Model (Introduction, Estimating the Parameters, Properties, Hypothesis Testing, Goodness of Fit, linear transformations, forecasting); -Violations of Assumptions (Model Specification, Multicollinearity, Heteroskedasticity, Serial Correlation); - Dummy variables.

Temeljni literatura in viri / Readings: N. Gujarati (2003). Basic Econometrics – Fourth Edition. McGraw-Hill, New York. W. H. Green (2003). Econometric Analysis – Fifth Edition. Prentice Hall, New Jersey. G. S. Maddala (2003). Introduction to Econometrics – Third Edition. John Wiley & Sons, New York.



Študentje naj bi dobili znanja in spretnosti, ki so potrebna za ekonometrično analizo. V okviru predmeta se bodo študentje učili tradicionalne ekonometrične metode. Razumeli bodo bistvene razlike med časovnimi vrstami in presečnimi podatki. Študentje bodo dobili spretnosti, ki so potrebne za oblikovanje in razvoj enostavnih in multiplih regresijskih modelov. Obravnavane metode bodo razumeli do te mere, da jih lahko uporabijo na realnih ekonomskih bazah podatkov z uporabo sodobnih ekonometričnih programov.

The students will get the knowledge and skills of econometric analysis. In the course the students will learn traditional econometric methods. They will understand differences between the time series and cross sections data. The students will get the skills of construction and development of simple and multiple regression models. The students will be able to apply methods on real economic data bases with modern econometric software.



Znanje in razumevanje: - poznavanje osnovnih matričnih operacij in

njihova aplikacija v linearnih regresijskih modelih;

- razumevanje predpostavk, na katerih temeljijo linearni regresijski modeli;

- razumevanje posledic odstopanja modela

Knowledge and understanding: - Use of basic matrix operations and their

application to the linear regression model; - understand the assumptions of the linear

regression model - awareness of the implications for the model

departures from assumptions;

od teh predpostavk; - poznavanje principov statističnega

testiranja; - poznavanje uporabe računalniških

programov za ocenjevanje in testiranje ekonometričnih modelov;

- interpretacija in komentiranje rezultatov; sposobnost prebiranja literature s področja kvantitativnih ekonomskih analiz, ki temeljijo na ekonometriji.

- understand statistical testing principles; - use software in the estimation and testing

of econometric models; - interpret and discuss results; be able to understand quantitative econ. literature that uses econometric methods.



- predavanja (predavatelj bo podal študentom vsebino ključnih teorij in tehnik);

- vodene vaje v računalniški učilnici (primeri modeliranja in razprava o domačih nalogah);

- individualne konzultacije s predavateljem; - samostojno delo v računalniški učilnici, s

posebnim poudarkom na uporabi interneta (izdelava domačih nalog z uporabo računalnika, delo z ekonomskimi bazami podatkov, učna gradiva na internetu, spletne predstavitve predavanj iz ekonometrije);

- samostojni študij gradiva

- lectures (lecturer will provide students with knowledge of the fundamental theories and techniques);

- guided classes in computer room (sample modeling is done and the main problems of home assignments are discussed);

- teachers' consultations; - self study in computer room, in particular

with the Internet (making home assignments using PC, work with economic data bases, study guides on the Internet, looking through sets of slides in Econometrics);

- self study with literature



Assessment:

- pisni izpit 100% - written examination

Reference nosilca / Lecturer's references: 1. ŽUNKO, Matjaž, JAGRIČ, Timotej. Raven razkrivanja z metodo tvegane vrednosti v slovenskih poslovnih bankah. Banč. vestn., apr. 2012, letn. 61, št. 4, str. 42-46. [COBISS.SI-ID 10994460]


2. ZDOLŠEK, Daniel, JAGRIČ, Timotej. Audit opinion identification using accounting ratios : experience of United Kingdom and Ireland. Aktual. probl. ekon., 2011, no. 1 (115), str. 285-310, graf. prikazi, tabele. [COBISS.SI-ID 10625564]

3. BEKŐ, Jani, JAGRIČ, Timotej. Demand models for direct mail and periodicals delivery services : results for a transition economy. Appl. econ., apr. 2011, vol. 43, no. 9, str. 1125-1138, doi: 10.1080/00036840802600244. [COBISS.SI-ID 10071324]

4. JAGRIČ, Vita, JAGRIČ, Timotej. Primerjalna presoja bančnih bonitetnih modelov za prebivalstvo. Banč. vestn., 2011, letn. 60, št. 1/2, str. 48-52. [COBISS.SI-ID 10593052]

5. JAGRIČ, Timotej, JAGRIČ, Vita. A comparison of growing cell structures neural networks and linear scoring models in the retail credit environment : a case of a small EU and EMU member country. East. Europ. econ., nov-dec 2011, vol. 49, no. 6, str. 74-96, doi: 10.2753/EEE0012-8775490605. [COBISS.SI-ID 10975772]


http://dx.doi.org/10.1080/00036840802600244







Predmet: Osnove informacijske tehnologije

Course title: Basic of information technology



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30 135 7

Nosilec predmeta / Lecturer: Krista RIZMAN ŽALIK

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Informacijska teorija.

Merilo informacije,

enačba informacije,

entropija informacije.

Algoritmična informacijska teorija.

Uporaba informacijske teorije v strojnem

učenju: Bayesovo učenje, lučenje odločitvenih

dreves.

Uveljavljene in novejše metode in orodja

razvoja informacijskih sistemov in programske

opreme.

Information theory.

Data and information.

Measure of information equation,

entropy of information.

Algorithmic information theory.

The use of information theory in machine

learning:

Bayesian inference, learning decision trees.

Enforced and new methods and tools for

software development of information systems

development.

Arhitekture informacijskih sistemov:

podatkovno usmerjena, pretočna arhitektura,

arhitektura z virtualnim strojem, arhitektura

klica in vrnitve, aktualne komponente

arhitekture.

Arhitektura aplikacij za svetovni splet in

distribuirani objektni sistemi.

Vzporedno programiranje in koncepti

vzporednost, večnitnost, sinhronizacija.

Načrtovalni vzorci.

Architectures: data cantered, dataflow

architecture, virtual machine architecture, call

and return architecture, actual component

architecture.

Architecture of internet applications and

distributed object systems.

Concurrent programming and concept

concurrency, parallelism, multithreading,

synchronization.

Design patterns.


U. Mesojedec, Java, programiranje za internet, Pasadena, 1997.

M. Campione, K.Walrath, The Java tutorial : object-oriented programming for the Internet,

Addison-Wesley, 1996.

Stevens, P., Pooley, R., Using UML: software engineering with objects and components, Addison-

Wesley, 2000.

Erich Gamma, Design Patterns: Elements of Reusable Object-Oriented Software (Addison-Wesley,

1995.

Eric Reiss, Practical Information Architecture. Harlow, UK: Pearson Education, 2000.



Poglobiti znanje iz pojmov informacij in

elementov teorije informacij in obdelave

informacij.

The main objective is to deepen the knowledge

about information, elements of information

theory and information management.




Znanje temeljnih teoretičnih konceptov

informacij, obdelav informacij in teorije

informacij in obdelave informacij ter različnih

arhitektur.


The knowledge of basic theoretical foundations

of information, manipulation of information and

information theory and different architectures.



Predavanja

Računalniške vaje

Lectures

Computer exercises


Assessment:


naloge, projekt)

- Računalniške vaje

- Pisni izpit



oceno.

- Pozitivna ocena pri vajah je pogoj


Delež (v %) /

Weight (in %)

50%

50%


project):

- Computer exercises

- Written exam



grade.

- Passing grade of the exercises is



references:

1. RIZMAN ŽALIK, Krista, ŽALIK, Borut. Validity index for clusters of different sizes

and densities. Pattern recogn. lett. (Print). [Print ed.], Jan. 2011, vol. 32, iss. 2, str. 221-

234, doi: 10.1016/j.patrec.2010.08.007. [COBISS.SI-ID 14640150]

2. RIZMAN ŽALIK, Krista. Cluster validity index for estimation of fuzzy clusters of

different sizes and densities. Pattern recogn.. [Print ed.], Oct. 2010, vol. 43, iss. 10, str.

3374-3390, doi:10.1016/j.patcog.2010.04.025. [COBISS.SI-ID 14640406]

3. RIZMAN ŽALIK, Krista, ŽALIK, Borut. A sweep-line algorithm for spatial

clustering. Adv. eng. softw. (1992). [Print ed.], Jun. 2009, vol. 40, iss. 6, str. 445-451,

doi: 10.1016/j.advengsoft.2008.06.003. [COBISS.SI-ID 12450582]

4. RIZMAN ŽALIK, Krista. An efficient k'-means clustering algorithm. Pattern recogn.

lett. (Print). [Print ed.], July 2008, vol. 29, iss. 9, str. 1385-

1391. http://dx.doi.org/10.1016/j.patrec.2008.02.014. [COBISS.SI-ID 12121366]

5. RIZMAN ŽALIK, Krista. Discovering significant biclusters in gene expression

data. WSEAS transactions on information science and applications, Sep. 2005, vol. 2,

iss. 9, str. 1454-1461. [COBISS.SI-ID14906120]

http://dx.doi.org/10.1016/j.patrec.2010.08.007


http://dx.doi.org/10.1016/j.patcog.2010.04.025


http://dx.doi.org/10.1016/j.advengsoft.2008.06.003


http://dx.doi.org/10.1016/j.patrec.2008.02.014




Predmet: Programiranje v diskretni matematiki

Course title: Programming in discrete mathematics



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 15 45 165 9

Nosilec predmeta / Lecturer: Andrej Taranenko

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:








- Boolova algebra






mathematics.


- Bool algebra























modelov








algoritmov



predmete







applications



algorithms



subjects



Predavanja, seminar

Računalniške vaje

Lectures, seminary

Computer exercises


Assessment:


Seminarska naloga

Projekt


na semester)

Delež (v %) /

Weight (in %)

20%

20%

40%

Mid-term testing:

Seminary work

Project



Izpit:






20%

Exams:







references:







ID19464968]










ID 15383641]



















Študijska smer

Study field

Letnik

Academic

year

Semester

Semester

Matematika Modul R2 1 ali 2 1 ali 3

Mathematics Module R2 1 or 2 1 or 3



Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 30 135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Jih ni. None.

Vsebina:




optimizacije:



programiranje.



algoritem.













problem.








se mreže.










seznama:




Problem urnika.


strojev.

















list:


programming.




processors.

Stock optimization.



















gospodarstva.












modeliranja.










optimizacije.






























sciences.









predmeta.

























of the results.


Assessment:


naloge, projekt)

Seminarska naloga

Ustni izpit





Delež (v %) /

Weight (in %)

80%,

20%


project):

Coursework report

Oral exam






references:
















15651862]

http://dx.doi.org/10.1007/s00453-011-9562-x








http://dx.doi.org/10.1080/00207160.2011.638375



Predmet: Izbrani algoritmi

Course title: Selected algorithms



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45 15 45 165 9

Nosilec predmeta / Lecturer: Aleksander Vesel

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Razreda NP in P. Primeri NP-polni polnih

problemov. Problemi kombinatorične

optimizacije.

Algoritmi urejanja in njihova zahtevnost.

Iskanje niza v besedilu. Klasični algoritmi:

Boyer-Mooreov algoritem, Knuth-Morris-

Prattov algoritem. Priponska drevesa:

Ukkonenov algoritem in Weinerjev algoritem.

Neeksaktno iskanje niza.

Aproksimacijski algoritmi. Lokalno iskanje.

Classes NP and P. NP-complete problems.

Combinatorial optimization problems.

Sorting algorithms in their complexity.

String matching. Classical methods: Boyer-

Moore algorithm, Knuth-Morris-Pratt algorithm.

Suffix trees: Ukkonen's algorithm, Weiner's

algoritem. Inexact matching.

Approximation algorithms. Local search.

Fundamentals of heuristics and metaheuristics

methods.

Osnove hevrističnih in metahevrističnih

algoritmov.

Zahtevnejša analiza algoritmov. Metoda

amortiziranih stroškov.

Advanced algorithm analysis. Amortized

analysis.


M. A. Weiss, Data Structures and Algorithm Analysis in C++, Addison-Wesley, 2007.

C.H. Papadimitriou, K. Steiglitz, Combinatorial Optimization - Algorithms and Complexity,

Prentice-Hall, 1998.

M. Dorigo, T. Stutzle, Ant colony optimization, MIT Press, 2004.

D. Gusfield, Algorithms on strings, trees and sequences, Cambridge University Press, 1999.

M. Mitchell, An introduction to genetic algorithms, MIT Press, 2002.



Poglobiti znanje iz izbranih algoritmov, tehnik

zahtevnejših analiz algoritmov in osnov teorije

NP-polnosti. Poglobiti znanje iz načinov

reševanja težkih (grafovskih) problemov.

Predstaviti algoritme iskanja niza.

To deepen the knowledge of selected

algorithms, techniques for advanced algorithm

analysis and the principles of NP-completeness

theory. To deepen the knowledge of skills for

solving hard (graph) problems. To present string

matching algorithms.




Poglobiti znanje iz osnovnih in

zahtevnejših grafovskih algoritmov.

Prepoznati težke probleme.

Razumeti pomen aproksimacijskih

algoritmov.

Poglobiti znanje iz različnih vrst

hevrističnih in metahevrističnih tehnik.

Razumevanje zahtevnejših postopkov

analize algoritmov.


Prenos znanja algoritmičnih tehnik na

druga področja (diskretna matematika,

biologija, ekonomija, ...).


To deepen the knowledge of elementary

and advanced graph algorithms

To recognize hard problems.

To understand the importance of

approximation algorithms.

To deepen the knowledge of a variety of

heuristics and metaheuristics techniques.

To understand techniques for advanced

algorithm analysis


Knowledge transfer of algorithmic

techniques into other fields (discrete

mathematics, computer science, biology,

economics, …).



Predavanja, seminar

Računalniške vaje

Lectures, seminary

Computer exercises


Assessment:


Seminarska naloga

Projekt


na semester)

Izpit:






Delež (v %) /

Weight (in %)

20%

20%

40%

20%

Mid-term testing:

Seminary work

Project



Exams:







references:




















Predmet: Osnove programiranja v diskretni matematiki

Course title: Basic programming in discrete mathematics



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30 135 7

Nosilec predmeta / Lecturer: Aleksander VESEL

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:








- Boolova algebra






mathematics.


- Bool algebra























modelov








algoritmov



predmete







applications



algorithms



subjects



Predavanja

Računalniške vaje

Lectures

Computer exercises


Assessment:


Projekt


na semester)

Izpit:






Delež (v %) /

Weight (in %)

40%

40%

20%

Mid-term testing:

Project



Exams:







references:




















Predmet: Poglavja iz algebre

Course title: Topics from algebra



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

60

45

165 9

Nosilec predmeta / Lecturer: Matej BREŠAR

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:

Poznavanje teorije grup. Knowledge of group theory.


Kategorije: osnovni pojmi in primeri.

Kolobarji: osnovni pojmi in primeri; glavni

kolobarji, faktorizacija; posebni razredi

kolobarjev.

Moduli: osnovni pojmi in primeri; posebni

razredi modulov; tenzorski produkt modulov in

algeber.

Categories: basic concepts and examples.

Rings: basic concepts and examples; principal

ideal domains, factorization; special classes of

rings.

Modules: basic concepts and examples; special

classes of modules; tensor products of modules

and algebras.

Fields: finite extensions, algebraic extensions;

Polja: končne razširitve, algebraične razširitve;

razpadna polja, algebraično zaprta polja;

konstruktibilna števila; osnove Galoisjeve

teorije.

splitting fields, algebraically closed fields;

constructible numbers; fundamentals of Galois

theory.


W. Y. Gilbert, W. K. Nicholson, Modern algebra with applications, Chichester: Wiley, 2004.

I. N. Herstein, Topics in algebra, Xerox, 1975.

T. W. Hungerford, Algebra, Springer-Verlag, 1980.

S. Lang, Undergraduate algebra, Springer, 2005.

I. Vidav, Algebra, DMFA, 1980.



Poglobiti znanje nekaterih osnovnih področij

abstraktne algebre. Deepening the knowledge of some fundamental

areas of abstract algebra..




Teorije kolobarjev in modulov

Teorije polj


Algebraične strukture so pojavljajo na vseh

matematičnih področjih, zato mora biti

profesionalni matematik z njimi poglobi znanje.


Ring and module theory

Field theory


Algebraic structures appear in all mathematical

areas, and therefore their knowledge is

necessary for every professional mathematician



Predavanja

Seminarske vaje

Lectures

Tutorial


Assessment:


naloge, projekt)

Pisni izpit

Delež (v %) /

Weight (in %)

100%


project):

Written exam


references:

1. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, ŠPENKO, Špela. Lie superautomorphisms

on associative algebras, II. Algebr. represent. theory, 2012, vol. 15, no 3, str. 507-525.


2. BIERWIRTH, Hannes, BREŠAR, Matej, GRAŠIČ, Mateja. On maps determined by zero

products. Commun. Algebra, 2012, vol. 40, no. 6, str. 2081-2090.


http://dx.doi.org/10.1007/s10468-010-9254-2


http://dx.doi.org/10.1080/00927872.2011.570833


3. BREŠAR, Matej, MAGAJNA, Bojan, ŠPENKO, Špela. Identifying derivations through the

spectra of their values. Integr. equ. oper. theory, 2012, vol. 73, no. 3, str. 395-411.


4. BAHTURIN, Jurij Aleksandrovič, BREŠAR, Matej, KOCHETOV, Mikhail. Group gradings on

finitary simple Lie algebras. Int. j. algebra comput., 2012, vol. 22, no. 5, 1250046 (46 str.).

http://dx.doi.org/10.1142/S0218196712500464. [COBISS.SI-ID 16339545]

5. ALAMINOS, J., BREŠAR, Matej, ŠEMRL, Peter, VILLENA, A. R. A note on spectrum-

preserving maps. J. math. anal. appl., 2012, vol. 387, iss. 2, str. 595-603.

http://dx.doi.org/10.1016/j.jmaa.2011.09.024. [COBISS.SI-ID 16067673]

http://dx.doi.org/10.1007/s00020-012-1975-7


http://dx.doi.org/10.1142/S0218196712500464





Predmet: Tehnologija znanja

Course title: Knowledge technology



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30 135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Uvod: metode odkrivanja znanja, proces

odkrivanja znanja, naloge podatkovnega

rudarjenja, aplikacije podatkovnega rudarjenja,

uporaba odkritega znanja pri inteligentnih,

odločitvenih in ekspertnih sistemih.

Predstavitev znanja in operatorji: izjavni račun,

predikatni račun prvega reda, diskriminante in

regresijske funkcije, verjetnostne porazdelitve.

Osnovne teorije naučljivosti: teorija

Introduction to knowledge discovery methods,

process of knowledge discovery, tasks of data

mining, applications of data mining and the use

of discovered knowledge by intelligent, decision

and expert systems.

Knowledge presentation and operators: first

order predicate calculus, regression functions,

probability distribution.

Basic theory of learn ability, theory of

izračunljivosti in teorija rekurzivnih funkcij,

formalna teorija učenja, naučljivost glede na

lastnosti učnih funkcij, vhodnih podatkov in

konvergence učenja.

Podatki in modeli, vizualizacija podatkov,

jeziki in arhitektura sistemov podatkovnega

rudarjenja.

Metode podatkovnega rudarjenja:

Rudarjenje pogostih vzorcev, asociacij in

korelacij podatkov.

Klasifikacija in napoved: Bayesova

klasifikacija, Bayesove verjetnostne mreže,

odločitvena drevesa, nevronske mreže, metoda

podpornih vektorjev,

genetski algoritmi.

Analiza gruč: delitvene metode, hierarhične

metode, metode gostote, mrežno razvrščanje,

samoorganizirajoče nevronske mreže-

Kohonenova nevronska mreža, ugotavljanje

redkih vrednosti in napak.

Rudarjenje kompleksnih podatkov: prostorskih,

večpredstavnostnih, časovnih vrst in zaporedij,

besedil in vsebin svetovnega spleta.

computability, theory of recursive functions,

formal theory of learning, learn ability regarding

the characteristics of learning functions, input

data and learning convergence.

Data and models, data visualization, languages

and architecture of data mining systems.

Methods of data mining:

Mining of patterns, associations and data

correlations.

Classification and prediction: Bayes classifier,

Bayes probability nets, decision trees, neural

networks, support vector machines, genetical

algorithms.

Cluster analysis: partition methods, hierarchical

methods, grid-based methods , self organizing

neural networks- Kohonen neural networks,

outlier detection.

Data mining of complex data: spatial,

multidimensional, time series and sequences,

documents and contents of internet.


Ian H. Witten, Eibe Frank: Data Mining: Practical Machine Learning Tools and Techniques with

Java Implementations, Morgan Kaufmann, 2005.

J.Han, M.Kamber: Data Mining: Concepts and Techniques, Morgan Kaufmann, 2001.

I. Kononenko, Strojno učenje, Založba FE in FRI, 2005.



Predstaviti osnovne teorije naučljivosti, tehnike

predstavitve znanja in operatorje.

Predstaviti principe odkrivanja znanja v

ogromnih količinah zbranih podatkov in

uporabo znanja v inteligentnih sistemih.

The main objective is to provide students with a

theory of learnability, techniques of knowledge

presentation and operators.

To provide students with principles of

knowledge discovery in great amount of

collected data and the use of data in the

intelligent systems.




• Razumevanje temeljnih principov

predstavitve in zajemanja znanja, operatorjev in

osnovne teorije naučljivosti.

• Poznavanje metod za podatkovno

rudarjenje, tako da se lahko uporabijo ali

prilagodijo za reševanje trenutnih problemov.


Understanding of basic principles of data

presentation and comprising of

knowledge, operators and basic theory of

learnability.

Knowing of data mining methods in

such depth, that they can be used and

adapted to solve current problems.



• Predavanja

• Računalniške vaje

• Computer exercises

• Written exam


Assessment:


naloge, projekt)


- Pisni izpit



oceno.



Delež (v %) /

Weight (in %)

50%

50%


project):


- Written exam



grade.




references:

1. RIZMAN ŽALIK, Krista, ŽALIK, Borut. Validity index for clusters of different sizes and

densities. Pattern recogn. lett. (Print). [Print ed.], Jan. 2011, vol. 32, iss. 2, str. 221-234, doi:

10.1016/j.patrec.2010.08.007. [COBISS.SI-ID 14640150]

2. RIZMAN ŽALIK, Krista. Cluster validity index for estimation of fuzzy clusters of different

sizes and densities. Pattern recogn.. [Print ed.], Oct. 2010, vol. 43, iss. 10, str. 3374-3390, doi:

10.1016/j.patcog.2010.04.025. [COBISS.SI-ID 14640406]

3. RIZMAN ŽALIK, Krista, ŽALIK, Borut. A sweep-line algorithm for spatial clustering. Adv.

eng. softw. (1992). [Print ed.], Jun. 2009, vol. 40, iss. 6, str. 445-451, doi:

10.1016/j.advengsoft.2008.06.003. [COBISS.SI-ID 12450582]

4. RIZMAN ŽALIK, Krista. An efficient k'-means clustering algorithm. Pattern recogn. lett.

(Print). [Print ed.], July 2008, vol. 29, iss. 9, str. 1385-1391.

http://dx.doi.org/10.1016/j.patrec.2008.02.014. [COBISS.SI-ID 12121366]

5. RIZMAN ŽALIK, Krista. Discovering significant biclusters in gene expression data. WSEAS

transactions on information science and applications, Sep. 2005, vol. 2, iss. 9, str. 1454-1461.



Predmet: Temelji finančnega inženiringa

Course title: Foundations of financial engineering



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30

135 7

Nosilec predmeta / Lecturer: Miklavž MASTINŠEK

Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


1.Matematične osnove

2.Izvedeni finančni instrumenti

3.Tveganje in varnost

4.Opcije

5.Vrednotenje opcij, hedging

6.Binomski model

7.Black-Scholesov

8.Delta, gamma, sigma

9.Monte-Carlo metoda

10.Vodenje portfelja

11.Realne opcije

1.Mathematical tools

2.Financial derivatives

3.Risk and security

5.Option valuation, hedging

6.Binomial model

7.Black-Scholes model

8.The greeks

9.Monte-Carlo method

10.Portfolio management

11.Real options


1. Hull J., »Options, Futures and other Derivative Securities«, New Jersey, Prentice Hall Int.,

1996.

2. Wilmott P.« Paul Wilmott on Quantitative Finance«, John Wiley, (2000).

3. Cuthbertson K., »Financial engineering: derivatives and risk management«, Wiley,

(2001)






nalog in procesov s področja finančnega

inženiringa. Prav tako je namen predmeta dati

osnovo za spremljanje sodobne literature in

nadaljnje strokovno izpopolnjevanje.



of financial engineering.



new methods.





korektno vodenje poslov s področja finančnega

inženiringa.



teoretičnega dela. Zmožnost nadaljnega študija

novih kvantitativnih

metod finančnega inženiringa.



practical skills of financial engineering.









Written examination

Seminary work


Assessment:


naloge, projekt)

Pisni izpit

seminarska naloga

Delež (v %) /

Weight (in %)

80%

20%


project):

Written exam

Semynar


references:

1. MASTINŠEK, Miklavž. Charm-adjusted delta and delta gamma hedging. J. deriv., 2012, vol.

19, no. 3, str. 69-76, doi: 10.3905/jod.2012.19.3.069. [COBISS.SI-ID 10970908]

2. MASTINŠEK, Miklavž. Financial derivatives trading and delta hedging = Trgovanje z

izvedenimi finančnimi instrumenti ter delta hedging. Naše gospod., 2011, letn. 57, št. 3/4, str. 10-

http://dx.doi.org/10.3905/jod.2012.19.3.069


15. [COBISS.SI-ID 10733084]

3. MASTINŠEK, Miklavž. Descrete-time delta hedging and the Black-Scholes model with

transaction costs. Math. methods oper. res. (Heidelb.). [Print ed.], 2006, vol. 64, iss. 2, str. [227]-

236, doi: 10.1007/s00186-006-0086-0. [COBISS.SI-ID 8939292]

4. MASTINŠEK, Miklavž. Identifiability for a partial functional differential equation. Acta sci.

math. (Szeged), 2003, vol. 69, str. 121-130. [COBISS.SI-ID 7029276]

5. MASTINŠEK, Miklavž. Norm continuity for a functional differential equation with fractional

power. International journal of pure and applied mathematics, 2003, vol. 5, no. 1, str. 49-56.



http://dx.doi.org/10.1007/s00186-006-0086-0





Predmet: Teorija programskih jezikov

Course title: Theory of programming languages



Študijska smer

Study field

Letnik

Academic

year

Semester

Semester


Mathematics, 2nd




Predavanja

Lectures

Seminar

Seminar

Sem. vaje

Tutorial

Lab. vaje

Laboratory

work

Teren. vaje

Field work

Samost. delo

Individ.

work

ECTS

45

30 135 7


Jeziki /

Languages:

Predavanja /

Lectures:

SLOVENSKO/SLOVENE




Prerequisits:


Formalna logika kot programski jezik,

avtomatsko dokazovanje izrekov kot

interpretiranje nepostopkovnih programov.

Formalna semantika programskih jezikov:

operacijska semantika, denotacijska semantika,

aksiomatska semantika.

Uporaba semantike (dokazovanje pravilnosti in

lastnosti programov, statična analiza

programov).

Formal logic as programming languages,

automatic proof of lemas as interpreting of

nonprocedural programs.

Semantic of programming languages:

operational semantics, denotational semantics,

axiomatic semantics, the use of semantic

(proving of corectnes, characteristics of

programmes,

static analysis of programms).

Koncepti objektno usmerjenih jezikov: meta-

razred, podrazredi in podtipi, kovarianca in

kontravarianca, polimorfizem. Formalni opis

objektno usmerjenih jezikov.

Funkcijski programski jeziki.

Lambda kalkulus: proste in vezane

spremenljivke, redukcije, pretvorbe, rekurzija,

izračunljive funkcije,

typed lambda calculus, second-order lambda

calculus.

Basic concepts of object-oriented programming

languages : meta-class, subclass and subtype,

covariance in contravariance, polimorphism.

Formal description of object-oriented languages.

Functional programing languages. Lambda

calculus: free and bound variables, reduction,

conversions, recursions, computable functions,

typed lambda calculus, second-order lambda

calculus.


D. A. Watt: Programming Language Concepts and Paradigms, Prentice-Hall, New York 1990.

H.R. Nielson, F. Nielson. Semantics with Applications: A Formal

Introduction. John Wiley & Sons, Chichester, 1992.

M. Abadi, L. Cardelli. A Theory of Objects. Springer-Verlag, New York, 1996.

K. Bruce. Foundations of Object-Oriented Languages: Types and Semantics.

The MIT Press, 2002.

H. P. Barendregt. The Lambda Calculus: Its Syntax and Semantics. Studies

in Logic and the Foundations of Mathematics, Volume 103, North-Holland, 1984.

H. P. Barendregt. Introduction to Lambda Calculus. Workshop on

Implementation of Functional Languages, 1988.



Poglobiti znanje iz teoretičnih osnov

programskih jezikov. The main objective is to provide students with a

theoretical background of programming

languages.




- Teoretičnih osnov programskih jezikov


- Theoretical background of programming

languages



• Predavanja

• Računalniške vaje

• Computer exercises

• Written exam


Assessment:


naloge, projekt)


- Pisni izpit



oceno.

Delež (v %) /

Weight (in %)

50%

50%


project):


- Written exam



grade.






references:

1. RIZMAN ŽALIK, Krista, ŽALIK, Borut. Validity index for clusters of different sizes and

densities. Pattern recogn. lett. (Print). [Print ed.], Jan. 2011, vol. 32, iss. 2, str. 221-234, doi:

10.1016/j.patrec.2010.08.007. [COBISS.SI-ID 14640150]

2. RIZMAN ŽALIK, Krista. Cluster validity index for estimation of fuzzy clusters of different

sizes and densities. Pattern recogn.. [Print ed.], Oct. 2010, vol. 43, iss. 10, str. 3374-3390, doi:

10.1016/j.patcog.2010.04.025. [COBISS.SI-ID 14640406]

3. RIZMAN ŽALIK, Krista, ŽALIK, Borut. A sweep-line algorithm for spatial clustering. Adv.

eng. softw. (1992). [Print ed.], Jun. 2009, vol. 40, iss. 6, str. 445-451, doi:

10.1016/j.advengsoft.2008.06.003. [COBISS.SI-ID 12450582]

4. RIZMAN ŽALIK, Krista. An efficient k'-means clustering algorithm. Pattern recogn. lett.

(Print). [Print ed.], July 2008, vol. 29, iss. 9, str. 1385-1391.

http://dx.doi.org/10.1016/j.patrec.2008.02.014. [COBISS.SI-ID 12121366]

5. RIZMAN ŽALIK, Krista. Discovering significant biclusters in gene expression data. WSEAS

transactions on information science and applications, Sep. 2005, vol. 2, iss. 9, str. 1454-1461.


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