Preddoktorski izpit

2022/2023

Program:

Doktorski študijski program 3. stopnje Matematika in fizika

Smer:

Matematika

Letnik:

1 letnik

Semester:

prvi ali drugi

Vrsta:

obvezni

ECTS:

Jezik:

slovenski, angleški

Nosilec predmeta:

prof. dr. Matej Brešar, prof. dr. Miran Černe, prof. dr. Primož Potočnik

Ure na teden – 1. ali 2. semester:

Predavanja

Seminar

Vaje

Laboratorij

Obnovitev temeljnih matematičnih pojmov s področij analize, algebre, diskretna matematika, teoretičnega računalništva in verjetnosti.

S. Lang, "Undergraduate Algebra", Springer, New York, 2005.

S. Lang, "Undergraduate Analysis, 2nd edition", Springer, New York, 1997.

W. Rudin, "Principles of Mathematical Analysis, 3rd edition", McGraw-Hill, New York-Auckland-Düsseldorf, 1976.

J. H. van Lindt, R.M. Wilson, "A course in combinatorics", Cambridge University Press, Cambridge, 1992.

D. Stirzaker, "Probability and Random Variables, A beginner's guide", Cambridge University Press, 1999.

Michael Sipser, Introduction to the Theory of Computation, Cengage Learning (2013).

Cilj predmeta je študentom priskrbeti temeljno znanje, ki je potrebno za spremljanje naprednejših predmetov in za raziskovalno delo.

Študenti obnovijo osnovno matematično znanje, potrebno za njihovo nadaljne delo.

Samostojni študij in konzultacije.

Pisni izpit
Ocene: opravil, ni opravil

Matej Brešar:
BREŠAR, Matej. Functional identities on tensor products of algebras. Journal of algebra, ISSN 0021-8693, 2016, vol. 455, str. 108-136. [COBISS-SI-ID 17625945]
BREŠAR, Matej. Algebras in which non-scalar elements have small centralizers. Linear and Multilinear Algebra, ISSN 0308-1087, 2015, vol. 63, no. 9, str. 1864-1871. [COBISS-SI-ID 17160537]
BREŠAR, Matej, ŠPENKO, Špela. Functional identities of one variable. Journal of algebra, ISSN 0021-8693, 2014, vol. 401, str. 234-244.[COBISS-SI-ID 16842329]

Miran Černe:
ČERNE, Miran, ZAJEC, Matej. Boundary differential relations for holomorphic functions on the disc. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2011, vol. 139, no. 2, str. 473-484. [COBISS-SI-ID 15710553]
ČERNE, Miran, FLORES, Manuel. On Beurling's boundary differential relation. Israel journal of mathematics, ISSN 0021-2172, 2014, vol. 199, iss. 2, str. 831-840. [COBISS-SI-ID 17144153]
ČERNE, Miran. Beurling's boundary differential relations on multiply connected domains. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2015, vol. 428, iss. 1, str. 544-562. [COBISS-SI-ID 17270873]

Primož Potočnik:
BERČIČ, Katja, POTOČNIK, Primož. Two-arc-transitive two-valent digraphs of certain orders. Ars mathematica contemporanea, ISSN 1855-3966. [Tiskana izd.], 2016, vol. 11, no. 1, str. 127-146. [COBISS-SI-ID 1538308036]
POTOČNIK, Primož, WILSON, Stephen. Linking rings structures and semisymmetric graphs: Cayley constructions. European journal of combinatorics, ISSN 0195-6698, 2016, vol. 51, str. 84-98. [COBISS-SI-ID 17462361]
POTOČNIK, Primož, SPIGA, Pablo, VERRET, Gabriel. Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs. Journal of combinatorial theory. Series B, ISSN 0095-8956, 2015, vol. 111, str. 148-180. [COBISS-SI-ID 1537132228]