Predoctoral exam

2025/2026

Programme:

Doctoral Programme Mathematics and Physics

Orientation:

Mathematics

Year:

1 year

Semester:

first or second

Kind:

mandatory

ECTS:

Language:

slovenian, english

Course director:

Assist. Prof. Dr. Marko Kandić

Hours per week – 1. or 2. semester:

Lectures

Seminar

Tutorial

Lab

There are no prerequisites.

Revision of basic mathematical notions from the fields of analysis, algebra, discrete mathematics, theoretical computer science and probability.

S. Lang: Undergraduate algebra, 2nd ed., New York : Springer, cop. 1990.
S. Lang: Undergraduate analysis, 2nd ed., New York : Springer, cop. 1997.
W. Rudin: Principles of mathematical analysis, 3rd ed., Auckland : McGraw-Hill, cop. 1976.
J. H. van Lint, R. M. Wilson: A course in combinatorics, 2nd ed., Cambridge : Cambridge Univ. Press, 2001.
D. Stirzaker: Probability and random variables : a beginner's guide, Cambridge : Cambridge University, cop. 1999.
M. Sipser: Introduction to the theory of computation, 2nd ed. - Boston : Course Technology, cop. 2006.

The goal of the course is to provide the students with the background material needed for following the advanced classes and for mathematical research.

The students revise some basic background material needed for their future work.

Individual learning and concultations.

Written exam
Grades: pass, fail.

Marko Kandić:
KANDIĆ, Marko. On algebras of polynomially compact operators. Linear and Multilinear Algebra, ISSN 0308-1087, 2016, vol. 64, no. 6, str. 1185-1196. [COBISS-SI-ID 17493337]
KANDIĆ, Marko. Ideal-triangularizability of nil-algebras generated by positive operators. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2011, vol. 139, no. 2, str. 485-490. [COBISS-SI-ID 15710809]
DRNOVŠEK, Roman, KANDIĆ, Marko. Positive operators as commutators of positive operators. Studia Mathematica, ISSN 0039-3223, 2019, tom 245, str. 185-200. [COBISS-SI-ID 18407769]