Introductory seminar

Overview of elementary functions.

Mathematical induction: examples and various applications.

Complex numbers: arithmetic, solving equations and systems of equations, absolute value, polar form, roots of unity.

Basics of set theory: sets, maps.

Basics of number theory: prime numbers, linear Diophantine equations with two variables (extended Euclidean algorithm), congruences.

Basics of combinatorial counting:
Basic principles of counting. Binomial and multinomial coefficients, set partitions, Stirling number of the first and second kind, Bell numbers, Lah numbers, partitions of integers. Twelve-fold way.

• Srednješolski učbeniki matematike.
• K. Cvetko Vah, D. Dolžan: Učbenik za proseminar. DMFA Založništo, 2014.
• G. Fijavž: Diskretne strukture, FRI, 2015, dostopno na http://matematika.fri.uni-lj.si/ds/ds.pdf
• M. Juvan, P. Potočnik: Teorija grafov in kombinatorika. Izbrana poglavja iz matematike in računalništva 39, DMFA Založništo, 2007.
• S. Klavžar, P. Žigert: Izbrana poglavja iz uporabne matematike, Pedagoška fakulteta, univerza v Mariboru, 2002.
• A. Cedilnik: Matematični priročnik, 2. izdaja, Didakta, Radovljica, 1997.

Through the examples in elementary mathematics the student learns the basic mathematical methods with an emphasis on logical thinking and principles of theorem proving.

Knowledge and understanding:
Students upgrade their high school knowledge of fundamental mathemematics and learn basic techniques for writing and proving mathematical statements.
Application: This is preparatory course for all mathematical courses.
Reflection: Understanding of basic mathematical concepts that are necessary for further studies.
Transferable skills: Student learns to read and understand a mathematical statement, distinguish assumptions from conclusions, and understand the deduction or proof.

Lectures, group and seminar work

Written exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Karin Cvetko Vah:
CVETKO-VAH, Karin, LEECH, Jonathan. Rings whose idempotents form a multiplicative set. Communications in algebra, ISSN 0092-7872, 2012, vol. 40, no. 9, str. 3288-3307. [COBISS-SI-ID 16432729]
CVETKO-VAH, Karin. On strongly symmetric skew lattices. Algebra universalis, ISSN 0002-5240, 2011, vol. 66, no. 1-2, str. 99-113. [COBISS-SI-ID 16219993]
CVETKO-VAH, Karin, DOLŽAN, David. Indecomposability graphs of rings. Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 2008, vol. 77, iss. 1, str. 151-159. [COBISS-SI-ID 14680409]
Primož Potočnik:
POTOČNIK, Primož, SPIGA, Pablo, VERRET, Gabriel. On the nullspace of arc-transitive graphs over finite fields. Journal of algebraic combinatorics, ISSN 0925-9899, 2012, vol. 36, no. 3, str. 389-401. [COBISS-SI-ID 16162137]
POTOČNIK, Primož. B-groups of order a product of two distinct primes. Mathematica slovaca, ISSN 0139-9918, 2001, vol. 51, no. 1, str. 63-67. [COBISS-SI-ID 10617433]
POTOČNIK, Primož, WILSON, Stephen. On the point-stabiliser in a transitive permutation group. Monatshefte für Mathematik, ISSN 0026-9255, 2012, vol. 166, no. 3-4, str. 947-504. [COBISS-SI-ID 15861081]