Introductory seminar

2022/2023
Programme:
Financial mathematics, First Cycle
Year:
1 year
Semester:
first
Kind:
mandatory
ECTS:
4
Language:
slovenian
Lecturers:
Hours per week – 1. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)

Elementary functions: an overview (polynomials, rational, algebraic, exponential and logarithmic, trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic functions), properties, computation, graphing, solving equations and inequalities.

Basic of functions with more variables: domains and graphs of functions eith two variables

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

Indefinite and definite integral of function of one variable; elementary integrals,basic integration methods.

Readings
  • Srednješolski učbeniki matematike.
  • K. Cvetko Vah, D. Dolžan: Učbenik za proseminar. DMFA Založništo, 2014.
  • S. Klavžar, P. Žigert: Izbrana poglavja iz uporabne matematike, Pedagoška fakulteta, univerza v Mariboru, 2002.
  • A. Cedilnik: Matematični priročnik, 2. izdaja, Didakta, Radovljica, 1997.
  • P. Mizori-Oblak: Matematika za študente tehnike in naravoslovja I, Fakulteta za strojništvo, Ljubljana, 2003.
  • G. Tomšič, B. Orel, N. Mramor Kosta: Matematika I, Založba FE in FRI, Ljubljana, 2004.
Objectives and competences

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

Intended learning outcomes

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.

Learning and teaching methods

Lectures, group and seminar work

Assessment

Type (examination, oral, coursework, project):

Written exam

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

Lecturer's references

Karin Cvetko Vah:
– 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]
– 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, 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]

Primož Potočnik:
– 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]
– 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]

Aleš Vavpetič:

  • VAVPETIČ, Aleš, ŽAGAR, Emil. A general framework for the optimal approximation of circular arcs by parametric polynomial curves. Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2019, vol. 345, str. 146-158. [COBISS-SI-ID 18388057]
  • VAVPETIČ, Aleš. Commutators of cycles in permutation groups. Ars mathematica contemporanea, ISSN 1855-3966, 2016, vol. 10, no. 1, str. 67-77 [COBISS-SI-ID 17731929],
    – VAVPETIČ, Aleš. Afina in projektivna geometrija. Ljubljana: samozal. A. Vavpetič, 2011. VI, 114 str., ilustr [COBISS-SI-ID 15994969]