Introductory seminar A

There are no prerequisites.

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.
Analytic geometry in the plane: a straight line, conic sections, mutual position, polar coordinates.
Linear algebra: vectors in plane and space, computational operations, small systems of linear equations and inequalities.
Complex numbers: arithmetic, solving equations and systems of equations, polar form.
Algebra of polynomials: computation with polynomials, real and complex factorization, partial fractions.

1. A. Cedilnik: Matematični priročnik, 3. izd., Radovljica : Didakta, 2006.
2. K. Cvetko Vah, D. Dolžan: Učbenik za proseminar, Ljubljana : DMFA - založništvo, 2014.

Student revises, consolidates and upgrades the contents of high school mathematics, which are necessary for following the courses in the first year.

Knowledge and understanding: A thorough knowledge of calculus of elementary functions, solving equations and inequalities, calculating with complex numbers, and basic knowledge of plane geometry.
Application: This is preparatory course for Analysis 1 and Algebra 1.
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

exam or two midterm tests

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

Jaka Cimprič:
CIMPRIČ, Jaka. Real algebraic geometry for matrices over commutative rings. Journal of algebra, ISSN 0021-8693, 2012, vol. 359, str. 89-103. [COBISS-SI-ID 16315993]
CIMPRIČ, Jaka, MARSHALL, Murray, NETZER, Tim. Closures of quadratic modules. Israel journal of mathematics, ISSN 0021-2172, 2011, vol. 183, no. 1, str. 445-474. [COBISS-SI-ID 15998041]
CIMPRIČ, Jaka. Archimedean operator-theoretic Positivstellensätze. Journal of functional analysis, ISSN 0022-1236, 2011, vol. 260, iss. 10, str. 3132-3145. [COBISS-SI-ID 15997529]
Sašo Strle:
DRINOVEC-DRNOVŠEK, Barbara, STRLE, Sašo. Naloge iz analize 1 : z odgovori, nasveti in rešitvami. 2. izd. Ljubljana: DMFA - založništvo, ISSN 1408-0850, 2012, 285 str. Izbrana poglavja iz matematike in računalništva, 46. [COBISS-SI-ID 264047360]
STRLE, Sašo. Analiza 1 : za študente Finančne matematike. Ljubljana: DMFA - založništvo, ISSN 1408-6247, 2021, 168 str.. Matematični rokopisi, 27. [COBISS-SI-ID 77526019]
RUBERMAN, Daniel, SLAPAR, Marko, STRLE, Sašo. On the Thom conjecture in CP^3. International mathematics research notices, ISSN 1687-0247, 2021, vol. 2022, 1 spletni vir (1 datoteka pdf (14 str.)). [COBISS-SI-ID 89922563]