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.

# Introductory seminar A

Srednješolski učbeniki matematike.

K. Cvetko Vah, D. Dolžan: Učbenik za proseminar, Učbeniki in priročniki 19, DMFA založništvo, Ljubljana, 2014.

A. Cedilnik: Matematični priročnik, 2. izdaja, Didakta, Radovljica, 1997.

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]

Peter Šemrl:

ŠEMRL, Peter. A characterization of normed spaces among metric spaces. Rocky Mountain journal of mathematics, ISSN 0035-7596, 2011, vol. 41, no. 1, str. 293-298. [COBISS-SI-ID 15865177]

ŠEMRL, Peter. Applying projective geometry to transformations on rank one idempotents. Journal of functional analysis, ISSN 0022-1236, 2004, vol. 210, no. , str. 248-257. [COBISS-SI-ID 13012825]

ŠEMRL, Peter. Comparability preserving maps on bounded observables. Integral equations and operator theory, ISSN 0378-620X, 2008, vol. 62, no. 3, str. 441-454. [COBISS-SI-ID 15005273]