Lecturer chooses topics that complement mathematical knowledge of a high school mathematics teacher. The topics include:
analysis (Morse theory on surfaces, functional equations, theory of function series, discrete dynamical systems etc.),
discrete mathematics (mathematical games, graphs, geometric configurations etc.),
geometry (geometry of hyperbolic plane, tesselations, geometry of curves and surfaces, classification of surfaces),
algebra (topics in linear algebra, ordered structures, structural algebra),
number theory (elementary, analytic).
Mathematical horizons *
2019/2020
Programme:
Mathematics Education
Year:
4 ali 5 year
Semester:
first
Kind:
mandatory
ECTS:
5
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 1. semester:
Lectures
3
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)
Readings
J. Bračič: Uvod v analitično teorijo števil, Podiplomski seminar iz matematike 26, DMFAS, 2003
M. Hladnik: Povabilo v harmonično analizo, Izbrana poglavja iz matematike in računalništva 26, DMFAS, Ljubljana 1992
B. Lavrič: Delno urejene grupe in delno urejeni kolobarji, Podiplomski seminar iz matematike 21, DMFAS, 1993
A. Ramsay, R. D. Richtmyer: Introduction to hyperbolic geometry, Springer, 1995
B. Zalar: Strukturna algebra za podiplomce in nespecialiste, Podiplomski seminar iz matematike 25, DMFAS, 2002
Objectives and competences
The course is aimed at the students of Mathematics education. It covers topics that build on their previous mathematical knowledge and are connected with the topics covered in high school curriculum.
Intended learning outcomes
Deeper knowledge of select fundamental mathematical topics which are connected to high school mathematics.
Better foundations and improved intuition of a high school teacher for topics taught to high school students. This is essential for motivating and educating all high school students and especially those above average.
Learning and teaching methods
lectures, recitations, homeworks, consultations
Assessment
Course grade consists of a single grade.
Two midterm exercise-based exams or final exercise-based exam.
Theoretical knowledge exam.
Grades: 6-10 (pass), 5 (fail) (according to the Statute of UL).
Lecturer's references
LAVRIČ, Boris. Compatible lattice orders and linear operators on R [sup] n. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 1998, let. 285, št. 1-3, str. 189-200. [COBISS-SI-ID 8444505]
LAVRIČ, Boris. Coherent Archimedean f-rings. Communications in algebra, ISSN 0092-7872, 2000, let. 28, št. 2, str. 1091-1096. [COBISS-SI-ID 9502041]
LAVRIČ, Boris. Delno urejene grupe in delno urejeni kolobarji, (Podiplomski seminar iz matematike, 21). Ljubljana: Inštitut za matematiko, fiziko in mehaniko: Fakulteta za naravoslovje in tehnologijo: Društvo matematikov, fizikov in astronomov Slovenije, 1993. 134 str. ISBN 961-212-010-2. [COBISS-SI-ID 36205056]
