GENERAL DESCRIPTION OF THE COURSEGENERAL DESCRIPTION OF THE COURSEThe course consists of three main parts: basics of mathematical analysis (derivative, integral and differential equations), basics of algebra (vectors, matrices and linear systems of equations) and basic geometry including symmetries and the analysis of patterns in the plane: frieze patterns, wallpaper patterns and finite patterns with different symmetry groups. We consider (semi)regular lattices in the plane and (semi)regular solids (i.e. Platonic and Archimedean solids). In case of less than 5 Erasmus students enrolled, the students are invited to attend the course in Slovene language (where the lecturer emphasizes the important things in English language) and have weekly meetings with the lecturer. All materials for Erasmus students: Text Book, Exam and Homework-exercises are in English language. Erasmus students have the same obligations as regular students: homework and written exam. Seminar work is optional (mostly sundials are considered as extra work). Some examples of the homework and seminar work is shown on figures below.COURSE CONTENTSThe course will cover the following topics: Basic trigonometry. Coordinate systems, ploting curves and surfaces Basic ideas about vector and matrix calculus Basic ideas of derivatives and computation of extrema Basic ideas from integration and center of mass of simpler bodies Basic ideas about differential equation, solutions of equations with constant coefficients Symmetry groups, geometric patterns in plane, (semi)regular solids.
STUDY MATERIALS: E. Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 2006. W. Holden, Shapes, Space and Symmetry, Dover, 2004 D. W. Farmer, Groups And Symmetry: A Guide To Discovering Mathematics, Universities Press. B. Guenbaum, G.C. Shephard, Tilings & Patterns, Dover Books on Mathematics, 2016.