Mathematics and Computer Science
Winter Semester
Brief description
The course introduces 3D modelling in the Blender environment. Students learn to create and modify 3D scenes using objects, curves, surfaces, transformations, cameras, lighting, and materials.
For whom
Bachelor students interested in computer graphics, geometry, and 3D modelling.
Prerequisites
Basic computer skills, spatial imagination, and elementary knowledge of geometry.
STAG information system: KAG/3DMBA
Brief description
The course introduces 3D modelling in the POV-Ray environment. Students learn to create 3D scenes using transformations, cameras, light sources, solids, colors, and surface properties.
For whom
Bachelor students interested in computer graphics, geometry, and 3D modelling.
Prerequisites
Basic computer skills, spatial imagination, and elementary knowledge of geometry.
STAG information system: KAG/3DMPA
Brief description
The course introduces the basic theory of groups and rings, including subgroups, quotient groups, homomorphisms, cyclic and symmetric groups, rings, ideals, and finite fields. Students develop understanding of abstract algebraic structures and their fundamental properties.
For whom
Advanced course for bachelor students in mathematics.
Prerequisites
Basic knowledge of set theory, functions, elementary algebra, and mathematical proof techniques.
STAG information system: KAG/MAL3A
Brief description
The course introduces the construction and properties of number fields, including natural, rational, real, and complex numbers. Students study algebraic structures such as groups, rings, and fields, with emphasis on ordering, divisibility, and extensions of number systems.
For whom
Advanced course for bachelor students in mathematics.
Prerequisites
Basic knowledge of algebra, number systems, sets, functions, and proof techniques.
STAG information system: KAG/ALG5A
Brief description
The course introduces the basic functions of AutoCAD and technical drawing in a 2D environment. Students learn to create, edit, dimension, and print technical drawings using standard CAD tools.
For whom
Beginners in bachelor studies, especially for students interested in technical drawing and computer-supported design.
Prerequisites
Basic computer skills and spatial imagination.
STAG information system: KAG/CAD1A
Brief description
The course provides an advanced overview of selected topics in calculus taught using the CLIL method in English. Students study curve integrals, differential equations, complex analysis, power series, and applications of mathematical analysis.
For whom
Advanced course for master students in mathematics, especially future mathematics teachers.
Prerequisites
Good knowledge of calculus, differential equations, complex numbers, and mathematical analysis.
STAG information system: KAG/MAN5A
Brief description
The course introduces the basic concepts of category theory, including categories, functors, natural transformations, limits, colimits, adjoint functors, monads, and algebras. Students gain an understanding of abstract mathematical structures and their relationships.
For whom
Advanced course for master students in mathematics, especially for students interested in algebra and theoretical mathematics.
Prerequisites
Good knowledge of algebra, set theory, and mathematical proof techniques.
STAG information system: KAG/TEK
Brief description
The course introduces the fundamentals of differentiable manifolds and Riemannian geometry. Students study tensors, affine connections, curvature, geodesics, and the relationship between local and global geometric structures.
For whom
Advanced course for master students in mathematics, especially for students interested in geometry and theoretical mathematics.
Prerequisites
Good knowledge of calculus, linear algebra, differential geometry, and basic tensor calculus.
STAG information system: KAG/DG
Brief description
The course introduces basic methods and principles of combinatorics, including counting techniques, permutations, combinations, recurrence relations, and graph-related discrete structures. Students develop precise reasoning and problem-solving skills in discrete mathematics.
For whom
Bachelor students in mathematics, especially students at the beginning of their studies.
Prerequisites
Basic knowledge of secondary school mathematics, logical thinking, and elementary proof techniques.
STAG information system: KAG/DM1
Brief description
Introduction to affine, isometric, similarity and circular transformations in Euclidean geometry. Students learn their analytical representation and applications in solving geometric construction problems.
For whom
Advanced course for bachelor students in mathematics, especially for students with an interest in geometry.
Prerequisites
Basic knowledge of linear algebra, analytic geometry, and Euclidean plane geometry.
STAG information system: KAG/GEZOA
Brief description
The course explores the historical development of imaging and geometric representation from antiquity to modern times. Students study the evolution of geometry, cartography, architecture, descriptive geometry, and projection methods in education and practice.
For whom
Master students in mathematics, especially future mathematics teachers and students interested in geometry and the history of mathematics.
Prerequisites
Basic knowledge of geometry and an interest in the historical development of mathematical and imaging methods.
STAG information system: KAG/HVZMA
Brief description
The course introduces lattices, Boolean algebras, universal algebra, and related algebraic structures. Students study ordered sets, homomorphisms, congruences, quotient algebras, and fundamental properties of algebraic systems.
For whom
Advanced course for master students in mathematics, especially for students interested in algebra and theoretical mathematics.
Prerequisites
Good knowledge of algebra, set theory, ordered structures, and mathematical proof techniques.
STAG information system: KAG/TSUAA
Brief description
The course provides practical introduction to different types of schools, mathematics teaching methods, and classroom observation. Students reflect on observed lessons using a two-phase reflection model guided by teachers and subject didacticians.
For whom
Master students in mathematics teacher education, especially future secondary school mathematics teachers.
Prerequisites
Interest in mathematics teaching, basic pedagogical awareness, and readiness for classroom observation and reflection.
STAG information system: KAG/SNPMA
Brief description
The course introduces the basic properties of topological spaces as generalizations of metric spaces. Students study open and closed sets, continuity, compactness, connectedness, metric spaces, and applications of topology in analysis and geometry.
For whom
Advanced course for master students in mathematics, especially for students interested in analysis, geometry, and theoretical mathematics.
Prerequisites
Good knowledge of calculus, linear algebra, metric spaces, and basic proof techniques.
STAG information system: KAG/TOP
Briem description
The course is intended for first-year students who have an elementary knowledge of algebraic and geometric concepts, such as numbers, functions, graphs, extreme values, vectors, matrices, and systems of linear equations.
For whom
Beginners in bachelor studies
Prerequisites
Simplifying algebraic expressions, solving linear and quadratic equations, intervals, linear equations, inequalities, drawing graphs of elementary functions, vector algebra, analytical geometry in the plane.
STAG information system: KMA/XMAT
Brief description
This course will take you through various application of Fourier analysis. We will cover some history, classical Fourier series and their applications, Fourier transforms and their application in differential equations and image processing.
For whom
Both undergraduate and graduate students of mathematics, engineering, and science are welcome.
Prerequisites
It is good to know multivariate calculus. Some programming is always helpful but not required.
STAG information system: KMA/SC
Brief description
The seminar aims to read and discuss scientific papers on emerging topics in data science that are not covered in standard courses.
For whom
Students in bachelor's degree programmes (ideally in their third year) and master's degree programmes.
Prerequisites
Fundamentals of calculus and statistics.
STAG information system: KMA/SR1
Brief description
The course provides the fundamentals of modern theory of information and its applications, as well as an introduction to coding.
For whom
Master students of computer science or mathematics who have completed their bachelor degree.
Prerequisites
Mathematics including probability theory at bachelor's level of computer science programs.
STAG information system: KMI/TINF
Summer Semester
Brief description
The course deepens students’ knowledge of classical and advanced number theory, including quadratic fields, reciprocity laws, finite fields, Diophantine equations, and analytic aspects such as the Riemann zeta function. Emphasis is placed on connections with other areas of mathematics.
For whom
Advanced course for master students in mathematics, especially for students interested in algebra and number theory.
Prerequisites
Good knowledge of elementary number theory, algebra, and mathematical proof techniques.
STAG information system: KAG/TC
Brief description
The course introduces divisibility theory in integral domains and the fundamentals of lattice theory. Students study ordered sets, lattices, Boolean algebras, and algebraic structures related to divisibility and order.
For whom
Advanced course for master students in mathematics, especially for students interested in algebra and theoretical mathematics.
Prerequisites
Good knowledge of abstract algebra, number theory, ordered structures, and mathematical proof techniques.
STAG information system: KAG/ALG4
Brief description
The course focuses on current topics in mathematics teaching at secondary schools, including curriculum reforms, assessment practices, didactic situations, and the use of modern educational technologies. Students develop critical reflection on teaching practice and mathematics education.
For whom
Master students in mathematics teacher education, especially future secondary school mathematics teachers.
Prerequisites
Basic knowledge of mathematics education, teaching practice experience, and interest in current trends in mathematics teaching.
STAG information system: KAG/APVMA
Brief description
The course introduces algebraic field extensions, algebraically closed fields, Galois groups, and the fundamental theorem of Galois theory. Students study solvability of algebraic equations and classical geometric constructions using straightedge and compass.
For whom
Advanced course for master students in mathematics, especially for students interested in algebra and number theory.
Prerequisites
Good knowledge of abstract algebra, field theory, and mathematical proof techniques.
STAG information system: KAG/GTA
Brief description
The course presents the major periods, key figures, and development of mathematical ideas from ancient times to modern mathematics. Students explore how mathematics evolved in response to practical, scientific, and philosophical problems.
For whom
Bachelor students in mathematics and future mathematics teachers.
Prerequisites
Basic knowledge of mathematics and an interest in historical and philosophical contexts of mathematical development.
STAG information system: KAG/DEMA
Brief description
The course introduces students to the basics of mathematics didactics, including the development of mathematics education, curriculum design, teaching resources, and methods used in primary and secondary schools. Students gain an overview of key principles of teaching mathematics.
For whom
Bachelor students in mathematics, especially future mathematics teachers at the beginning of their studies.
Prerequisites
Basic knowledge of school mathematics and an interest in mathematics education and teaching.
STAG information system: KAG/MDIMA
Brief description
The course introduces the basics of linear programming and its practical applications. Students learn graphical methods, the simplex method, duality, and optimization problems such as transportation and distribution models.
For whom
Advanced course for bachelor students in mathematics and related fields.
Prerequisites
Basic knowledge of linear algebra, analytic geometry, and elementary optimization concepts.
STAG information system: KAG/LIPRA
Brief description
The course provides practical introduction to different types of schools, mathematics teaching methods, and classroom observation. Students reflect on observed lessons using a two-phase reflection model guided by teachers and subject didacticians.
For whom
Master students in mathematics teacher education, especially future secondary school mathematics teachers.
Prerequisites
Interest in mathematics teaching, basic pedagogical awareness, and readiness for classroom observation and reflection.
STAG information system: KAG/SNPMA
Brief description
The course is a continuation of the basic course in probability, intended for third-year students. The aim is to provide applications of random changes and processes with one and more variables. The main aim is to present some geometric properties and structures, introduction and analysis of some stochastic processes.
For whom
Advanced course for students in master studies
Prerequisites
Student has to pass the basic courses of Probability and Statistics. Standard knowledge from mathematical analysis and linear algebra. Elemental experience with computation on PC.
STAG information system: KMA/APROB
Brief description
In a broader sense, compositional data are considered positive multivariate or functional data that carry relative information, such as proportions, percentages, probabilities, concentrations, and density functions. The aim of the course is to introduce methods and approaches for analysing compositional/density data, illustrated with empirical data.
For whom
Master's degree students.
Prerequisites
Fundamentals of linear algebra, calculus and statistics, and basic notions of multivariate statistics.
STAG information system: KMA/CS
Brief description
The seminar aims to read and discuss scientific papers on emerging topics in data science that are not covered in standard courses.
For whom
Students in bachelor's degree programmes (ideally in their third year) and master's degree programmes.
Prerequisites
Fundamentals of calculus and statistics.
STAG information system: KMA/SR2