Module: Virtual Mobility in Mathematics (KMD/E-VRM)

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  • Number of credits: 20
  • Lecturer: Ing. Tomáš Barot, Ph.D.
  • Lessons (Lectures + Exercises + Seminars): 2 + 2 + 2 [hours/week] online
  • Semester: Winter or Summer
  • Language of instruction: English
  • Language of consultation: English
  • Level of qualification (Bc., Mgr.): Bc., Mgr.
  • Method of completion: Examination

Synopsis / description / annotation:

Module “Virtual Mobility in Mathematics” is aimed for the international students, which would like to study online due to fulfilling the conditions of the concrete international exchange program. In the module, 20 credits are integrated during 4 important mathematical issues of Arithmetic (5 Credits), Geometry (5 Credits), Algebra (5 Credits) and Statistics (5 Credits). Each of these parts are structured in favour of the mathematical preparation of the future math teachers. For purposes of the guarantee of this aim, the general principles of mathematics are presented, discussed and practically proven. The application is provided in the area of education.

Requirements on student:

An active participation in the online form of the education, an active approach to solving tasks, the successful passing of the final exam.


The first part of the module – Arithmetic

  • Number fields, number systems.
  • Construction of natural numbers using Pean's axioms.
  • Sets, operation with sets, problems solved by sets.
  • Cartesian multiplication and binary relations.
  • Properties of binary relations.
  • Projections.

The second part of the module – Geometry

  • Planimetrics - basic figures (point, line, plane, half-line, line segment, convex and non-convex figure, polygon)
  • Geometrical transformations in plane (displacement, rotation, center symmetry, axis symmetry, uniformity)
  • Position properties in planimetrics
  • Construction problems in planimetrics
  • Stereometry - basic solids (polyhedral and rotating solid)
  • Position properties of solids in stereometry
  • Construction problems based on sections
  • Conic sections

The third part of the module – Algebra

  • Polynomials, rational functions.
  • Linear equations, quadratic equations.
  • Quadratic equations with complex roots.
  • Sets of linear equations.
  • Matrices, property of matrices.
  • Operations with matrices.
  • Determinants, determinants of higher order.
  • Solving the sets of linear equations by matrix calculus.

The fourth part of the module – Statistics

  • Descriptive statistical characteristics.
  • Combinatorics.
  • Probability distributions of random variable.
  • Normal Gaussian probability distribution.
  • Statistical significance in the quantitative research,
  • Testing normality of data.
  • Testing hypotheses on the significance level.
  • Cluster analysis.

Course results:

After finishing the module, in which an understanding of topics of the mathematical chapter is offered, students will have knowledge about the advanced aspects of these parts of mathematics. Student will have abilities to solve problems in the frame of the mathematical disciplines, which are necessary in the university grade of education.

Assessment methods:

  • Online examination
  • Continuous analysis of student’s achievements

Teaching methods:

  • Online education
  • Computer-based tutoring
  • Dialogic (discussion, dialogue, brainstorming)
  • Individual tutoring


  • Bowser, E. Elements of Plane and Solid Geometry. Forgotten Books, 2013. ISBN 978-1332788927.
  • Lang, S. Undergraduate Algebra. Springer, 2005. ISBN 0-387-22025-9.
  • Rusczyk, R. Introduction to Geometry. AoPS, 2008.
  • Triola, F. M. Elementary Statistics. The Benjamin/Cummings Publishing Company, Redwood City, 1989. ISBN 0-8053-0271-9.

Updated: 03. 10. 2022