Seminar in Mathematics (KMD/E-SMM)

  • 6 credits
  • Lecturer: Ing. Tomáš Barot, Ph.D.
  • Lessons (Lectures + Exercises + Seminars): 1 + 0 + 1
  • Semester: Winter / Summer
  • Language of instruction: English
  • Language of consultation: English
  • Level of qualification (Bc., Mgr.):Bc., Mgr. (M7503 Erasmus+)
  • Method of completion: Examination

Synopsis / description / annotation:

As the main aim of this course, a strengthening the basic mathematical knowledge of the student is considered. From the initial recapitulation of number fields and arithmetic chapters, the student continues through the topics of the linear algebra solving the conditions of solvability of mathematical problems. The algebraic calculus is explained using numerical and graphical methods. In more complex problems, including absolute values and inequalities, the zero-point method can be suitably applied for purposes of the clarification of the process of solving the given task. The overview of elementary functions of a real variable is continuously followed by an introduction to combinatorics. Finally, the number field of complex numbers is described with implementation of particular operations. The practical application of mathematical chapters will be demonstrated in software Octave, wxMaxima, LibreOffice, SimReal and GeoGebra.

Content:

  1. Overview of number fields and determination of conditions for purposes of solving the mathematical problem
  2. Relational, logical and set operators; examples on propositional logic and sets
  3. Operations with algebraic fractions.
  4. Algebraic rules for polynomial expansion, operations with polynomials
  5. Algebraic linear and quadratic equations
  6. Algebraic inequalities – zero-point method
  7. Equations and inequalities with absolute values
  8. Systems of linear equations
  9. Domain of a function, range of a function, plot of elementary functions, properties of functions.
  10. Graphical solution of systems of the linear equations
  11. Introduction to vectors and vector operations
  12. Combinatorics
  13. Complex number field with operations.
  14. Solving the mathematical problems using software (Octave, wxMaxima, LibreOffice, SimReal and GeoGebra)

Literature:

  • AHBEL, N.P. Functions, Statistics, and Trigonometry. The University of Chicago School Mathematics Project, 1998.
  • BEARDON, A.F. Algebra and Geometry. Cambridge University Press, 2005.
  • HAMILTON, S. Mastering . Hamilton Education Guides, 1996.
  • TUSSY, A.S., GUSTAFSON, R.D. Elementary and Intermediate Algebra. 2013.

Updated: 06. 02. 2020