Course detail

Mathematical Seminar

FEKT-BPC-MASAcad. year: 2025/2026

Foundations of mathematics, equations, inequalities, vectors, elementary functions, complex numbers, sequences.

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

RNDr. Štěpán Křehlík, Ph.D.

Department

Department of Mathematics (UMAT)

Entry knowledge

Students should have at least superficial knowledge of work with expressions and elementary functions within the scope of standard secondary school requirements.

Rules for evaluation and completion of the course

 

Aims

The goal of the course is to supplement secondary school knowledge of mathematics necessary for further studies.

Study aids

Not applicable.

Prerequisites and corequisites

Basic literature

Kolářová E.: Matematický seminář, VUT, 2014. (CS)

Recommended reading

Lhotský, K.: Sbírka úloh z matematiky, Karolinum, ISBN 978-80-246-5192-7, 2022. (CS)

Classification of course in study plans

  • Programme BPC-NCP Bachelor's 1 year of study, winter semester, compulsory-optional
  • Programme BPC-EMU Bachelor's 1 year of study, winter semester, compulsory-optional
  • Programme BPC-AMT Bachelor's 1 year of study, winter semester, compulsory-optional

  • Programme BPC-AUD Bachelor's

    specialization AUDB-ZVUK , 1 year of study, winter semester, elective
    specialization AUDB-TECH , 1 year of study, winter semester, elective

  • Programme BPC-BTB Bachelor's 0 year of study, winter semester, elective
  • Programme BPC-ECT Bachelor's 1 year of study, winter semester, elective
  • Programme BPC-IBE Bachelor's 1 year of study, winter semester, elective
  • Programme BPC-MET Bachelor's 1 year of study, winter semester, compulsory-optional
  • Programme BPC-SEE Bachelor's 1 year of study, winter semester, compulsory-optional
  • Programme BPC-TLI Bachelor's 1 year of study, winter semester, elective
  • Programme SPC-STC Bachelor's 1 year of study, winter semester, elective

Type of course unit

 

Fundamentals seminar

14 hod., compulsory

Teacher / Lecturer

Mgr. Eva Sedláková
RNDr. Štěpán Křehlík, Ph.D.
Mgr. Libuše Vévodová

Syllabus

1. Základní matematické pojmy,
2. Úpravy algebraických výrazů I.
3. Úpravy algebraických výrazů II.
4. Lineární a kvadratické rovnice, nerovnice.
5. Rovnice, nerovnice s absolutní hodnotou.
6. Funkce - základní pojmy.
7. Racionálně lomené funkce.
8. Exponenciální a logaritmické funkce.
9. Goniometrické funkce.
10. Analytická geometrie.
11. Komplexní čísla.
12. Aritmetické a geometrické posloupnosti.

Computer-assisted exercise

12 hod., compulsory

Teacher / Lecturer

Mgr. Eva Sedláková
RNDr. Štěpán Křehlík, Ph.D.
Mgr. Libuše Vévodová

Syllabus

1. Foundations of mathematics.
2. Vectors, lines, planes (analytical geometry).
3. Manipulation with algebraic expressions.
4. Linear equations, inequalities, systems.
5. Partial fraction decomposition.
6. Elementary functions 1.
7. Elementary functions 2.
8. Limits, asymptotes.
9. Derivatives, limits, tangent lines.
10. Complex numbers 1.
11. Complex numbers 2.
12. Arithmetic and geometric sequence, geometric series.
13. Recapitulation.

E-learning texts

Kolářová: Matematický seminář
Matematicky_seminar.pdf 0.69 MB