Course detail

Mathematical Seminar

FEKT-BPC-MASAcad. year: 2025/2026

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

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

Students can collect course points in the following activities:
• Completing a quiz in the eLearning part of the course. The eLearning contains 42 quizzes, each for 10 points, hence it is possible to collect maximum 420 points for quizzes in total.
• Written test. There are 2 written test during the course, each for 10 points, hence it is possible to collect maximum 20 points for written tests in total.

For the course-unit credit it is necessary to meet the following conditions:
i. collect at least 378 points (rounded down) of the maximum 420 points for completed quizzes in the eLearning part of the course,
ii. collect at least 8 points (rounded down) of the maximum 20 points for written tests,
iii. submit 2 home preparations in the form and within the deadlines announced by the lecturer responsible for the course at the beginning of a semester in the eLearning part of the course,
iv. within given deadlines, submit 1-3 short evaluations (about 3 sentences) of the home preparations submitted by peers, assigned to students the day after the deadline of the home preparation submission according to part iii.

Participation in the controlled teaching activities is compulsory. Procedures of excusing oneself from the controlled teaching activity and substituting the missed controlled teaching activity are defined in the Study Regulations of the Faculty.

Aims

The goal of the course is to supplement secondary school knowledge of mathematics necessary for further studies.
After completing the course, students should be able to:
- transform and simplify expressions;
- solve basic equations and inequalities;
- find the domain and the range of a function;
- differentiate using basic formulas;
- perform calculations with complex numbers;
- work with arithmetic and geometric sequences and infinite series.

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

RNDr. Štěpán Křehlík, Ph.D.

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.

Computer-assisted exercise

12 hod., compulsory

Teacher / Lecturer

RNDr. Štěpán Křehlík, Ph.D.

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