Course detail

Seminar of Mathematics

FIT-ISMAcad. year: 2025/2026

Modifying algebraic expressions. Basic elementary functions and operations with functions. Equations and inequalities. Complex numbers. Analytical expressions of straight line and plane. Conic sections 

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

Mgr. Irena Hlavičková, Ph.D.

Department

Department of Mathematics (UMAT)

Entry knowledge

Basic high school numeracy skills. 

Rules for evaluation and completion of the course

In the seminar, two test papers will be written for 2 x 10 points on the discussed material. There is also the possibility of getting 3 points for independent and error-free counting of the discussed examples at the blackboard. 

Aims

The goal is to improve or to repeat knowledge of high school mathematics needed for further study.The aim of the subject is to repeat and possibly supplement the missing knowledge of secondary school mathematics needed for further study. In particular, emphasis is placed on repeating the material and practicing skills, which are a necessary prerequisite for the further study of mathematical analysis in the subject IMA1. The subject can be especially useful for students who did not graduate in mathematics.
 

Study aids

Not applicable.

Prerequisites and corequisites

Basic literature

Kolářová, E.: Matematický seminář, UMAT FEKT VUT v Brně, 2014. (CS)
Krupková, V., Fusek,M: Matematický seminář pro FIT, UMAT FEKT VUT v Brně, 2018. (CS)

Recommended reading

Polák, J.: PŘEHLED středoškolské matematiky, Praha, Prometheus, 2016. (CS)
Polák, J.: Středoškolská matematika v úlohách II, Praha, Prometheus, 2018. (CS)

Classification of course in study plans

  • Programme BIT Bachelor's 1 year of study, winter semester, elective
  • Programme BIT Bachelor's 1 year of study, winter semester, elective

Type of course unit

 

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

Mgr. Libuše Vévodová
Mgr. Jiří Vítovec, Ph.D.
Mgr. Zdeněk Polický, Ph.D.

Syllabus

  1. Modifications of algebraic expressions.
  2. Equations and inequalities - first part (linear, quadratic, rational fraction and with absolute value). 
  3. The concept of a function, graph, functional prescription, properties. Shifts and transformations of graf. Linear and quadratic functions.  
  4. Power and linear fraction functions, exponential and logarithmic functions. Coalculation of inverse functions. 
  5. Trigonometric functions (including their properties and transformations), problems from trigonometry. Composition of functions.
  6. Complex numbers - introduction, first test on 10 points (50 minutes). 
  7. Complex numbers - completion. 
  8. Equations and inequalities - second part (exponential and logarithmic). 
  9. Equations and inequalities - third part (irrational, trigonometric and combinations of several types). 
  10. Analytical geometry (especially analytical expression of straight lines and planes, relative positions, distances, etc.).
  11. Conic sections.
  12. Conic sections - possible completion, second test on 10 points (50 minutes). 
  13. Reserve, repetition, possible replacement paper for those who have not written one.