Course details

Seminar of Mathematics

ISM Acad. year 2024/2025 Winter semester 2 credits

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

Guarantor

Course coordinator

Language of instruction

Czech, English

Completion

Credit

Time span

  • 26 hrs exercises

Department

Instructor

Learning objectives

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.
 

Compulsory co-requisites

Prerequisite knowledge and skills

Basic high school numeracy skills. 

Syllabus of numerical exercises

  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.

 

Progress assessment

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. 

Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Tue exercise lectures D0207 10:0011:5064 1BIA 1BIB 2BIA 2BIB xx Vítovec
Tue exercise lectures A113 14:0015:5064 1BIA 1BIB 2BIA 2BIB xx Hliněná
Wed exercise lectures A113 17:0018:5064 1BIA 1BIB 2BIA 2BIB xx Polický
Thu exercise lectures A113 16:0017:5064 1BIA 1BIB 2BIA 2BIB xx Polický
Thu exercise lectures A113 18:0019:5064 1BIA 1BIB 2BIA 2BIB xx Polický
Fri exercise lectures A113 14:0015:5064 1BIA 1BIB 2BIA 2BIB xx Vévodová
Fri exercise lectures A113 16:0017:5064 1BIA 1BIB 2BIA 2BIB xx Vévodová

Course inclusion in study plans

  • Programme BIT, 1st year of study, Elective
  • Programme BIT (in English), 1st year of study, Elective
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