Course details

# Seminar of Mathematics

ISM Acad. year 2023/2024 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

News

 Classes start in the first week of the semester, i.e. in the week of 9/18/2023.

Guarantor

Course coordinator

Language of instruction

Czech, English

Completion

Credit

Time span

• 26 hrs exercises

Department

Instructor

Course Web Pages

Current information on the subject and other study materials can be found here in the subject's eLearning.

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.

Why is the course taught

The course is intended especially for students who have gaps in high school mathematics and lack the ability to easily solve basic high school examples. In particular, emphasis is placed on repeating the material and calculating examples related to the functions of one real variable.

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 (irrational and exponential).
9. Equations and inequalities - third part (logarithmic and trigonometric).
10. Analytical geometry (especially analytical expression of straight lines and planes, relative positions, distances, etc.).
11. Conic sections - first part (circle, ellipse), second test on 10 points (50 minutes).
12. Conic sections - second part (hyperbola, parabola), repetition, a possible replacement test for those who did not write 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.

Exam prerequisites

In order to receive credit, the following two conditions must be fulfilled

• Get a total of at least 8 points out of a total of possible 23 points.
• Active participation in exercises. Any absence must be properly excused.

Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Tue exercise lectures A113 14:0015:5064 1BIA 1BIB 2BIA 2BIB xx Vítovec
Tue exercise lectures A113 16:0017:5064 1BIA 1BIB 2BIA 2BIB xx Polický
Wed exercise lectures A113 17:0018:5064 1BIA 1BIB 2BIA 2BIB xx Vítovec
Thu exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 16:0017:5064 1BIA 1BIB 2BIA 2BIB xx Polický
Thu exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 18:0019:5064 1BIA 1BIB 2BIA 2BIB xx Polický
Fri exercise 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 13. of lectures A113 14:0015:5064 1BIA 1BIB 2BIA 2BIB xx Vévodová
Fri other 2023-12-08 E112 14:0015:50154 1BIA 1BIB 2BIA 2BIB xx Vévodová
Fri exercise 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 13. of 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
• Programme IT-BC-3, field BIT, 1st year of study, Elective