Seminar of Mathematics

• 26 hrs exercises

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.
 

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. 

• Discrete Mathematics (IDM)

Basic high school numeracy skills. 

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.

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. 

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.