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### Terms for 2017

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#### September, 14

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# Essentials of mathematics

The course is designed for the students of the first year, whose have large gaps in knowledge from previous studies and is focused on developing of good habits and practicing of ordinary mathematical skills. The emphasis is given on understanding the key principles and contexts. Students are taught mainly correct thinking. The course content does not exceed the requirements of basic levels of GCSE exam from mathematics. The course is intended primarily for students of second and third grade who have successfully completed courses Entertaining mathematics 1 and Entertaining mathematics 2.

## What are you going to learn

1. Getting Started - introduction to the subject, organization and teaching goals.
2. Algebraic expressions - from fractions over powers to the factoring out and to decomposition into a product.
3. Equations and inequalities - all about linear and quadratic equations, inequalities and their systems.
4. Properties of numbers - numerical sets, features of divisibility of natural numbers, the absolute value of real numbers.
5. Sets - open and closed interval, set operations: union, intersection, set difference, complement of a set.
6. Power functions - linear functions, linear fractional functions and quadratic functions, monotony and bounded functions, absolute value functions.
7. Goniometrie - the sine, cosine, tangent and cotangent functions and their graphs; including trigonometric equations.
8. Exponential and logarithm - properties of functions and their graphs, mutual relationships; including exponential and logarithmic equations.
9. Triangle and Quadrangle - properties such as medians of the triangle, circle circumscribed and inscribed and others, including Pythagoras´ theorem and Thales' circle.
10. Plane geometry - plane geometry, the relative position of points, lines and circles (circles), a set of points given properties, planar mapping.
11. Stereometry - geometry in three-dimensional space, the properties of geometric objects, other coordinate systems (polar coordinates, spatial angle), the principle of transfer to the n-dimensional space and to the analytical geomerii.
12. Final revision - total repetition, preparing for the exam test.

## How the course is organized

### Full time study

The course is taught in 12 seminars, each one 1.5 hours.

### Part time study

The course is taught in 4 tutorials, each one 3 hours.

## Recommended literature

• COHEN, D., LEE, T. B., SKLAR, D.: Precalculus, 7th edition. Cengage Learning, 2009.
• STEWART, J., REDLIN, L., WATSON, S. Precalculus: Mathematics for Calculus. Cengage Learning, 2013.