Preparatory Mathematics

Tomáš Kalvoda, KAM FIT ČVUT Antonella Marchesiello (translation), KAM FIT ČVUT Jitka Rybníčková (translation), KAM FIT ČVUT

Contents

1 Introduction

1.1 Notes to the text

2 Mathematics is not only about computing

2.1 Computation and abstraction

2.2 The structure of a mathematical text

2.3 What is a proof?

2.4 A few examples of proofs

2.5 What is not a proof?

3 Basic concepts

3.1 Note on mathematical notation

3.2 Sets and set operations

3.3 Number sets

3.4 Significant subsets of real numbers

3.5 Propositions and logical connectives

3.6 Abbreviated writing of sums and products

3.7 Factorial and binomial coefficient

3.8 Important constants

4 Elementary functions

4.1 What is it a function?

4.2 The absolute value

4.3 Lower and upper integer part

4.4 Linear function

4.5 Quadratic function

4.6 Polynomial function

4.7 Roots

4.8 Rational function

4.9 Trigonometric functions

4.10 Exponantiation and logarithm

5 Analytical geometry

5.1 Basic notions

5.2 The line

5.3 The circle and the ellipse

6 Warning

6.1 Smart calculators are too smart

6.2 Frequently asked questions

7 List of the used symbols