This text serves as a review of the basic concepts and results of high school mathematics, that the students of the course Fundamentals of Mathematical Analysis ( BIE-ZMA) should already well know and master. In addition, the topics treated here partially coincide with the first introductory lecture of BIE-ZMA. The course Preparatory Mathematics ( BIE-PKM) takes place electronically in the first half of the winter semester of the academic year 2019/2020.
The text is divided into several chapters associating thematically similar problems. The purpose of the text is not a systematic presentation of secondary school program, but its review, highlighting important contexts or interpretations of the subjects from a new perspective. For this reason, different chapters and their sections might not follow in logical order.
After these introductory paragraphs, in the second chapter we deal with the meaning of proof and the mathematical approach to problem solving. In the third chapter we introduce the mathematical notation and symbols, and discuss the properties of sets and numerical operations. The fourth chapter then presents a brief overview of the so-called elementary functions, especially polynomial functions, rational functions, trigonometric functions, exponential and logarithmic functions. The fifth chapter summarizes the basic methods of describing some geometrical objects on the plane by using analytical geometry.
Now let us summarize some of the conventions used in this text. For the reader's convenience, the text is accompanied by a list of the used symbols. At the very end of the document there is also a relatively detailed index of terms and a few references to used sources or interesting publications.
Significant equations in this document are numbered within the chapters. Equation (3.5) is the equation number 5 in the third chapter. We use the same numbering method for pictures and tables as well. Thus, picture 1.3 means the third pictures in the first chapter. Only references to equations are traditionally indicated by brackets. These links are active in the electronic version of the document. When decimal digits are used, we use a decimal point instead of a decimal comma.
We would like to thank doc. Ing. Stepan Starost, Ph.D. Mgr. Jan Starý, Ph.D., Ing. Daniel Vašata, Ph.D. and Mgr. Lenka Nováková for comments and suggestions. If a kind reader finds errors or confusion in the following lines can always contact the authors of this document preferably by email.