Proofs

Title: Proofs Author: Jakub Hofman Department: Department of Mathematics Education Supervisor: RNDr. Jakub Staněk, Ph.D., Department of Mathematics Edu- cation Abstract: This bachelor thesis should clarify the concept of a mathematical proof, briefly describe the individual proof methods and provide examples of proved theorems from various branches of mathematics. Another objective of this thesis is to provide a high school pupil with a study material which with it structure corresponds to mathematical textbooks and lecture notes provided by universities. In the first part of the thesis the basic terms of logic are introduced to the pupil. These are terms a pupil can usually encounter in math classes at school. The knowledge of these terms is essential for understanding the principles of the individual proof methods. The main part of the thesis is focused on explaining the individual proof methods and their application in proving mathematical theorems with di- fficulty appropriate to a pupil of secondary education. The theorems are ordered by the difficulty of their proof; they do not follow from one another nor do they form a coherent mathematical theory as that is not the goal of this thesis. The thesis also contains a list of theorems which a pupil should be ca- pable of proving after being acquainted with..