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Geometric Proofs
Hanusová, Tereza ; Štěpánová, Martina (advisor) ; Halas, Zdeněk (referee)
Title: Geometric Proofs Author: Tereza Hanusová Department: Department of Mathematics Education Supervisor: RNDr. Martina Štěpánová, Ph.D., Department of Mathematics Edu- cation Abstract: This Bachelor's thesis treats such proofs of mathematical theorems in which pictures and secondary school geometry play a significant role. Its aim is to promote an unusual approach to theorem proving which enables to literally see the way they function. The proofs described include three categories: figu- rate numbers, polygons and areas of plane figures with curved boundaries. The thesis can be useful to teachers to liven up their secondary school mathematics lessons or to students of maths-oriented programmes to enrich their knowledge by an unusual approach to theorem proving. Keywords: proof, geometry, figurate number, polygon, area of plane figure 1
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Proofs
Hofman, Jakub ; Staněk, Jakub (advisor) ; Rmoutil, Martin (referee)
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...
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Beginnings of Greek mathematics - Thales, Pythagoras and Euclid
Ebelová, Gabriela ; Kvasz, Ladislav (advisor) ; Jančařík, Antonín (referee)
Title: The beginnings of Greek mathematics - Thales, Pythagoras and Euclid Author: Gabriela Ebelová Department: Department of Matematics and Mathematical Education Supervisor: Prof. RNDr. Ladislav Kvasz, Ph.D. The work deals with a new look at the history of mathematics in Greece and its use in teaching mathematics today. The first part presents the three mathematicians Thales, Pythagoras and Euclid. It describes their lives and important works. The second part of the book is devoted to the analysis Arpad Szabo The Begginings of Greek Mathematics. There is presented a different view of the history of Greek mathematics. Content of the third and last part is the use of history in the teaching of mathematics. Also, comparing teaching methods in historical Greece and currently. Klíčová slova: history of mathematics, Arpád Szabó, teaching of mathematics
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Teaching web application for secondary school mathematical logic
Moravec, Luboš
Teaching web application for secondary school mathematical logic Luboš Moravec Abstract: The head part of thís work is a website intended especially for secondary school students which teaches mathematical logic. The website is divided into two parts - a teaching text and tests. The teaching text, which is divided into seven chapters, explains the idea of propositions and their negations, basic logic connectives (conjunction, disjunction, implication, equivalence), a problem of finding truth value of composite propositions and their negations, work with quantifiers, set operations, Venn's diagrams and proof techniques. Except the teaching chapters there are also tests for verifing new knowledge. The questions in tests are randomly selected from a group of similar questions, so a repeated test has new questions. This text contains an user guide, a programmer documentation and a printed version of teaching chapters.
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Nerovnosti a jejich aplikace
TESAŘOVÁ, Jaroslava
This Thesis deals with mathematical inequalities, their use in mathematics and applications to thermodynamics. The main emphasis is placed on proofs of inequalities and solving examples. The following thing explains the mathematical concept such as norm or metric, needed to understand these procedures, and also some of basic concepts of thermodynamics. To understand this Thesis the knowledge of analysis and thermodynamics is required.
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Personological proof of God's existence against atheism
Čápová, Eva ; Bouma, David (advisor) ; Novotný, Vojtěch (referee) ; Svoboda, David (referee)
The mankind is looking for Creator since the beginning of its existence and is trying to know Him. "Is there a God?" so is an atheist, agnostic and sometimes even a faithful asking. Philosophers and theologists are trying to prove or deny His existence. The purpose of this proof is nothing more than to prove that a man has his Creator, to whom he is responsible and he has no chance to opt out of this responsibility. Personological proof that I submit aspires to apodictic proof of God's existence. The thesis are divided into three parts. The first part deals with the most familiar evidence of God's existence chronologically, starting with the ontological proof of St.. Augustine, St. Anselm, St. Thomas Aquinas and teleological proof. To conclude this section I offer the current state of research in this field, especially the view, which is profiled in the magazine Distance, a respected online magazine of critical thinking. In the second part I present my own proof of God's existence. For this I use purely intellectual apparatus without the acceptance of faith and I achieve the proof by means of syllogism. From two generally accepted premises I come to a new statement. I support scripture and dogma of the recognizability of God's existence by the natural light of human reason as analogy of harmony...
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Elementary mathematics from an advanced standpoint
Kučera, Jiří ; Bečvář, Jindřich (advisor) ; Staněk, Jakub (referee)
Mine thesis is written for self-study of secondary school graduates students which prepare for the mathematically oriented high schools. It clarifies theoretical approach to mathematics. It was chosen topics exponents, square roots, logarithms and equations that contain these objects for this purpose. For this reason students are given the opportunity to gain stance to university mathematics knowledge that should be known from high school. In addition, his work allows him to enlarge knowledge of those topics and learn heavier and unusual examples.
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Busy Beaver Problem
Kropitz, Pavel ; Holan, Tomáš (advisor) ; Mráz, František (referee)
The work's purpose was to develop and implement optimalization methods that could be used for solving Busy Beaver problem with order of 5+. The result of the work is the theoretical part and its implementation in form of two programs - simulator of Turing Machines which shows the computation of the machine in detail along with application of theory, and program searching the space of Turing Machines. The latter was ran for machines with four to six states. The quality of the methods was proven by small number of machines that the program could not detect and by nding a new record machine - candidate for 6-state Busy Beaver.
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