|
| |
|
|
Divisibility for talented students of secondary schools
Živčáková, Andrea ; Robová, Jarmila (advisor) ; Bečvář, Jindřich (referee)
This thesis is an educational text for high school students. It aims to teach them how to solve typical problems concerning divisibility found in mathematical correspondence seminars and mathematical olympiad. Basic notions from the theory of divisibility are recalled (e.g. prime numbers, divisors, multiples). Criteria of divisibility by 2 to 20 are introduced, as well as diophantine equations and practical applications of prime numbers in real life. One whole chapter is dedicated to problems and exercises. Powered by TCPDF (www.tcpdf.org)
|
|
|
The Description of the Program for Factorization of Large Numbers
Levek, Vladimír
The article describes the algorithm for factorization of large numbers. If there is the result of the product of two prime numbers, then the program can find the factors. The first part of the article generally introduces the problem of factoring large integers and its impact in the field of the cryptography. The next part describes the algorithm and the program for calculation. At the end of the article there is a summary of the possibilities of the program.
|
|
|
Divisibility for talented students of secondary schools
Živčáková, Andrea ; Robová, Jarmila (advisor) ; Bečvář, Jindřich (referee)
This thesis is an educational text for high school students. It aims to teach them how to solve typical problems concerning divisibility found in mathematical correspondence seminars and mathematical olympiad. Basic notions from the theory of divisibility are recalled (e.g. prime numbers, divisors, multiples). Criteria of divisibility by 2 to 20 are introduced, as well as diophantine equations and practical applications of prime numbers in real life. One whole chapter is dedicated to problems and exercises. Powered by TCPDF (www.tcpdf.org)
|
|
|
Theory of Numbers in Ancient Greece
Smrčka, Zdeněk ; Bečvář, Jindřich (advisor) ; Halas, Zdeněk (referee)
Title: Theory of Numbers in Ancient Greece Author: Bc. Zdenek Smrcka Department: The Department of Mathematics Education Supervisor: doc. RNDr. Jindřich Bečvář, CSc. Abstract: The goal of this thesis is to write up clearly and comprehensibly numeric theoretical research and its results in Ancient Greece between 6 century before Christ and 4 century after Christ. In this thesis we try show examples use of Greece's Mathematics for improvement teaching in education and better understanding abstract thinking in Mathematics. We want so that students understand thinking and abilities Greece's mathematicians. We compare high school view on searching greatest common divisor and Euclidean algorithm. We present important Greece's knowledges as sieve of Eratosthenes, arithmetic of Diofantos etc.. Something of Greece's knowledges as Euclidean algorithm, sieve of Eratosthenes etc. are use of up to now. Keywords: Mathematics in Ancient Greece, figurate number, theory of numbers, Continual fraction, Euclidean algorithm
|
|
|
Probabilistic algorithms for testing primality
Tejkalová, Natálie ; Švejdar, Vítězslav (advisor) ; Glivický, Petr (referee)
Attention has been paid mostly to the new deterministic algorithm for primality testing AKS recently. However, probabilistic algorithms remain an efficient tool for primality testing. Our thesis focuses mostly on two most well-known probabilistic algorithms for primality testing. It describes the main idea and gives proofs of correctness of Solovay-Strassen and Rabin-Miller algorithms. Apart from that, it also tries to look at the subject of probabilistic algorithms from a wider perspective. It presents a definition of a probabilistic algorithm and various complexity classes that correspond to Monte Carlo or Las Vegas algorithms. Besides pure mathematical theory, we mention also some philosophical aspects that need to be considered when we decide to use the probabilistic method. Powered by TCPDF (www.tcpdf.org)
|
guest ::
