Τελευταία ενημέρωση: 09-04-2020Adobe PDF (1.66 MB)
EPUB (1.2 MB)
Download
Brochure
Download
Title Details:
Computational Number Theory
Authors: Poulakis, Dimitrios
Reviewer: Tzanakis, Nikolaos
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY > COMPUTATIONAL NUMBER THEORY
MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE
MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE > ALGORITHMS AND COMPLEXITY
Keywords:
Computational Number Theory
Cryptography
Description:
Abstract:
The last thirty years, Number Theory has been applied in many areas of Science and Technology, as Cryptography, Coding Theory, etc. This book is an introduction to Number Theory with emphasis in its computational aspect. Its aim is to give the necessary tools for the understanding of the contemporary applications of Number Theory. The necessary knowledge for the study of the book is that of secondary education. In the first chapter, the divisibility of integers is studied and an elementary introduction to the algorithms of integers is given. Further, the Euclidian algorithm is analysed. The second chapter is devoted to continuous fractions and their properties.
In the third chapter, the prime numbers are studied, some classical theorems on their distributions are proved and some special classes of prime numbers are presented. The basic properties of algebraic structures, monoids, groups, rings and fields, as well as polynomials are given in the fourth chapter. The fifth chapter, is devoted to the congruence relations of integers and their properties. Further,
the linear congruences, the primitive roots, the symbols of Legendre and Jacobi are studied. Moreover, the solution of quadratic congruences is studied. Finally, the finite fields are introduced. In the sixth chapter, some classical primality tests are given and the unique deterministe polynomial time algorithm AKS is analysed. The seven chapter deals with the integer factorization and some classical algorithm are presented. Finally, the last chapter is devoted to the discrete logarithm problem and some algorithm for the computatin of discrete algorithm are given.
Table of Contents:
The book contains the following chapters:
1. Integers
2. Continuous Fractions
3. Primes
4. Groups - Rings - Polynomials
5. Congruences
6. Primality
7. Integer factorization
8. Discrete Logarithm
Technical Editors: Karakostas, Anastasios
Type: Undergraduate textbook
Creation Date: 2015
Item Details:
ISBN 978-960-603-127-4
License: http://creativecommons.org/licenses/by-nc-nd/3.0/gr
Handle http://hdl.handle.net/11419/1045
Bibliographic Reference: Poulakis, D. (2015). Computational Number Theory [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/1045
Language: Greek
Consists of: 1. Integers
2. Prime Numbes
3. Congruences
4. Primality
5. Ιnteger Factorization
6. Discrete Logarithm
7. Continuous Fractions
8. Groups - Rings - Polynomials
Number of pages 290
Publication Origin: Kallipos, Open Academic Editions