# Algorithms: Main Ideas and Applications

Book

Part of the Mathematics and Its Applications book series (MAIA, volume 251)

1. Front Matter
Pages i-xii

Pages 1-2

Pages 3-4
4. ### Fundamental Discoveries of the General Theory of Algorithms

1. Front Matter
Pages 5-6
Pages 7-16
Pages 17-21
Pages 22-30
Pages 31-44
Pages 45-45
Pages 46-47
Pages 48-57
Pages 58-65
Pages 66-67
Pages 68-69
Pages 70-72
Pages 73-76
Pages 77-79
Pages 80-83
Pages 84-97
Pages 98-107

### Introduction

Today the notion of the algorithm is familiar not only to mathematicians. It forms a conceptual base for information processing; the existence of a corresponding algorithm makes automatic information processing possible. The theory of algorithms (together with mathematical logic ) forms the the­ oretical basis for modern computer science (see [Sem Us 86]; this article is called "Mathematical Logic in Computer Science and Computing Practice" and in its title mathematical logic is understood in a broad sense including the theory of algorithms). However, not everyone realizes that the word "algorithm" includes a transformed toponym Khorezm. Algorithms were named after a great sci­ entist of medieval East, is al-Khwarizmi (where al-Khwarizmi means "from Khorezm"). He lived between c. 783 and 850 B.C. and the year 1983 was chosen to celebrate his 1200th birthday. A short biography of al-Khwarizmi compiled in the tenth century starts as follows: "al-Khwarizmi. His name is Muhammad ibn Musa, he is from Khoresm" (cited according to [Bul Rozen Ah 83, p.8]).

### Keywords

Notation algorithms arithmetic boundary element method complexity design entropy form hardware information information theory logic mathematical logic randomness semantics

#### Authors and affiliations

1. 1.Department of Mathematical Logic, Faculty of Mechanics and MathematicsMoscow Lomonosov UniversityMoscowRussia

### Bibliographic information

• Book Title Algorithms: Main Ideas and Applications
A.L. Semenov
• Series Title Mathematics and Its Applications
• DOI https://doi.org/10.1007/978-94-015-8232-2