Algebra for Computer Science / by Lars Gårding, Torbjörn Tambour
(Universitext)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | New York, NY : Springer US |
| 出版年 | 1988 |
| 本文言語 | 英語 |
| 大きさ | IX, 198 p : online resource |
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| 内容注記 | 1 Number theory 1.1 Divisibility 1.2 Congruences 1.3 The theorems of Fermat, Euler and Wilson 1.4 Squares and the quadratic reciprocity theorem 1.5 The Gaussian integers 1.6 Algebraic numbers 1.7 Appendix. Primitive elements and a theorem by Gauss Literature 2 Number theory and computing 2.1 The cost of arithmetic operations 2.2 Primes and factoring 2.3 Pseudo-random numbers Literature 3 Abstract algebra and modules 3.1 The four operations of arithmetic 3.2 Modules 3.3 Module morphisms. Kernels and images 3.4 The structure of finite modules 3.5 Appendix. Finitely generated modules Literature 4 The finite Fourier transform 4.1 Characters of modules 4.2 The finite Fourier transform 4.3 The finite Fourier transform and the quadratic reciprocity law 4.4 The fast Fourier transform Literature 5 Rings and fields 5.1 Definitions and simple examples 5.2 Modules over a ring. Ideals and morphisms 5.3 Abstract linear algebra Literature 6 Algebraic complexity theory 6.1 Polynomial rings in several variables 6.2 Complexity with respect to multiplication 6.3 Appendix. The fast Fourier transform is optimal Literature 7 Polynomial rings, algebraic fields, finite fields 7.1 Divisibility in a polynomial ring 7.2 Algebraic numbers and algebraic fields 7.3 Finite fields Literature 8 Shift registers and coding 8.1 The theory of shift registers 8.2 Generalities about coding 8.3 Cyclic codes 8.4 The BCH codes and the Reed-Solomon codes 8.5 Restrictions for error-correcting codes Literature 9 Groups 9.1 General theory 9.2 Finite groups Literature 10 Boolean algebra 10.1 Boolean algebras and rings 10.2 Finite Boolean algebras 10.3 Equivalence classes of switching functions Literature 11 Monoids, automata, languages 11.1 Matrices with elements in a non-commutative algebra 11.2 Monoids and languages 11.3 Automata and rational languages 11.4 Every rational language is accepted by a finite automaton Literature References |
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| 一般注記 | The aim of this book is to teach the reader the topics in algebra which are useful in the study of computer science. In a clear, concise style, the author present the basic algebraic structures, and their applications to such topics as the finite Fourier transform, coding, complexity, and automata theory. The book can also be read profitably as a course in applied algebra for mathematics students |
| 著者標目 | *Gårding, Lars author Tambour, Torbjörn author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical logic FREE:Mathematics FREE:Mathematical Logic and Foundations |
| 分 類 | DC23:511.3 |
| 巻冊次 | ISBN:9781461387978 
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| ISBN | 9781461387978 |
| URL | http://dx.doi.org/10.1007/978-1-4613-8797-8 |
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