Name: Algebra for Computer Science By Lars Garding
SKU: 9780387967806
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Algebra for Computer Science Summary

Algebra for Computer Science by Lars Garding

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.

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.- 9.1.1 Groups and subgroups.- 9.1.2 Groups of bijections and normal subgroups.- 9.1.3 Groups acting on sets.- 9.2 Finite groups.- 9.2.1 Counting elements.- 9.2.2 Symmetry groups and the dihedral groups.- 9.2.3 The symmetric and alternating groups.- 9.2.4 Groups of low order.- 9.2.5 Applications of group theory to combinatorics.- 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.

Additional information

Sku

NPB9780387967806

ISBN 13

9780387967806

ISBN 10

038796780X

Title

Algebra for Computer Science by Lars Garding

Author

Lars Garding

Series

Universitext

Condition

New

Binding type

Paperback

Publisher

Springer-Verlag New York Inc.

Year published

1988-08-01

Number of pages

198

Prizes

N/A

Cover note

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

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This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

Algebra for Computer Science Lars Garding

Algebra for Computer Science by Lars Garding

Summary

Algebra for Computer Science Summary

Algebra for Computer Science by Lars Garding

Table of Contents

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