LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	511.3
Title	Algebra for Computer Science ([EBook]) / by Lars Gårding, Torbjörn Tambour.
Author	Gårding, Lars. , 1919-
Added Personal Name	Tambour, Torbjörn
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1988.
Physical Details	IX, 198 p. : online resource.
Series	Universitext 0172-5939
ISBN	9781461387978
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4613-8797-8
Links to Related Works	Subject References: Mathematical logic . Mathematical Logic and Foundations . Mathematics . Authors: author . Gårding, Lars. 1919- . Gårding, Lars, 1919- . Tambour, Torbjörn . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 511.3 .

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Algebra for Computer Science

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