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Algebra for Computer Science
Buch
Buch
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Fachbuch
1988

Algebra for Computer Science

Kollektion

Universitext

ISBN
EAN
978-0-387-96780-6
9780387967806
Artikel-Nr.
RRVGWNV
Kostenloser Versand
Rabatt
-11.3
%
CHF 100.00
CHF
88.68
Anzahl
1
Maximale
Lieferzeit
20
Arbeitstage
Montag
23.08.2021
speech-bubble-svg Beschreibung
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.
Inhaltsverzeichnis
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.
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Herausgeber/-innen
Publikation
Vereinigte Staaten
01.08.1988
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Sprache
Englisch
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Softcover
212 Seiten
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Kostenloser Versand: Schweiz & Liechtenstein
Für den Versand nach Deutschland oder Frankreich werden die Versandgebühren der Schweizerischen Post berechnet. Diese werden Ihnen im Warenkorb für Ihre gesamte Bestellung berechnet.
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