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Algebra Interactive! : Learning Algebra in an Exciting Way - Arjeh M. Cohen

Algebra Interactive!

Learning Algebra in an Exciting Way

Book with Other Items Published: 25th August 1999
ISBN: 9783540653684
Number Of Pages: 159

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Algebra Interactive! is an HTML-based course for undergraduate students in all fields of science, e.g. mathematics, computer science, physics and (electrical) engineering. The novel features of Algebra Interactive are the interactive examples and tools for computing in the various structures. Many of these tools and examples use the computer package GAP, which comes with Algebra Interactive, as a back engine. Moreover, abstract notations are enlivened by Java applets, which go beyond the classical examples given in traditional textbooks. The course contains numerous exercises. Apart from the classical type of exercise (with hints and solutions), the product also presents interactive multiple-choice questions on each page and at the end of each chapter. A comprehensive accompanying printed book summarizes the contents of Algebra Interactive.

Arithmeticp. 1
Divisors and multiplesp. 1
Euclid's algorithmp. 2
Linear diophantine equationsp. 5
Prime numbersp. 6
Factorizationp. 7
Exercisesp. 9
Modular arithmeticp. 10
Arithmetic modulo np. 10
Linear congruencesp. 12
The a-ary number systemp. 14
The RSA cryptosystemp. 15
Radar detectionp. 16
Exercisesp. 18
Polynomialsp. 20
The notion of a polynomialp. 20
Division of polynomialsp. 22
Polynomial functionsp. 25
Factorizationp. 27
Shift registersp. 30
Exercisesp. 33
Arithmetic modulo polynomialsp. 35
Congruence modulo a polynomialp. 35
The residue class ringp. 37
Two special casesp. 41
Inverses and fieldsp. 43
Finite fieldsp. 45
Error correcting codesp. 46
Exercisesp. 50
Permutationsp. 53
Symmetric Groupsp. 53
Cyclesp. 55
Alternating groupsp. 59
Exercisesp. 62
Monoids and groupsp. 65
Binary operationsp. 65
Monoidsp. 68
Invertibility in monoidsp. 73
Groupsp. 75
Cyclic groupsp. 80
Cosetsp. 82
Exercisesp. 85
Rings and fieldsp. 88
The structure ringp. 88
Constructions with ringsp. 93
Domains and fieldsp. 96
Fieldsp. 102
Idealsp. 109
Residue class ringsp. 114
Finite fieldsp. 118
Exercisesp. 124
Permutation groupsp. 127
Permutation groupsp. 127
Orbitsp. 131
Orderp. 135
Automorphismsp. 140
Quotient groupsp. 144
Small groupsp. 146
Exercisesp. 150
Appendix: A guide to Algebra Interactivep. 157
Using Algebra Interactivep. 157
Authorsp. 159
Acknowledgementsp. 159
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540653684
ISBN-10: 3540653686
Audience: Professional
Format: Book with Other Items
Language: English
Number Of Pages: 159
Published: 25th August 1999
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 25.4 x 20.3  x 1.91
Weight (kg): 0.59