+612 9045 4394

CHECKOUT

# Algebra Interactive!

### Learning Algebra in an Exciting Way

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

### Book with Other Items

RRP \$202.99
\$146.25
28%
OFF
Ships in 7 to 10 business days

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.

 Arithmetic p. 1 Divisors and multiples p. 1 Euclid's algorithm p. 2 Linear diophantine equations p. 5 Prime numbers p. 6 Factorization p. 7 Exercises p. 9 Modular arithmetic p. 10 Arithmetic modulo n p. 10 Linear congruences p. 12 The a-ary number system p. 14 The RSA cryptosystem p. 15 Radar detection p. 16 Exercises p. 18 Polynomials p. 20 The notion of a polynomial p. 20 Division of polynomials p. 22 Polynomial functions p. 25 Factorization p. 27 Shift registers p. 30 Exercises p. 33 Arithmetic modulo polynomials p. 35 Congruence modulo a polynomial p. 35 The residue class ring p. 37 Two special cases p. 41 Inverses and fields p. 43 Finite fields p. 45 Error correcting codes p. 46 Exercises p. 50 Permutations p. 53 Symmetric Groups p. 53 Cycles p. 55 Alternating groups p. 59 Exercises p. 62 Monoids and groups p. 65 Binary operations p. 65 Monoids p. 68 Invertibility in monoids p. 73 Groups p. 75 Cyclic groups p. 80 Cosets p. 82 Exercises p. 85 Rings and fields p. 88 The structure ring p. 88 Constructions with rings p. 93 Domains and fields p. 96 Fields p. 102 Ideals p. 109 Residue class rings p. 114 Finite fields p. 118 Exercises p. 124 Permutation groups p. 127 Permutation groups p. 127 Orbits p. 131 Order p. 135 Automorphisms p. 140 Quotient groups p. 144 Small groups p. 146 Exercises p. 150 Appendix: A guide to Algebra Interactive p. 157 Using Algebra Interactive p. 157 Authors p. 159 Acknowledgements p. 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