A Concrete Introduction to Higher Algebra - Brossura

Childs, Lindsay N. N.

Brossura

ISBN 10: 0387989994 ISBN 13: 9780387989990

Casa editrice: Springer, 2000

Riassunto

An informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated in a well-motivated fashion and made relevant by many applications -- to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.

Su questo libro

Recensione:

From the reviews:

"The user-friendly exposition is appropriate for the intended audience. Exercises often appear in the text at the point they are relevant, as well as at the end of the section or chapter. Hints for selected exercises are given at the end of the book. There is sufficient material for a two-semester course and various suggestions for one-semester courses are provided. Although the overall organization remains the same in the second edition¿Changes include the following: greater emphasis on finite groups, more explicit use of homomorphisms, increased use of the Chinese remainder theorem, coverage of cubic and quartic polynomial equations, and applications which use the discrete Fourier transform." MATHEMATICAL REVIEWS

Contenuti:

1 Numbers 2 Induction 3 Euclid's Algorithm 4 Unique Factorization 5 Congruences 6 Congruence Classes 7 Applications of Congruences 8 Rings and Fields 9 Fermat's and Euler's Theorems 10 Applications of Fermat's and Euler's Theorems 11 On Groups 12 The Chinese Remainder Theorem 13 Matrices and Codes 14 Polynomials 15 Unique Factorization 16 The Fundamental Theorem of Algebra 17 Derivatives 18 Factoring in Q[x],I 19 The Binomial Theorem in Characteristic p 20 Congruences and the Chinese Remainder Theorem 21 Applications of the Chinese Remainder Theorem 22 Factoring in Fp[x] and in Z[x] 23 Primitive Roots 24 Cyclic Groups and Primitive Roots 25 Pseudoprimes 26 Roots of Unity in Z/mZ 27 Quadratic Residues 28 Congruence Classes Mopdulo a Polynomial 29 Some Applications of Finite Fields 30 Classifying Finite Fields

Su questa edizione

• Editore: Springer
• Data di pubblicazione: 2000
• ISBN 10: 0387989994
• ISBN 13: 9780387989990
• Rilegatura: Copertina flessibile
• Numero di pagine: 544