A Concrete Introduction to Higher AlgebraSpringer Science & Business Media, 26 нояб. 2008 г. - Всего страниц: 604 This book is 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. The new examples and theory are built 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 are found throughout the book. |
Содержание
Numbers | 3 |
Euclids Algorithm | 27 |
Unique Factorization | 53 |
Congruence | 71 |
Congruence Classes | 93 |
Rings and Fields 123 | 122 |
Matrices and Codes | 147 |
Fermats and Eulers Theorems 171 | 169 |
Polynomials in Qx | 339 |
Congruences and the Chinese Remainder Theorem | 355 |
Fast Polynomial Multiplication 373 | 372 |
Carmichael Numbers | 413 |
Quadratic Reciprocity | 433 |
Quadratic Applications 459 | 458 |
Congruence Classes Modulo a Polynomial 479 | 477 |
Homomorphisms and Finite Fields | 495 |
Applications of Eulers Theorem | 201 |
Groups | 223 |
The Chinese Remainder Theorem | 253 |
Polynomials | 285 |
The Fundamental Theorem of Algebra | 307 |
BCH Codes | 511 |
Factoring in Zx | 531 |
Irreducible Polynomials | 557 |
| 595 | |
Другие издания - Просмотреть все
Часто встречающиеся слова и выражения
abelian group Algebra Alice Bezout's Identity Carmichael numbers Chapter Chinese Remainder Theorem commutative ring complete set complex numbers compute congruence classes congruent modulo coprime Corollary cosets defined digits divides Division Theorem element of G encrypted equation errors Euclid's Algorithm evaluate example Exercises exponent Fermat numbers Fermat's theorem follows function greatest common divisor group of units hence induction integers inverse irreducible polynomials isomorphism Latin squares least common multiple Lemma Let G matrix mod m(x mod q monic polynomial natural numbers nonzero number of elements odd number odd prime one-to-one polynomial f(x polynomials of degree prime number primitive root modulo Proof Proposition prove quadratic rational numbers real numbers root of unity safeprime Section sequence set of representatives Show solve Springer Science+Business Media square modulo Suppose trial division unique units modulo units of Z/mZ vector write Z/pZ zero divisors α2 α
Ссылки на эту книгу
Discrete Mathematics Using Latin Squares Charles F. Laywine,Gary L. Mullen Ограниченный просмотр - 1998 |