A concrete introduction to higher algebra
Author(s)
Bibliographic Information
A concrete introduction to higher algebra
(Undergraduate texts in mathematics)
Springer, c2009
3rd ed
Available at 33 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references (p. 595-598) and index
Description and Table of Contents
Description
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.
Table of Contents
Numbers.- Numbers.- Induction.- Euclid's Algorithm.- Unique Factorization.- Congruence.- Congruence classes and rings.- Congruence Classes.- Rings and Fields.- Matrices and Codes.- Congruences and Groups.- Fermat's and Euler's Theorems.- Applications of Euler's Theorem.- Groups.- The Chinese Remainder Theorem.- Polynomials.- Polynomials.- Unique Factorization.- The Fundamental Theorem of Algebra.- Polynomials in ?[x].- Congruences and the Chinese Remainder Theorem.- Fast Polynomial Multiplication.- Primitive Roots.- Cyclic Groups and Cryptography.- Carmichael Numbers.- Quadratic Reciprocity.- Quadratic Applications.- Finite Fields.- Congruence Classes Modulo a Polynomial.- Homomorphisms and Finite Fields.- BCH Codes.- Factoring Polynomials.- Factoring in ?[x].- Irreducible Polynomials.
by "Nielsen BookData"