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A Concrete Introduction to Higher Algebra (Undergraduate Texts in Mathematics)

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A Concrete Introduction to Higher Algebra (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

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. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. 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, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix.

Table of Contents

Preface.- Numbers.- Induction.- Euclid's Algorithm.- Unique Factorization.- Congruence.- Congruence Classes.- Rings and Fields.- Matrices and Codes.- Fermat's and Euler's Theorems.- Applications of Fermat's and Euler's Theorems.- Groups.- The Chinese Remainder Theorem.- Polynomials.- Unique Factorization.- The Fundamental Theorem of Algebra.- Polynomials in Q[x].- Congruences and the CRT.- Fast Polynomial Multiplication.- Cyclic Groups and Cryptography.- Carmichael Numbers..- Quadratic Reciprocity.- Quadratic Applications.- Congruence Classes Modulo a Polynomial.- Homomorphism and Finite Fields.- BCH Codes.- Factoring in Z[x].- Irreducible Polynomials.- Answers and Hints to the Exercises.- References.- Index.-

Product Details

ISBN:
9781441925619
Author:
Childs, Lindsay N.
Publisher:
Springer
Subject:
Algebra - General
Subject:
Algebra
Subject:
Algebra <P>This book is written as an introduction to higher algebra for students with a background of a year of calculus. It has been used as a successful undergraduate text for more than 20 years. The objective of the book is to give students enough exp
Subject:
Mathematics - Algebra
Copyright:
Edition Description:
Softcover reprint of hardcover 3rd ed. 2009
Series:
Undergraduate Texts in Mathematics
Publication Date:
20101119
Binding:
TRADE PAPER
Language:
English
Pages:
617
Dimensions:
235 x 155 mm 925 gr

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