A Concrete Introduction to Higher Algebra

• Corporate Author: SpringerLink (Online service)
• Other Authors: Childs, Lindsay N. (Editor)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Algebra.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-74725-5

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 f...

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.-.