Abstract Algebra: A Gentle Introduction

✍ Scribed by Gary L. Mullen, James A. Sellers

• Publisher: Chapman and Hall/CRC
• Year: 2016
• Tongue: English
• Leaves: 214
• Series: Textbooks in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra.

Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors

who need to have an introduction to the topic.

As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic.

Features

• Groups before rings approach
• Interesting modern applications
• Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers.
• Numerous exercises at the end of each section
• Chapter "Hint and Partial Solutions" offers built in solutions manual

✦ Table of Contents

Contents
Preface
Chapter 1. Elementary Number Theory
1.1 Divisibility
1.1 Exercises
Solutions 1.1
1.2 Primes and factorization
1.2 Exercises
Solutions 1.2
1.3 Congruences
1.3 Exercises
Solutions 1.3
1.4 Solving congruences
1.4 Exercises
Solutions 1.4
1.5 Theorems of Fermat and Euler
1.5 Exercises
Solutions 1.5
1.6 RSA cryptosystem
1.6 Exercises
Solutions 1.6
Chapter 2. Groups
2.1 Definition of a group
2.2 Examples of groups
2.2 Exercises
Solutions 2.2
2.3 Subgroups
2.3 Exercises
Solutions 2.3
2.4 Cosets and Lagrange’s Theorem
2.4 Exercises
Solutions 2.4
Chapter 3. Rings
3.1 Definition of a ring
3.1 Exercises
Solutions 3.1
3.2 Subrings and ideals
3.2 Exercises
Solutions 3.2
3.3 Ring homomorphisms
3.3 Exercises
Solutions 3.3
3.4 Integral domains
3.4 Exercises
Solutions 3.4
Chapter 4. Fields
4.1 Definition and basic properties of a field
4.1 Exercises
Solutions 4.1
Chapter 5. Finite Fields
5.1 Number of elements in a finite field
5.1 Exercises
Solutions 5.1
5.2 How to construct finite fields
5.2 Exercises
Solutions 5.2
5.3 Properties of finite fields
5.3 Exercises
Solutions 5.3
5.4 Polynomials over finite fields
5.4 Exercises
Solutions 5.4
5.5 Permutation polynomials
5.5 Exercises
Solutions 5.5
5.6 Applications
5.6.1 Orthogonal Latin squares
5.6.2 Diffie/Hellman key exchange
5.6 Exercises
Solutions 5.6
Chapter 6. Vector Spaces
6.1 Definition and examples
6.1 Exercises
Solutions 6.1
6.2 Basic properties of vector spaces
6.2 Exercises
Solutions 6.2
6.3 Subspaces
6.3 Exercises
Solutions 6.3
Chapter 7. Polynomials
7.1 Basics
7.1 Exercises
Solutions 7.1
7.2 Unique factorization
7.2 Exercises
Solutions 7.2
7.3 Polynomials over the real and complex numbers
7.3 Exercises
Solutions 7.3
7.4 Root formulas
7.4 Exercises
Solutions 7.4
Chapter 8. Linear Codes
8.1 Basics
8.2 Hamming codes
8.3 Encoding
8.4 Decoding
8.5 Further study
8.6 Exercises
Solutions 8.6
Chapter 9. Appendix
9.1 Mathematical induction
9.1 Exercises
Solutions 9.1
9.2 Well-ordering Principle
9.2 Exercises
Solutions 9.2
9.3 Sets
9.3 Exercises
Solutions 9.3
9.4 Functions
9.4 Exercises
Solutions 9.4
9.5 Permutations
9.5 Exercises
Solutions 9.5
9.6 Matrices
9.6 Exercises
Solutions 9.6
9.7 Complex numbers
9.7 Exercises
Solutions 9.7
Chapter 10. Hints and Partial Solutions to Selected Exercises
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Bibliography
[14]
[30]
Index
abcd
efghi
klmnop
qrstuv
wz