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Full Description
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
Contents
Elementary Number Theory
Divisibility
Primes and factorization
Congruences
Solving congruences
Theorems of Fermat and Euler
RSA cryptosystem
Groups
De nition of a group
Examples of groups
Subgroups
Cosets and Lagrange's Theorem
Rings
Defiition of a ring
Subrings and ideals
Ring homomorphisms
Integral domains
Fields
Definition and basic properties of a field
Finite Fields
Number of elements in a finite field
How to construct finite fields
Properties of finite fields
Polynomials over finite fields
Permutation polynomials
Applications
Orthogonal latin squares
Die/Hellman key exchange
Vector Spaces
Definition and examples
Basic properties of vector spaces
Subspaces
Polynomials
Basics
Unique factorization
Polynomials over the real and complex numbers
Root formulas
Linear Codes
Basics
Hamming codes
Encoding
Decoding
Further study
Exercises
Appendix
Mathematical induction
Well-ordering Principle
Sets
Functions
Permutations
Matrices
Complex numbers
Hints and Partial Solutions to Selected Exercises
