Abstract Algebra

A Gentle Introduction

Gary L. Mullen, James A. Sellers

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Hardback

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English

CRC Press Inc
20 December 2016

Algebra; Applied mathematics

Series: Textbooks in Mathematics

"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"

By: Gary L. Mullen, James A. Sellers
Imprint: CRC Press Inc
Country of Publication: United States
Dimensions: Height: 229mm, Width: 152mm,
Weight: 480g
ISBN: 9781482250060
ISBN 10: 1482250063
Series: Textbooks in Mathematics
Pages: 204
Publication Date: 20 December 2016
Audience: General/trade , College/higher education , ELT Advanced , Primary
Format: Hardback
Publisher's Status: Active

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 Di□e/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

"Gary Mullen is Professor of Mathematics, The Pennsylvania State University, where he earned his Ph.D. His main interest is finite fields, and is founder of the journal ""Finite Fields and Their Introduction."" He is also the Editor of The Handbook of Finite Fields published by CRC Press. James Sellers is Professor and Associate Head for Undergraduate Mathematics, The Pennsylvania State University, where he also earned his Ph.D. He has published many research articles and won awards related to his efforts to advance mathematics education."

Reviews for Abstract Algebra: A Gentle Introduction

As the subtitle implies, those seeking a standard undergraduate text in abstract algebra should look elsewhere. The authors provide readers with a very brief introduction to some of the central structures of algebra: groups, rings, fields, and vector spaces. As an example of the textaEURO (TM)s brevity, its treatment of groups consists of definitions, examples, and a discussion of subgroups and cosets that culminates in LaGrangeaEURO (TM)s theorem. There is no mention of group homomorphisms, normal subgroups, or quotient groups. Nonetheless, various applications of the subject not often addressed in traditional texts are treated within this work. It appears that the intent is to provide enough content for readers to comprehend these applications. Just enough elementary number theory is presented to allow a discussion of the RSA cryptosystem. Sufficient material on finite fields is given for a discussion of Latin squares and the Diffie-Hellman public key exchange. Adequate linear algebra topics foster a discussion of Hamming codes. This text will be suitable for an algebra-based course introducing students to abstract mathematical thought or an algebra course with an emphasis on applications. --D. S. Larson, Gonzaga University, Choice magazine 2016