Abstract Algebra A Gentle Introduction

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 majorswho 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. FeaturesGroups before rings approachInteresting modern applicationsAppendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers.Numerous exercises at the end of each sectionChapter "Hint and Partial Solutions" offers built in solutions manual

Elementary Number TheoryDivisibilityPrimes and factorizationCongruences Solving congruencesTheorems of Fermat and EulerRSA cryptosystemGroupsDe nition of a groupExamples of groups Subgroups Cosets and Lagrange's Theorem Rings Defiition of a ringSubrings and idealsRing homomorphisms Integral domains Fields Definition and basic properties of a fieldFinite Fields Number of elements in a finite fieldHow to construct finite fieldsProperties of finite fieldsPolynomials over finite fieldsPermutation polynomials Applications Orthogonal latin squares Die/Hellman key exchange Vector Spaces Definition and examples Basic properties of vector spaces Subspaces PolynomialsBasics Unique factorization Polynomials over the real and complex numbers Root formulas Linear CodesBasics Hamming codes Encoding Decoding Further study Exercises AppendixMathematical induction Well-ordering PrincipleSetsFunctionsPermutationsMatrices Complex numbersHints 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.