Abstract algebra : a gentle introduction

著者

    • Mullen, Gary L.
    • Sellers, James A.

書誌事項

Abstract algebra : a gentle introduction

Gary L. Mullen, James A. Sellers

（Textbooks in mathematics）

CRC Press, c2017

  • : hardback

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注記

"A Chapman & Hall Book"

Includes bibliographical references (p. 195-197) and index

内容説明・目次

内容説明

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

目次

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

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