John W. Lawrence

Abstract Algebra (eBook, PDF)

A Comprehensive Introduction

• Format: PDF

Produktbeschreibung

Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Grobner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 15. April 2021
• Englisch
• ISBN-13: 9781108865517
• Artikelnr.: 66183612

Autorenporträt

John W. Lawrence is Professor Emeritus at the University of Waterloo. He was born in Ottawa, Canada, and received degrees from Carleton University and McGill University. After a year of postdoctoral work at the University of Chicago, he joined the Pure Mathematics Department of the University of Waterloo. He now lives with his wife Louise, in Thornhill Canada, where he continues his research in mathematics and probability.

Inhaltsangabe

Contents
Preface
1. A refresher on the integers
2. A first look at groups
3. Groups acting on sets
4. Basics on rings-mostly commutative
5. Primes and unique factorization
6. Algebraic field extensions
7. Applications of galois theory
8. Modules over principal ideal domains
9. Division algorithms
Appendix A: Infinite sets.