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> Abstract Algebra

Abstract Algebra A Comprehensive Introduction

Authors

John W. Lawrence, University of Waterloo, Ontario, Frank A. Zorzitto, University of Waterloo, Ontario
Published 2021

Description

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 Gröbner 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…

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Key features

  • Balances accessibility with rigor, allowing motivated students to gain mastery of advanced topics
  • Takes a 'definitions first, examples next' approach, striking the right balance between abstract material and its motivation
  • Prepares students for advanced studies in mathematics by offering a uniquely wide base of knowledge in key topics
  • Coverage includes: finite abelian groups, Sylow theory, semi-direct products, solvable groups, unique factorization, irreducibility of polynomials, Galois theory and solvability by radicals, ruler and compass constructions, module theory over principal ideal domains, and a novel approach to Gröbner bases

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