Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks. This book is offered as a manual to a new way of thinking. The author aims to instill the desire to understand the material, to encourage more discovery, and to appreciate the subject for its own sake.
Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks. This book is offered as a manual to a new way of thinking. The author aims to instill the desire to understand the material, to encourage more discovery, and to appreciate the subject for its own sake.
Steve Rosenberg is a professor in the Mathematics and Computer Science Department at the University of Wisconsin-Superior. He received his Ph.D. from the Ohio State University. As an educator, Dr. Rosenberg has both developed and taught a wide array of courses in mathematics and computer science. As a researcher, he has published results in the areas of algebraic number theory, cryptographic protocols, and combinatorial designs, among others. As a software developer, his clients included Coca-Cola Enterprises and the pension agency of Cook County Illinois. He has extensive experience in computer science and software engineering.
Inhaltsangabe
Preface Symbols 1.Review of Sets, Functions, and Proofs 2.Introduction: A Number Game 3.Groups 4.Subgroups 5.Symmetry 6.Free Groups 7.Group Homomorphisms 8.Lagrange's Theorem 9.Special Types of Homomorphisms 10.Making Groups 11.Rings 12.Results on Commutative Rings 13.Vector Spaces 14.Polynomial Rings 15.Field Theory 16.Galois Theory 17.Direct Sums and Direct Products 18.The Structure of Finite Abelian Groups 19.Group Actions 20.Learning from Z 21.The Problems of the Ancients 22.Solvability of Polynomial Equations by Radicals 23.Projects Bibliography Index
Preface Symbols 1.Review of Sets, Functions, and Proofs 2.Introduction: A Number Game 3.Groups 4.Subgroups 5.Symmetry 6.Free Groups 7.Group Homomorphisms 8.Lagrange's Theorem 9.Special Types of Homomorphisms 10.Making Groups 11.Rings 12.Results on Commutative Rings 13.Vector Spaces 14.Polynomial Rings 15.Field Theory 16.Galois Theory 17.Direct Sums and Direct Products 18.The Structure of Finite Abelian Groups 19.Group Actions 20.Learning from Z 21.The Problems of the Ancients 22.Solvability of Polynomial Equations by Radicals 23.Projects Bibliography Index
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