A Concrete Approach to Abstract Algebra

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Courier Dover Publications, Aug 10, 2018 - Mathematics - 240 pages
Brief, clear, and well written, this introduction to abstract algebra bridges the gap between the solid ground of traditional algebra and the abstract territory of modern algebra. The only prerequisite is high school–level algebra.
Author W. W. Sawyer begins with a very basic viewpoint of abstract algebra, using simple arithmetic and elementary algebra. He then proceeds to arithmetic and polynomials, slowly progressing to more complex matters: finite arithmetic, an analogy between integers and polynomials, an application of the analogy, extending fields, and linear dependence and vector spaces. Additional topics include algebraic calculations with vectors, vectors over a field, and fields regarded as vector spaces. The final chapter proves that angles cannot be trisected by Euclidean means, using a proof that shows how modern algebraic concepts can be used to solve an ancient problem. Exercises appear throughout the book, with complete solutions at the end.
 

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User Review  - bookaholixanon - LibraryThing

See my review of Mathematician's Delight. Basically, anything written by W. W. Sawyer is pure gold, and worth reading. This book shows that Sawyer is just as adept with advanced as with elementary material. Read full review

Contents

Introduction
1
Arithmetics and Polynomials
26
Finite Arithmetics
71
An Analogy Between Integers and Polynomials
83
An Application of the Analogy
94
Extending Fields
115
Linear Dependence and Vector Spaces
131
Algebraic Calculations with Vectors
157
Vectors Over a Field
167
Fields Regarded as Vector Spaces
185
Trisection of an Angle
208
Answers to Exercises
223
Index
233
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About the author (2018)

Walter Warwick Sawyer (1911–2008) studied mathematics at St. John's College, Cambridge, and taught all over the world, starting at the universities of Dundee and Manchester and later at the University of Ghana and Canterbury College in New Zealand. He was Professor of Mathematics at Wesleyan University in Connecticut and on the faculty at the University of Toronto. His 11 books include the Dover publications Prelude to Mathematics, Mathematician's Delight, Vision in Elementary Mathematics, and A First Look at Numerical Functional Analysis.

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