A Concrete Approach to Abstract Algebra

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  • Format: Paperback
  • Copyright: 2018-08-15
  • Publisher: Dover Publications

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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.

Author Biography

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.

Table of Contents

1. The Viewpoint of Abstract Algebra
2. Arithmetics and Polynomials
3. Finite Arithmetics
4. An Analogy Between Integers and Polynomials
5. An Application of the Analogy
6. Extending Fields
7. Linear Dependence and Vector Spaces
8. Algebraic Calculations with Vectors
9. Vectors Over a Field
10. Fields Regarded as Vector Spaces
11. Trisection of an Angle
Answers to Exercises

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