A Concrete Approach to Abstract Algebra
A Concrete Approach to Abstract Algebra
- ISBN 13:
9780486824611
- ISBN 10:
0486824616
- Format: Paperback
- Copyright: 08/15/2018
- Publisher: Dover Publications
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Summary
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.