A Concrete Approach to Abstract Algebra
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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LibraryThing ReviewUser 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
Arithmetics and Polynomials
An Analogy Between Integers and Polynomials
An Application of the Analogy
Linear Dependence and Vector Spaces
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