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A concrete approach to abstract algebra

Author: W W Sawyer
Publisher: Mineola, New York : Dover Publications, 2018.
Series: Dover books on mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Sawyer, W.W. (Walter Warwick), 1911-2008.
Concrete approach to abstract algebra.
Mineola, New York : Dover Publications, Inc., 2018
(DLC) 2018012819
(OCoLC)1030447519
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: W W Sawyer
ISBN: 9780486833316 0486833313
OCLC Number: 1048924289
Notes: Includes index.
Description: 1 online resource (234 pages)
Contents: The viewpoint of abstract algebra --
Arithmetics and polynomials --
Finite arithmetics --
An analogy between integers and polynomials --
An application of the analogy --
Extending fields --
Linear dependence and vector spaces --
Algebraic calculations and vectors --
Vectors over a field --
Fields regarded as vector spaces --
Trisection of an angle.
Series Title: Dover books on mathematics.
Responsibility: W.W. Sawyer.

Abstract:

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.

Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.

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