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Fundamental Concepts of Abstract Algebra

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MAA Review

This is a competent but uninspiring first course in abstract algebra, concentrating on groups, rings, and fields; but with an extensive coverage of vector spaces, much more than is needed to explain extension fields. It is an unaltered reprint of a 1991 work published by PWS-Kent.

The book includes a large number of exercises, most of moderate difficulty. A novel feature is that each problem section starts with a set of easy true-false questions to test the student’s understanding; for example, an exercise on p. 188 is “the polynomial x⁴ + 3x³ + 9x² + 9x + 18 is irreducible over the rational field”, and an exercise on p. 332 is “a regular 680-gon is constructible”.

Another book with similar coverage, but much more interesting and idiosyncratic, is Clark’s Elements of Abstract Algebra.

Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.

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