Preface; A guide to this guide; 1. Algebra: classical, modern, and ultramodern; 2. Categories; 3. Algebraic structures; 4. Groups and their representations; 5. Rings and modules; 6. Fields and skew fields; Bibliography; Index of notations; Index.
Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.
Fernando Q. Gouvêa is the Carter Professor of Mathematics at Colby College, Maine. He was editor of MAA Focus, the newsletter of the Mathematical Association of America, from 1999 to 2010 and is currently editor of MAA Reviews and the Carus Mathematical Monographs book series. He has written several books, including Math Through the Ages, with William P. Berlinghoff, which was awarded the 2007 Beckenbach Book Prize.
… Billed as delivering a concise, graduate-level overview of the
theory of groups, rings, and fields, it emphasizes the main ideas
and how they hang together, as well as the ways these subjects are
used in other parts of mathematics. … Overall, an enjoyable
volume." - F.E.J. Linton, CHOICE
"This expository algebra book is highly unusual—but in a very
successful manner." - Tom De Medts, Mathematical Reviews
"This book is one of the latest in the MAA series of guides to
different areas of mathematics intended to summarize the material
graduate students need to know in preparing for PhD comprehensive
exams. This one in particular, is welcome since the area, abstract
algebra is a required exam subject at many universities. The
organization of the book is straightforward with three brief
introductory chapters (totalling 28 pages) giving a bit of history,
a very little bit of category theory, and some observations on the
organization of the subject. … number theorists, operator
theorists, and students in most other areas will find this book
most satisfactory in all respects." - CMS Notes
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