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A friend of mine, who is a high school math teacher and majored in math in college, recently asked me for a good book to read on Abstract Algebra (presumably, group theory). She is looking for something to read semi-casually, so no serious textbooks which hide intuition.

My own education largely skipped the basics. I read through Pinter in the library one afternoon, and that was pretty much it. So, can people recommend a good book on abstract algebra/groups for the casual learner?

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6 Answers 6

"A Book on Abstract Algebra" by Charles Pinter is a great book for the casual reader. It's an easy read yet maintains rigour throughout all of the topics discussed.

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The exercises in this book are especially worthwhile. –  user12998 Nov 3 '11 at 0:08
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It depends the level of the casual reader (unless by casual you meant low prereqs). If you are looking for a book that requires a little more sophistication, but pays back two-fold in intuition I believe Artin's book Algebra is a good place to look. In particular, it helps motivate abstract groups by looking at the much more managable, understandable, notion of matrix groups.

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She will love Fearless Symmetry by Ash / Gross. Mostly group theory but that's the best start, don't you think so?

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Pinter is an excellent book, but I'd like to also recommend Abstract Algebra and Solution by Radicals, by John and Margaret Maxfield. It's very readable, and takes a semi-casual path through group theory, ending with elementary Galois theory and impossible constructions. This book was my first introduction to abstract algebra several years ago. If your friend wants a gentle introduction to the subject, I think it could be ideal.

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I second the recommendation of Maxfield/Maxfield. In fact, I was going to recommend it myself until I saw that you beat me to it. (By over two years, as I now happened to notice from your answer date!) –  Dave L. Renfro Mar 20 at 14:24
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A gentle introductory book full of intuition on group theory is Nathan Carter's Visual Group Theory. This answer is doubtless much too late for the OP, but may help others looking for casual books on abstract algebra.

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