- Paperback: 314 pages
- Publisher: Richard Hammack; Revised edition (May 31, 2013)
- Language: English
- ISBN-10: 0989472108
- ISBN-13: 978-0989472104
- Product Dimensions: 7 x 0.7 x 10 inches
- Shipping Weight: 1.2 pounds (View shipping rates and policies)
- Average Customer Review: 63 customer reviews
- Amazon Best Sellers Rank: #35,350 in Books (See Top 100 in Books)
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Book of Proof Revised Edition
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This is a wonderful book. Written as a text for a one-semester "transition to higher mathematics" course, it introduces the undergraduate to logic and proofs and to the basic objects and language used in higher mathematics. It is ideal for the many American undergraduates who come to college with little or no experience with proof or formal reasoning and need to be brought up to speed quickly in order to succeed in upper-level mathematics courses. -- Mathematical Association of America, maa.org/press/maa-reviews/book-of-proof
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In preparation for a (live) class in Abstract Algebra, I needed to learn to do formal proofs, and I didn't want to sit through a full semester of that. So I looked for a self-study book, and "Book of Proof" turned out to be the book. It's tailor-made for self-study, and as a bonus, it's very affordable.
Dr. Hammack literally starts at the beginning, with the basics of notation, sets, logic, etc. He introduces proofs gently enough to allow a determined self-student stay with it. There are plenty of exercises with odd-numbered solutions and these of course should not be skipped.
Dr. Hammack then works through what amounts to a survey of various formal proof types, with plenty of examples and sufficient discussion. All of the major types are covered. My one minor criticism is that I think proof by induction could have used more attention, but you can supplement that elsewhere if you have the need or the urge.
I wouldn't call this book either "deep" or "comprehensive" but that's not a criticism. The book is what it should be, a survey course, and it's at least enough to prepare a student for the next steps. Combined with a course in Linear Algebra, Abstract Algebra will come within reach, as will other higher-level, deeper, and more specialized courses.
Of course, it almost goes without saying that if you elect self-study, you've got to pay attention and work at things. No skimming! But I'm finding the payoff is high. This is clearly the right book for home use. It's lucid, literate, well-constructed, and affordable. Hats off to Dr. Hammack for his contribution to the determined learner.
Apparently it is available online for free, but I wouldn't know. I got a hardcopy from Amazon and am very pleased with it.