How to Prove It: A Structured Approach
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
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LibraryThing ReviewUser Review - billlund - LibraryThing
This should be required reading for all math majors and those who want to learn how to write formal proofs. It is well written with lots of examples. Read full review
As accessible as it is relevant, this title is an unpretentious "how-to" guide for those seeking a framework in which to write their proofs. The subject matter is exclusively the exposition and manipulation of logical forms, but the examples draw from set and number theory. The chapter and section layout is a bit disorganized, and the included exercises appear without solutions. Even with these slight detractions, Velleman's text is definitely worth purchase.