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How to Prove It: A Structured Approach Paperback – Jan 16 2006
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"The prose is clear and cogent ... the exercises are plentiful and are pitched at the right level.... I recommend this book very highly!"
"The book provides a valuable introduction to the nuts and bolts of mathematical proofs in general."
"This is a good book, and an exceptionally good mathematics book. Thorough and clear explanations, examples, and (especially) exercised with complete solutions all contribute to make this an excellent choice for teaching yourself, or a class, about writing proofs."
Brent Smith, SIGACT News
Beginning with the basic concepts of logic and set theory, this book teaches the language of mathematics and how it is interpreted. The author uses these concepts as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. He 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.See all Product Description
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Top Customer Reviews
Velleman elucidates complex concepts in math extremely clearly, by carefully and thoroughly building on concepts one at a time. His explanation of basic set theory had me looking at the definitions I had already known in an entirely new, fresher and clearier perspective, like I was seeing them again for the first time. Flipping through the book at the beginning, without any knowledge of the symbols, it feels like it's written in code. Two chapters in and you'll find that voila! it is you who are writing that code, fluently.
I am eagerly anticipating finishing the book. The later chapters from my current level of understanding seem sort of incomprehensible. All the greater the sense of accomplishment however, when I reach the end and find I can read it as well as if I've learned another language.
I've been studiously working through the problems Velleman includes solved at the back of the book. This book would be *perfect* if all the problems included solutions, then I would attempt all of them, since there would be no fear of reinforcing misunderstanding by believing incorrect answers to be correct.
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