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Synopsis
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This textbook 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 familiarise 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 'scratchwork' sections to expose the machinery of proofs about the natural numbers, relations, functions and infinite sets. Numerous exercises give students the opportunity to construct their own proofs. 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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Review
'... we can warmly advise this excellent book for those who need to get acquainted with or must teach course on formalism and proof techniques.' Acta Scientiarum Mathematicarum
From the Author
Related software available
Macintosh software that helps you learn to write proofs using the methods explained in this book can be downloaded from my homepage at:
http://www.cs.amherst.edu/~djv
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How to Prove It: A Structured Approach
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Cambridge University Press, 1994
ISBN 10: 0521446635
ISBN 13: 9780521446631
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How to Prove It: A Structured Approach
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How to Prove It: A Structured Approach
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How to Prove It: A Structured Approach
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How to Prove It: A Structured Approach
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How to Prove It: A Structured Approach
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How to Prove It: A Structured Approach
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How to Prove It: A Structured Approach
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How to Prove It: A Structured Approach
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