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Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This book will prepare students for such courses by teaching them techniques for writing and reading proofs. No background beyond high school mathematics is assumed. The book begins with logic and set theory, to familiarize students with the language of mathematics and how it is interpreted.
This understanding of the language of mathematics serves as the basis for a detailed discussion of the most important techniques used in proofs, when and how to use them, and how they are combined to produce complex proofs. Material on the natural numbers, relations, functions, and infinite sets provides practice in writing and reading proofs, as well as supplying background that will be valuable in most theoretical mathematics courses.
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Previews available in: English
Showing 7 featured editions. View all 7 editions?
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1
How to Prove It: A Structured Approach
2019, University of Cambridge ESOL Examinations
in English
1108539890 9781108539890
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2
How to Prove It: A Structured Approach
2019, Cambridge University Press
in English
1108439535 9781108439534
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3
How to Prove It: A Structured Approach
2019, Cambridge University Press
in English
110842418X 9781108424189
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4
How to Prove It: A Structured Approach
2012, University of Cambridge ESOL Examinations
in English
0511808232 9780511808234
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5
How to prove it: a structured approach
2006, Cambridge University Press
in English
- 2nd ed.
0521861241 9780521861243
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6 |
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7
How to prove it: a structured approach
1994, Cambridge University, Cambridge University Press, Brand: Cambridge University Press
in English
0521441161 9780521441162
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Book Details
Edition Notes
Includes bibliographical references (p. 304) and index.
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Work Description
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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Feedback?December 20, 2023 | Edited by ImportBot | import existing book |
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