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.
- ISBN10 6611836624
- ISBN13 9786611836627
- Publish Date 1 January 2006 (first published 25 November 1994)
- Publish Status Active
- Out of Print 26 October 2011
- Publish Country US
- Imprint Cambridge University Press
- Format eBook
- Pages 397
- Language English