Geared to preparing students to make the transition from solving problems to proving theorems, this text teaches 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. To help students 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. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5
1. Sentential logic; 2. Quantificational logic; 3. Proofs; 4. Relations; 5. Functions; 6. Mathematical induction; 7. Infinite sets.
"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