How to Prove It: A Structured ApproachGeared 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 |
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LibraryThing Review
User Review - billlund - LibraryThingThis should be required reading for all math majors and those who want to learn how to write formal proofs. It is well written with lots of examples. Read full review
LibraryThing Review
User Review - timoDM - LibraryThingNot yet read--deals with logical and mathematical proofs using examples from a variety of fields. Read full review
Contents
Sentential Logic | 8 |
Quantificational Logic | 55 |
Proofs | 84 |
Relations | 163 |
Functions | 226 |
Mathematical Induction | 260 |
Infinite Sets | 306 |
Solutions to Selected Exercises | 329 |
Proof Designer | 373 |
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Common terms and phrases
A X B Analyze the logical arbitrary element assume assumption choose conclude countable counterexample defined definition disjoint element of F equation equivalence classes equivalence relation example exercise existential f is one-to-one fact false family of sets Figure find finite first following proof form xP(x free variables function f Givens Goal Hint Induction step inductive hypothesis Let f logical forms mathematical induction means minimal element modus ponens natural number negation law notation ordered pairs partial order plug positive integer prime numbers proof by contradiction Proof Designer proof strategies prove a goal quantifier real number recursive reexpress reflexive Scratch Similarly smallest element Solution Theorem stand statement P(x strict partial order subset Suppose f symbols symmetric closure Theorem total order transitive closure truth set truth table universe of discourse Venn diagrams Vx G words write
Bibliographic information
| Title | How to Prove It: A Structured Approach |
| Author | Daniel J. Velleman |
| Edition | illustrated, reprint, revised |
| Publisher | Cambridge University Press, 2006 |
| ISBN | 0521861241, 9780521861243 |
| Length | 384 pages |
| Subjects | › Mathematics / Combinatorics Mathematics / General Mathematics / History & Philosophy Mathematics / Logic |
| Export Citation | BiBTeX EndNote RefMan |