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Author Velleman, Daniel J.

Title How to prove it : a structured approach / Daniel J. Velleman.

Published Cambridge [England] ; New York : Cambridge University, 1994.


Location Call No. Status
 UniM Bund  511.3 VELL {Bund10 20110701}    DUE 22-07-19
Physical description ix, 309 p. : ill. ; 24 cm.
Bibliography Includes bibliographical references (p. 304) and index.
Contents 1. Sentential Logic. 1.1. Deductive reasoning and logical connectives. 1.2. Truth tables. 1.3. Variables and sets. 1.4. Operations on sets. 1.5. The conditional and biconditional connectives -- 2. Quantificational Logic. 2.1. Quantifiers. 2.2. Equivalences involving quantifiers. 2.3. More operations on sets -- 3. Proofs. 3.1. Proof strategies. 3.2. Proofs involving negations and conditionals. 3.3. Proofs involving quantifiers. 3.4. Proofs involving conjunctions and biconditionals. 3.5. Proofs involving disjunctions. 3.6. Existence and uniqueness proofs. 3.7. More examples of proofs -- 4. Relations. 4.1. Ordered pairs and Cartesian products. 4.2. Relations. 4.3. More about relations. 4.4. Ordering relations. 4.5. Closures. 4.6. Equivalence relations -- 5. Functions. 5.1. Functions. 5.2. One-to-one and onto. 5.3. Inverses of functions. 5.4. Images and inverse images: a research project -- 6. Mathematical Induction. 6.1. Proof by mathematical induction. 6.2. More examples.
6.3. Recursion. 6.4. Strong induction. 6.5. Closures again -- 7. Infinite sets. 7.1. Equinumerous sets. 7.2. Countable and uncountable sets. 7.3. The Cantor-Schroder-Bernstein theorem.
Summary 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.
Subject Logic, Symbolic and mathematical.
ISBN 0521441161 (hardback)
0521446635 (pbk.)