Format:
XIII, 384 S.
,
graph. Darst.
,
24 cm
Edition:
2. ed., 1. publ.
ISBN:
0521861241
,
0521675995
,
9780521861243
,
9780521675994
Content:
"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 for the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains more than 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."--Jacket
Content:
Introduction -- 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 -- Quantificational logic -- 2.1 Quantifiers -- 2.2 Equivalences involving quantifiers -- 2.3 More operations on sets -- 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 -- 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 -- 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 -- Mathematical induction -- 6.1 Proof by mathematical induction -- 6.2 More examples -- 6.3 Recursion -- 6.4 Strong induction -- 6.5 Closures again -- Infinite sets -- 7.1 Equinumerous sets -- 7.2 Countable and uncountable sets -- 7.3 The cantor--Schroder--Bernstein theorem -- Appendix 1: Solutions to selected exercises -- Appendix 2: Proof designer -- Suggestions for further reading -- Summary for proof techniques -- Index
Note:
Includes bibliographical references and index
,
Hier auch später erschiene, unveränderte Nachdrucke
Language:
English
Subjects:
Mathematics
,
Psychology
Keywords:
Beweis
;
Mathematik
;
Mathematik
;
Beweis
URL:
http://www.loc.gov/catdir/enhancements/fy0659/2005029447-d.html
URL:
http://www.loc.gov/catdir/enhancements/fy0733/2005029447-b.html
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