MARC状态：已编 文献类型：西文图书 浏览次数：27
- 题名/责任者:
- How to prove it : a structured approach Daniel J. Velleman.
- 版本说明:
- 2nd ed.
- 出版发行项:
- New York : Cambridge University Press, 2006.
- ISBN:
- 9780511159435
- ISBN:
- 9780521861243
- 载体形态项:
- 1 online resource (xiii, 384 p.) : ill.
- 个人责任者:
- Velleman, Daniel J.
- 论题主题:
- Mathematics.
- 中图法分类号:
- O141
- 一般附注:
- Descriptionbasedonprintversionrecord.
- 书目附注:
- Includes bibliographical references (p. 375) and index.
- 内容附注:
- 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.
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