书籍详情
怎样证明数学题（英文版·第2版）
作者：（美）费林曼 著
出版社：人民邮电出版社
出版时间：2009-07-01
ISBN：9787115209689
定价：¥59.00
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内容简介
《怎样证明数学题（英文版·第2版）》介绍了数学证明的基本要点，内容通俗而不失严谨，可以帮助高中以上程度的学生熟悉数学语言，迈入数学殿堂。新版添加了200多个练习题，附录中给出部分练习的答案或提示。《怎样证明数学题（英文版·第2版）》适用于任何对逻辑和证明感兴趣的人，数学、计算机科学、哲学、语言学专业的读者都可以从中获益匪浅。
作者简介
Daniel J. Velleman 艾姆赫斯特（Amherst）学院数学与计算机科学系教授，《美国数学月刊》主编。另著有 Which Way Did The Bicycle Go和Philosophies of Mathematics。他的研究兴趣广泛，主攻数理逻辑，在组合、拓扑、分析、数学方法论、量子力学等多个领域都发表了大量论文。
目录
Introduction
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-Schr6der-Bernstein Theorem
Appendix 1: Solutions to Selected Exercises
Appendix 2: Proof Designer
Suggestions for Further Reading
Summary of Proof Techniques
Index
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-Schr6der-Bernstein Theorem
Appendix 1: Solutions to Selected Exercises
Appendix 2: Proof Designer
Suggestions for Further Reading
Summary of Proof Techniques
Index
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