Daniel J. Velleman 艾姆赫斯特（Amherst）學院數(shù)學與計算機科學系教授，《美國數(shù)學月刊》主編。另著有 Which Way Did The Bicycle Go和Philosophies of Mathematics。他的研究興趣廣泛，主攻數(shù)理邏輯，在組合、拓撲、分析、數(shù)學方法論、量子力學等多個領域都發(fā)表了大量論文。
圖書目錄
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
鄂公網(wǎng)安備 42010302001612號 