Basic Concepts of Mathematics and Logic基础数学和逻辑概念
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作者： Michael C. Gemignani著
出 版 社：
出版时间： 2004-4-1字数：版次： 1页数： 280印刷时间： 2004/04/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780486435060包装： 平装内容简介
This text emphasizes logic and the theory of sets。 Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics。 Others will discover the foundations for future studies — set theory，logic，counting，numbers，functions，and more。1968 edition。 43 figures。 25 tables。
目录
Chapter 1 Introduction
1.1 Abstraction and Mathematics
1.2 Mathematics and “Reality”
1.3 An Example
1.4 Mathematical Statements
1.5 Notation
1.6 On Rigor
Chapter 2 introduction to Logic
2.1 Necessary and Sufficient Conditions
2.2 Negations
2.3 Mathematical Disproofs
2.4 Conjunction and Disjunction
2.5 Truth Tables
2.6 Logical Equivalence. Tautologies
Chapter 3 More about Logic
3.1 Converses and Contrapositives
3.2 On the Validity of a Proof
3.3 Some Elementary Arguments
3.4 More Elementary Arguments
3.5 Proofs by Contradiction
3.6 Summary
Chapter 4 Sets
4.1 The Notion of a Set
4.2 Set-Building Notation
4.3 Subsets. Equality of Sets
4.4 Union and Intersection
4.5 The Difference of Two Sets. Complements
Chapter 5 Set Theory and Logic
5.1 Set Diagrams
5.2 Sets and Language. Venn Diagrams
5.3 Applying Set Theory to Arguments
Chapter 6 Counting
6.1 The Notion of Counting
6.2 More About Infinity
6.3 More About Countable Sets
6.4 The Notion of Number
6.5 The Addition of Cardinal Numbers
Chapter 7 The Cartesian Product. Functions
7.1 The Cartesian Product of Two Sets
7.2 The Multiplication of Cardinal Numbers
7.3 Functions
7.4 More About Functions
7.5 Composition of Functions
Chapter 8 Relations
8.1 The Notion of a Relation
8.2 Equivalence Relations
8.3 A Definition of the Integers
8.4 0rderings
Chapter 9 More about Total Ordering
9.1 The Ordering of the Integers, an Intuitive View
9.2 The Ordering of the Integers, a Formal View
9.3 Finite Induction
9.4 Another Definition of the Integers
Chapter 10 Probability
10.1 The Nature of Probability
10.2 The Basic Rules of Probability
10.3 Methods of Assigning Probabilities
10.4 Sampling
10.5 Some Special Probabilities
Chapter 11 An Elementary Geometry
11.1 The Projective Plane
11.2 Basic Properties of the Projective Plane
11.3 The Affine Plane
Chapter 12 Conclusion
Appendix
Answer to Odd-Numbered Exercises
Index of Symbols
Index