离散数学简明教程(双语版)

Contents
Part ⅠMathematical Logic
Chapter 1Propositional Logic
1.1Propositions and Connectives
1.2Propositional Formula and Translation
1.3Truth Tables and Equivalent Formulas
1.4Tautology and Implication
1.5Duality and Normal Form
1.6The Reasoning Theory of Propositional Calculus
1.7Application of Propositional Logic
Exercises
Chapter 2Predicate Logic
2.1Predicate and Quantifier
2.2Predicate Formula and Translation
2.3Constraints on Variables
2.4Equivalence and Implication of Predicate Calculus
2.5Prenex Normal Forms
2.6Inference Theory of Predicate Calculus
2.7Application of Predicate Logic
Exercises
Part ⅡSet Theory
Chapter 3Set and Relation
3.1The Concept and Representation of the Set
3.2Operation of Set
3.3Inclusion Exclusion Principle
3.4Ordered Pair and Cartesian Product
3.5Relation and Its Nature
3.6Inverse and Compound Relations
3.7Closure Operations
3.8Equivalence Relation and Compatible Relation
3.9Partial Order Relation
3.10Application of Set and Relation
Exercises
Chapter 4Function
4.1The Concept and Representation of Function
4.2Inverse Function and Compound Function
4.3The Concept of Characteristic Function and Fuzzy Subset
4.4Common Functions
Contents目录Exercises
Part ⅢThe Algebraic Structure
Chapter 5Algebra System
5.1The Introduction of Algebraic Systems
5.2Operations and Properties of Algebraic Systems
5.3Homomorphism and Isomorphism of Algebraic Systems
5.4Congruence and Quotient Algebra
5.5Product Algebra
Exercises
Chapter 6Group
6.1Semigroup
6.2Group and Subgroup
6.3Homomorphism and Isomorphism of Groups
6.4Abelian Groups and Cyclic Groups
Exercises
Chapter 7Lattice and Boolean Algebra
7.1The Concept and Properties of Lattice
7.2Distributive Lattice
7.3Complemented Lattice
7.4Boolean Algebra
7.5Boolean Expression
ExercisesPart ⅣGraph TheoryChapter 8Basic Concepts of Graphs
8.1Concept of Graph
8.2Subgraph and Isomorphic Graph
8.3Path and Loop
8.4Matrix Representation of Graph
Exercises
Chapter 9Euler Graph and Hamiltonian Graph
9.1Euler Graph
9.2Hamiltonian Graph
9.3Application of Euler Graph and Hamiltonian Graph
Exercises
Chapter 10Planar Graph
10.1Basic Concepts of the Planar Graph
10.2Euler Formula and Judgment of Planar Graph
10.3Dual Graph and Properties
10.4Application of the Planar Graph
Exercises
Chapter 11Tree
11.1The Concept and Properties of Trees
11.2Spanning Tree
11.3Directed Tree
11.4Root Trees and Their Applications
Exercises Reference目录
第1篇数 理 逻 辑
第1章命题逻辑
1.1命题与联结词
1.2命题公式与翻译
1.3真值表与等价公式
1.4重言式与蕴含式
1.5对偶与范式
1.6命题演算的推理理论
1.7命题逻辑的应用
习题
第2章谓词逻辑
2.1谓词与量词
2.2谓词公式与翻译
2.3变元的约束
2.4谓词演算的等价式与蕴含式
2.5前束范式
2.6谓词演算的推理理论
2.7谓词逻辑的应用
习题
第2篇集 合 论
第3章集合与关系
3.1集合的概念与表示
3.2集合的运算
3.3容斥原理
3.4序偶与笛卡儿积
3.5关系及其性质
3.6关系的逆与复合
3.7关系的闭包运算
3.8等价关系与相容关系
3.9偏序关系
3.10集合与关系的应用
习题
第4章函数
4.1函数的概念与表示
4.2逆函数与复合函数
4.3特征函数与模糊子集的概念
4.4常用函数
习题
Contents目录第3篇代 数 结 构
第5章代数系统
5.1代数系统的引入
5.2代数系统的运算及其性质
5.3代数系统的同态与同构
5.4同余关系与商代数
5.5积代数
习题
第6章群
6.1半群
6.2群与子群
6.3群的同态与同构
6.4阿贝尔群与循环群
习题
第7章格与布尔代数
7.1格的概念与性质
7.2分配格
7.3有补格
7.4布尔代数
7.5布尔表达式
习题第4篇图论第8章图的基本概念
8.1图的概念
8.2子图与图的同构
8.3路与回路
8.4图的矩阵表示
习题
第9章欧拉图与哈密顿图
9.1欧拉图
9.2哈密顿图
9.3欧拉图与哈密顿图的应用
习题
第10章平面图
10.1平面图的基本概念
10.2欧拉公式与平面图的判断
10.3对偶图及其性质
10.4平面图的应用
习题
第11章树
111树的概念与性质
112生成树
113有向树
114根树及其应用
习题参考文献