Part Ⅰ Mat ematlcal Logic Chapter 1 Propositional Logic 1.1 Propositions and Connectives 1.2 Propositional Formula and Translation 1.3 Truth Tables and Equivalent Formulas 1.4 Tautology and Implication 1.5 Duality and Normal Form 1.6 The Reasoning Theory of Propositional Calculus 1.7 Application of Propositional Logic Exercises Chapter 2 Predicate Logic 2.1 Predicate and Quantifier 2.2 Predicate Formula and Translation 2.3 Constraints on Variables 2.4 Equivalence and Implication of Predicate Calculus 2.5 Prenex Normal Forms 2.6 Inference Theory of Predicate Calculus 2.7 Application of Predicate Logic Exercises Part Ⅱ Set Theory Chapter 3 Set and Relation 3.1 The Concept and Representation of the Set 3.2 Operation of Set 3.3 Inclusion Exclusion Principle 3.4 Ordered Pair and Cartesian Product 3.5 Relation and Its Nature 3.6 Inverse and Compound Relations 3.7 Closure Operations 3.8 Equivalence Relation and Compatible Relation 3.9 Partial Order Relation 3.10 Application of Set and Relation Exercises Chapter 4 Function 4.1 The Concept and Representation of Function 4.2 Inverse Function and Compound Function 4.3 The Concept of Characteristic Function and Fuzzy Subset 4.4 Common Functions Exercises Part Ⅲ The Algebraic Structure Chapter 5 Algebra System 5.1 The Introduction of Algebraic Systems 5.2 Operations and Properties of Algebraic Systems 5.3 Homomorphism and Isomorphism of Algebraic Systems 5.4 Congruence and Quotient Algebra 5.5 Product Algebra Exercises Chapter 6 Group 6.1 Semigroup 6.2 Group and Subgroup 6.3 Homomorphism and Isomorphism of Groups
6.4 Abelian Groups and Cyclic Groups Exercises Chapter 7 Lattice and Boolean Algebra 7.1 The Concept and Properties ot" Lattice 7.2 Distributive Lattice 7.3 Complemented Lattice 7.4 Boolean Algebra 7.5 Boolean Expression Exercises Part Ⅳ Graph Theory Chapter 8 Basic Concepts of Graphs 8.1 Concept of Graph 8.2 Subgraph and Isomorphic Graph 8.3 Path and Loop 8.4 Matrix Representation of Graph Exercises Chapter 9 Euler Graph and Hamiltonian Graph 9.1 Euler Graph 9.2 Hamiltonian Graph 9.3 Application of Euler Graph and Hamiltonian Graph Exercises Chapter 10 Planar Graph 10.1 Basic Concepts of the Planar Graph 10.2 Euler Formula and Judgment of Planar Graph 10.3 Dual Graph and Properties 10.4 Application of the Planar Graph Exercises Chapter 11 Tree 11.1 The Concept and Properties of Trees 11.2 Spanning Tree 11.3 Directed Tree 11.4 Root Trees and Their Applications Exercises Reference
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