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Catalogue of discrete mathematics books
First set theory

Chapter I Collection

The Concept and Representation of 1. 1 Set

Basic operation of 1.2 set

1.3 Cartesian product

Exercise 1

Chapter II Relations

2. 1 relation and its representation

2.2 the operation of the relationship

2.3 equivalence relation

2.4 Sequence relationship

Exercise 2

Chapter III Forecast

3. 1 Basic concepts

3.2 Mapping operation

Exercise 3

Chapter IV Countable Sets and Uncountable Sets

4. 1 equipotential

4.2 Cardinality of a set

4.3 Countable set and uncountable set

Exercise 4

Second graph theory

Chapter V Graph and Subgraph

5. The concept of1graph

5.2 Isomorphism of Graphs

5.3 degree vertex

5.4 Operation of subgraphs and graphs

5.5 Path and Connection Diagram

5.6 Matrix representation of graphics

5.7 Application

Exercise 5

Chapter VI Trees

6. Definition of1tree

6.2 Spanning Tree

6.3 Application

Exercise 6

Chapter 7 Connectivity of Graphs

7. 1 vertex connectivity and edge connectivity

7.2 yuan

7.3 Application

Exercise 7

Chapter 8 e and h graphs

8. 1 seven-bridge problem and E-diagram

8.2 Travel around the world and H chart

8.3 Application

Exercise 8

Chapter 9 Matching and Point Independent Sets

9. 1 match

9.2 Independent Kit and Cover

9.3 Ramsey number

9.4 Application

Exercise 9

Chapter X Coloring of Graphs

10. 1 vertex coloring

10.2 edge coloring

10.3 color polynomial

10.4 application

Exercise 10

Chapter 11 Plan

1 1. 1 the concept of planning

1 1.2 Euler formula

1 1.3 flatness measurement

1 1.4 plan surface coloring

1 1.5 application

Exercise eleven

Chapter 12 Directed Graph

12. 1 the concept of directed graph

12.2 directed paths and directed loops

12.3 directed tree and its application

12.4 application

Exercise 12

Chapter 13 Large Network Traffic

13. 1 network traffic and cutting

13.2 maximum flow minimum cut theorem

13.4 application

Exercise 13

Chapter III Mathematical Logic

Chapter 14 Propositional Logic

14. 1 Propositions and logical connectors

14.2 propositional formula and equivalent calculus

Duality and Paradigm

14.4 reasoning theory

Axiomatic system of 14.5 propositional calculus

Exercise 14

Chapter 15 First-order Logic

15. 1 Predicates and quantifiers

Anti-interpretation of 15.2 combination formula

15.3 equivalent formula and normal form

15.4 first-order logical reasoning theory

Exercise 15

The fourth article algebraic structure

Chapter 16 Integer

Divisibility of 16. 1

16.2 prime factorization

16.3 congruence

16.4 grandson theorem Euler function

Application of 16.5 number theory in computer cryptography

Exercise 16

Chapter 17 Organizations

The concept of 17. 1 group

17.2 team

17.3 permutation group

17.4 coset and lagrange theorem

17.5 Homomorphism and Isomorphism

The application of 17.6 in computer science and technology

Exercise 17

Chapter 18 Rings and Domains

18. 1 rings and subrings

18.2 ring homomorphism

Characteristics and quality domains of 18.3 domain

18.4 finite field

The structure of 18.5 finite field

18.6 error correction code

Polynomial coding method and its implementation in 18.7

Exercise 18

Zhangge and Boolean Algebra in the 19th Century

Definition of 19. 1 lattice

Properties of 19.2 lattice

19.3 Some Special Lattices

19.4 Boolean algebra

The structure of 19.5 finite Boolean algebra

Application of 19.6 Lattice and Boolean Algebra in Computer Science and Technology

Exercise nineteen

The fifth chapter is a preliminary analysis of the combination.

Chapter 20 General counting method of permutation and combination

20. 1 Two Basic Counting Rules

20.2 Counting method of basic permutation and combination

20.3 Counting method of repeatable permutation and combination

Exercise 20

Chapter 2 1 Principles of Tolerance and Exclusion

2 1. 1 incompatibility principle

2 1.2 has prohibited arrangement.

Exercise 2 1

Chapter 22 Recursive Relation and Generating Function

22. 1 recursive relation and its solution

22.2 generating function

Exercise 22

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