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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