ISBN:730 105366
Author: Geng Suyun/Qu Wanling/Wang Hanpin
Publishing House: Peking University Publishing House
Pricing: 49 pounds
Page count: 636
Release date: 1900- 1- 1
Version: 1
Format: large 16 format
Packing: paperback
Introduction: This book is divided into five parts. The first part is set theory, including the basic concepts of sets, binary relations, functions, natural numbers, cardinality and ordinal numbers. The second part is graph theory, including the basic concept of graph, connectivity of graph, Euler graph and hamiltonian graph, tree, plane graph, coloring of graph, matrix representation of graph, covering set, independent set, matching, weighted graph and its practicability. The third part is algebraic structure, including the basic concepts of algebraic systems and several important algebraic systems: semigroups, groups, rings, fields, lattices and Boolean algebras. The fourth part is combinatorial sensitivity, including combinatorial existence, combinatorial counting, hierarchical design and coding and combinatorial optimization. The fifth part is mathematical logic, including propositional logic, first-order predicate logic, Her-brand theorem and intuitive logic.
This book is rigorous in system and rich in content, with a large number of examples and exercises, which are closely combined with the theory and practice of computer science.
This book is not only suitable for undergraduate or graduate students in computer science and related fields, but also suitable for scientific and technical personnel in computer science.
Directory:
The first part is set theory.
Chapter I Collection
1.？ 1 preparatory knowledge
1.？ 2 the concept of set and the relationship between sets
1.？ Operation of 3 units
1.？ Four basic set identities
1.？ Limit of 5 groups of sequences
Exercise 1
Chapter II Binary Relationship
2.？ 1 ordered pairs and cartesian products
2.？ 2 binary relation
2.？ 3 Relationship Matrix and Chart
2.？ 4 the nature of the relationship
2.？ 5 Power operation of binary relation
2.？ Close 6 relationships
2.？ 7 equivalence relation and division
2.？ Eighth-order relation
Exercise 2
Chapter III Functions
3.？ Basic concept of 1 function
3.？ Properties of two functions
3.？ Combination of three functions
3.？ 4 inverse function
Exercise 3
Chapter IV Natural Numbers
4.？ Definition of 1 natural number
4.？ 2 transitive set
4.？ 3 the operation of natural numbers
4.？ Ordered relation on 4N
Exercise 4
Chapter V Cardinality (Potential)
5.？ The equipotential of 1 set
5.？ 2 finite sets and infinite sets
5.？ Cardinality 3
5.？ Comparison of radix 4
5.？ 5 radix operation
Exercise 5
* Chapter VI Ordinal Number
6.？ Further discussion on the order relation in 1
6.？ 2 transfinite recursion theorem
6.？ 3 ordinal number
6.？ 4 Further discussion on cardinality
Exercise 6
The second painting
discuss
Chapter VII Numbers
7.？ Basic concepts of 1 graph
7.？ 2 paths and circuits
7.？ 3 connectivity of undirected graphs
7.？ 4 connectivity of undirected graphs
7.？ Connectivity of five directed graphs
Exercise 7
Chapter VIII Euler and hamiltonian graph
8.？ 1 eulatu
8.？ 2 hamiltonian graph
Exercise 8
Chapter 9 Trees
9.？ Definition and properties of 1 undirected tree
9.？ Spanning tree
9.？ Third ring road space
9.？ 4 fault set space
9.？ 5 keshu
Exercise 9
Chapter 10 Matrix Representation of Graphs
10.？ 1 incidence matrix
10.？ Adjacency matrix and adjacency matrix
Exercise 10
Chapter 11 Plan
1 1.？ 1 the basic concept of the plan.
1 1.？ 2 Euler formula
1 1.？ 3 the judgment of the plan
1 1.？ Dual graph of 4- plane graph
1 1.？ 5 external plan
1 1.？ 6 Plan and hamiltonian graph
Exercise eleven
Chapter 12 Coloring of Graphs
12.？ 1 point coloring
12.？ Bichromatic polynomial
12.？ 3 coloring of maps and point coloring of planar graphs
12.？ Four-sided coloring
Exercise 12
Chapter 13 leading set. Covering set. Independent setting and matching
13.？ 1 dominating set. Point covering set. Point independent set
13.？ 2- Edge Covering Sets and Matching
13.？ 3 Matching in Bipartite Graphs
Exercise 13
Chapter 14 Weighted Graph and Its Application
14.？ 1 shortest path problem
14.？ 2 critical path problem
14.？ 3 Chinese postman problem
14.？ 4 Minimum spanning tree
14.？ 5 best tree
14.？ The peddler took on the problem
Exercise 14
Part III Algebraic Structure
Chapter 15 Algebraic System
15.？ Binary operation of 1 and its properties
15.？ Algebraic system. Subalgebra and product algebra
15.？ Homomorphism and isomorphism of three algebraic systems
15.？ 4 congruence relation and quotient algebra
15.？ five
algebra
Exercise 15
Chapter 16 Semigroups and Uniqueness
16.？ 1 semigroup and uniqueness
16.？ finite automaton
Exercise 16
Chapter 17 Organizations
17.？ Definition and properties of 1 group
17.？ 2 groups
17.？ 3-ring group
17.？ 4 transformation groups and permutation groups
17,? 5-group decomposition
17.？ 6 Normal subgroups and quotient groups
17.？ Homomorphism and isomorphism of 7 groups
17.？ Direct product of 8 groups
Exercise 17
Chapter 18 Rings and Domains
18.？ Definition and properties of 1 ring
18.？ 2 subrings. Ideal. Quotient ring and ring homomorphism
18.？ Polynomial rings over 3 finite fields
Exercise 18
Zhangge and Boolean Algebra in the 19th Century
19.？ Definition and properties of 1 lattice
19.？ 2 sub-grids. Homomorphism of Lattice and Direct Product of Lattice
19.？ Three modules. Distributive lattice and complementary lattice
19.？ 4 Boolean algebra
Exercise nineteen
Part IV Combinatorial Mathematics
Chapter 20 combinatorial existence theorem
20.？ 1 pigeon nest principle and Ramsey theorem
20.？ 2 different representative lines
Exercise 20
Chapter 21 Basic Counting Formula
2 1.？ Two Counting Principles of 1
2 1.？ 2 arrangement and combination
2 1.？ Binomial Theorem and Combinatorial Identities
2 1.？ 4 multinomial theorem
Exercise 2 1
Chapter 22 Combination Counting Method
22.？ Formula solution of 1 recurrence equation
22.？ 2 other solutions to recursive equations
22.？ 3 Definition and properties of generating function
22.？ 4 generating function and combination counting
22.？ 5 Exponential Generating Function and the Arrangement of multiset
22.？ 6 Catalan number and Stirling number
Exercise 22
Chapter 23 Combination Counting Theorem
23.？ 1 contains the principle of exclusion.
23.？ 2 symmetrical sieve formula and its application
23.？ 3 Burnside Lemma
23.？ 4 Dorian theorem
Exercise 23
Chapter XXIV Combination Design and Coding
24.？ 1 Latin square
24.？ 2t- design
24.？ 3 coding
24.？ 4 coding and design
Exercise 24
Chapter 25 combinatorial optimization problem
25.？ 1 General concept of combinatorial optimization problem
25.？ Maximum flow problem of 2 networks
Exercise 25
The fifth part is mathematical logic
Chapter 26 Propositional Logic
26.？ 1 formal system
26.？ 2 propositions and conjunctions
26.？ 3 propositional form and truth table
26.？ Complete works of 4 conjunctions
26.？ 5 reasoning form
26.？ 6 Natural reasoning formal system of propositional calculus n
26.？ 7 propositional calculus formal system
26.？ The equivalence between 8N and corpse
26.？ 9 homework
26.？ 10 reliability. Harmony and integrity
Exercise 26
Chapter 27 First-order predicate calculus
27.？ Symbolization of 1 first-order predicate calculus
27.？ 2 First-order language
27.？ 3 natural deductive formal system of first-order predicate calculus n
27.？ 4 formal system k of first-order predicate calculus
27.？ 5N？ With k? Equivalent to
27.？ 6K？ Interpretation and distribution of
27.？ The Reliability and Coordination of 7K
27.？ Completeness of 8K
Exercise 27
Chapter 28 Principles of Digestion
28.？ Solution of 1 propositional formula
28.？ 2Herbrand theorem
28.？ 3 Substitution and unit substitution
28.？ 4 Analysis of the first-order predicate formula
Exercise 28
Chapter 29 Intuitionistic Logic
29.？ 1 intuitive introduction of intuitive logic
29.？ 2 Intuitionistic first-order predicate calculus natural deductive formal system
29.？ 3 intuitive first-order predicate calculus formal system IK
29.？ 4 Kripke semantics of intuitionistic logic
29.？ 5 completeness of intuitive logic
Exercise 29
Appendix 1 Symbolic Notes and Terminology Index of Part I and Part II
Appendix 2 Symbolic Notes and Terminology Index of Parts III and IV
Appendix 3 Part V Symbolic Notes and Terminology Index
Bibliography and literature