圖書信息
出版社: 清華大學出版社; 第1版 (2009年11月1
外文書名: A First Course in Discrete Mathematics
叢書名: Springer 大學數學圖書
平裝: 200頁
正文語種: 英語
開本: 16
ISBN: 9787302214823
條形碼: 9787302214823
尺寸: 24 x 17.2 x 1.2 cm
重量: 821 g
作者簡介
作者：(美國)安德遜(Ian Anderson)
內容簡介
《離散數學引論》以簡潔和通俗的形式介紹組合數學的一些本質性內容圖論的重要問題，計數方法和試驗設計，其中圖論約占一半篇幅。《離散數學引論》很適於和中國中學數學教材的內容相銜接，閱讀《離散數學引論》所需的預備知識只是中學數學（唯一的例外是在圖論中需要矩陣的描述方式，但即使沒有學過線性代數，也是可以接受的）。
書中有大量習題和例題，習題附有部分解答和提示，適於自學。《離散數學引論》可用作數學、計算機科學、信息科學等專業大學本科生的組合數學教材，可在大學一年級講授。
目錄
Contents
1. Counting and Binomial Coefficients
1.1 Basic Principles
1.2 Factorials
1.3 Selections
1.4 Binomial Coefficients and Pascal's Triangle
1.5 Selections with——Repetitions
1.6 AUsefulMatrixInversion
2. recurrence
2.1 Some Examples
2.2 The Auxiliary Equation Method
2.3 Generating Fhnctions
2.4 Derangements
2.5 Sorting Algorithms
2.6 Catalan Numbers
3. Introduction to Graphs
3.1 The Concept of a Graph
3.2 Paths in Graphs
3.3 Trees
3.4 Spanning Trees
3.5 bipartite Graphs
3.t5 Planarity
3.7 Polyhedra.
4. Travelling Round a Graph
4 1 Hamiltonian Graphs
4.2 Planarity and Hamiltonian Graphs
4.3 The Travelling Salesman Problem
4.4 Gray Codes
4.5 EulerianDigraphs
5. Partitions and Colourings
5.1 Partitions of a Set
5.2 StirlingNumbers
5.3 Counting Functions
5.4 Vertex Colourings of Graphs
5.5 Edge Colourings of Graphs
6 The Inclusion-Exclusion Principle
6.1 The Principle
6.2 Counting Surjections
6.3 Counting Labelled Trees
6.4 scrabble.
15.5 The MSnage Problem
7. Latin Squares and Hall's Theorem.
7.1 Latin-Squares and -Orthogonality
7.2 Magic Squares
7.3 Systems of Distinct Representatives
7.4 From Latin Squares to Affine Planes
8 Schedules and 1-Factorisations
8.1 The Circle Method
8.2 Bipartite Tournaments and 1-Factorisations of Kn
8.3 Tournaments from Orthogonal Latin Squares
9. Introduction to Designs.
9.1 balanced Incomplete Block Designs
9.2 resolvable Designs
9.3 Finite Projective Planes
9.4 Hadamard Matrices and Designs
9.5 Difference Methods
9.5 Hadamard Matrices and Codes
Appendix
Solutions
Further Reading
Bibliography
Index
