A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series) pdf epub mobi txt 電子書 下載2025

1 Counting and binomial coefficients (計數和二項式定理)
1.1 Basic principle
1.2 Factorials
1.3 Selection
1.4 Binomial coefficients and Pascal triangles
1.5 Selections with repetitions
1.6 A useful matrix inversion
2 Recurrence (遞歸)
2.1 Some examples
2.2 The auxiliary equation method
2.3 Generating functions
2.4 Derangements
2.5 Sorting algorithms
2.6 Catalan numbers
3 Introduction to graphs (圖論)
3.1 The concept of a graph
3.2 Paths in graphs
3.3 Trees
3.4 Spanning trees
3.5 Bipartite graphs
3.6 Planarity
3.7 Polyhedra
4 Travelling round a graph (圖的遍曆)
4.1 Hamiltonian graphs
4.2 Plararity and Hamiltonian graphs
4.3 The travelling salesman problem
4.4 Gray codes
4.5 Eulerian graphs
4.6 Eulerian Digraphs
5 Partition and colourings (分割和上色問題)
5.1 Partitions of a set
5.2 Stirling numbers
5.3 Counting functions
5.4 Vertex colourings of graphs
5.5 Edge colourings of graphs
6 Inclusion-exclusion principle (容斥原理)
6.1 The principle
6.2 Counting surjections
6.3 Counting labelled trees
6.4 Scabble
6.5 The Mélange problem
7 Latin square (拉丁方陣和Hall定理)
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,n
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 designs
9.4 Hadamard matrices and designs
9.5 Difference methods
9.6 Hadamard matrices and codes
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