离散数学：基础与提高

Preface1 Let s Count! 1.1 A Party 1.2 Sets and the Like 1.3 The Nunmber of Subsets 1.4 The Approximate Number of Subsets 1.5 Sequences 1.6 Permutations 1.7 The Number of Ordered Subsets 1.8 The Number of Subsets of a Given Size2 Combinatorial Tools 2.1 Induction 2.2 Comparing and Estimationg numbers 2.3 Inclusion-Exclusion 2.4 Pigeonholes

Preface1 Let s Count! 1.1 A Party 1.2 Sets and the Like 1.3 The Nunmber of Subsets 1.4 The Approximate Number of Subsets 1.5 Sequences 1.6 Permutations 1.7 The Number of Ordered Subsets 1.8 The Number of Subsets of a Given Size2 Combinatorial Tools 2.1 Induction 2.2 Comparing and Estimationg numbers 2.3 Inclusion-Exclusion 2.4 Pigeonholes 2.5 The Twin Paradox and the Good Old Logarithm3 Binomial Coefficients and Pascal s Triangle 3.1 The Binomial Theorem 3.2 Distributing Presents 3.3 Anagrams 3.4 Distributing Money 3.5 Pascal s Trianglc 3.6 Identities in pascal s Triangle 3.7 A Bird s -Eye View of Pascal s Triangle 3.8 All Eagle s -Eye View:Fine Details4 Fibonacci Numbers 4.1 Fibonacci s Exercise 4.2 Lots of Identities 4.3 A Formula for the Fibonacci Nunbers5 Combinatorial Probability 5.1 Events and Probabilities 5.2 Independent Repetition of an Experiment 5.3 The Law of Large Numbers 5.4 The Law of Small Numbers and t he Law of Very Large Nmmbers6 Integers,Divisors and Primes 6.1 Divisibility of Integers 6.2 Primes and Their History 6.3 Factorization into Primes 6.4 On the Set of primes 6.5 Fermat s Little Theorem 6.6 The Fuclidean lgorithm 6.7 Congruences 6.8 Strange Numbers 6.9 Nunber Theory and Combiatorics 6.10 How to Test Whether a Number is a Prime?7 Graphs 7.1 Even and Odd Dergrees 7.2 Paths Cycles and Connectivitry 7.3 Eulerian Walkd and Hamiltnian Cycles8 Trees 8.1 How to Define Trees 8.2 How to Grow Trees 8.3 HOw to Count Trees? 8.4 How to Store Trees 8.5 The Number of Unlabeled Trees9 Finding the Optimum 9.1 Finding the Best Tree 9.2 The Traveling Salesman Problem10 Matvchings in Graphs 10.1 A Dancing Problem ……11 Combinatorics in Geometry12 Euler s Formula13 Coloring Maps and Graphs14 Finite Geometries,Codes,Latin Squares,and Other Pretty Creatures15 A Glimpse of COmplexity and Cryptography16 Answers to ExercisesIndex

本书包括组合、图论及它们在优化和编码等领域的应用。全书只有约300页，但涵盖了信息领域一些广泛而有趣的应用，及离散数学领域新颖而前沿的研究课题。 本书非常适合计算机科学、信息与计算科学等专业作为“离散数学”引论课程的教材或参考书。