离散数学

2006-9  

清华大学  

罗瓦茨  

290  

无  

　　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。

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

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离散数学 PDF格式下载

很多页面的反面印刷的很不清晰，清华出版社该狠抓下印刷质量了。

　　这本书和传统的离散数学教材区别很大，完全不同于通常的“数理逻辑”——“近世代数”——“图论”这样的体系结构，而是从一个简单的组合数学的问题入手，穿插有基础数论以及较多的图论。整本书并没有很明晰的知识体系划分，而是三个领域的方法互相交错，且毫无生涩感，作者功力可见一斑（毕竟是拿过Wolf Prize的神牛啊）。
　　
　　另外这本书里对于很多知识点都列出了很漂亮的应用，例如给树编码的Prufer Code，第一次看到时真的是令人击节赞叹。且个人认为书中不少定理的证明是我所见过的最干净的，有关图匹配的那一章就是最好的例子。
　　
　　最后，这本书绝对是面向初学者的，基本不需要任何预备知识，但也因此造成其覆盖面有限，很多题材都是点到为止、个人认为适合入门，可以很好地引起兴趣，若要深入则还是得去看大部头的《离散数学及其应用》。