離散數(shù)學(xué)

內(nèi)容概要

　　本書包括組合、圖論及它們在優(yōu)化和編碼等領(lǐng)域的應(yīng)用。全書只有約300頁，但涵蓋了信息領(lǐng)域一些廣泛而有趣的應(yīng)用，及離散數(shù)學(xué)領(lǐng)域新穎而前沿的研究課題?！　”緯浅＿m合計(jì)算機(jī)科學(xué)、信息與計(jì)算科學(xué)等專業(yè)作為“離散數(shù)學(xué)”引論課程的教材或參考書。

書籍目錄

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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