离散数学：基础与提高

图书标准信息

• 作者 罗瓦茨 著
• 出版社 清华大学出版社
• 出版时间 2006-09
• 版次 1
• ISBN 9787302138266
• 定价 39.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 290页

【内容简介】

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。

【目录】

Preface
1LetsCount!
1.1AParty
1.2SetsandtheLike
1.3TheNunmberofSubsets
1.4TheApproximateNumberofSubsets
1.5Sequences
1.6Permutations
1.7TheNumberofOrderedSubsets
1.8TheNumberofSubsetsofaGivenSize
2CombinatorialTools
2.1Induction
2.2ComparingandEstimationgnumbers
2.3Inclusion-Exclusion
2.4Pigeonholes
2.5TheTwinParadoxandtheGoodOldLogarithm
3BinomialCoefficientsandPascalsTriangle
3.1TheBinomialTheorem
3.2DistributingPresents
3.3Anagrams
3.4DistributingMoney
3.5PascalsTrianglc
3.6IdentitiesinpascalsTriangle
3.7ABirds-EyeViewofPascalsTriangle
3.8AllEagles-EyeView:FineDetails
4FibonacciNumbers
4.1FibonaccisExercise
4.2LotsofIdentities
4.3AFormulafortheFibonacciNunbers
5CombinatorialProbability
5.1EventsandProbabilities
5.2IndependentRepetitionofanExperiment
5.3TheLawofLargeNumbers
5.4TheLawofSmallNumbersandtheLawofVeryLargeNmmbers
6Integers,DivisorsandPrimes
6.1DivisibilityofIntegers
6.2PrimesandTheirHistory
6.3FactorizationintoPrimes
6.4OntheSetofprimes
6.5FermatsLittleTheorem
6.6TheFuclideanlgorithm
6.7Congruences
6.8StrangeNumbers
6.9NunberTheoryandCombiatorics
6.10HowtoTestWhetheraNumberisaPrime?
7Graphs
7.1EvenandOddDergrees
7.2PathsCyclesandConnectivitry
7.3EulerianWalkdandHamiltnianCycles
8Trees
8.1HowtoDefineTrees
8.2HowtoGrowTrees
8.3HOwtoCountTrees?
8.4HowtoStoreTrees
8.5TheNumberofUnlabeledTrees
9FindingtheOptimum
9.1FindingtheBestTree
9.2TheTravelingSalesmanProblem
10MatvchingsinGraphs
10.1ADancingProblem
……
11CombinatoricsinGeometry
12EulersFormula
13ColoringMapsandGraphs
14FiniteGeometries,Codes,LatinSquares,andOtherPrettyCreatures
15AGlimpseofCOmplexityandCryptography
16AnswerstoExercises
Index