圖書信息
具體數學副標題:計算機科學基礎
原作名:ConcreteMathematics
作者:[美]RonaldL.Graham/DonaldE.Knuth/OrenPatashnik
出版社:機械工業出版社
出版年:2002-8
頁數:657
定價:49.00元
裝幀:平裝
ISBN:9787111105763
內容簡介
ThisbookintroducesthemathematicsthatsupportsadvancedcomputerProgrammingandtheanalysisofalgorithms.Theprimaryaimofitswell-knownauthorsistoprovideasolidandrelevantbaseofmathematicalskills--theskillsneededtosolvecomplexproblems,toevaluatehorrendoussums,andtodiscoversubtlePatternsindata.Itisanindispensabletextandreferencenotonlyforcomputerscientists--theauthorsthemselvesrelyheavilyonit!butforserioususersOfmathematicsinvirtuallyeverydiscipline.
ConcretemathematicsisablendingofcontinuousanddisCRETEmathematics:"Moreconcretely,"theauthorsexplain,"itisthecontrolledmanipulationofmathematicalformulas,usingacollectionoftechniquesforsolvingproblems."ThesubjectmaterisprimarilyanexpansionoftheMathematicalPreliminariessectioninKnuth'sc1assicArtofComputerProgramming,butthestyleofpresentationismoreleisurely,andindividualtopicsarecoveredmoredeeply.Severalnewtopicshavebeenadded,andthemostsignificantideashavebeentracedtotheirhistoricalroots.Thebookincludesmorethan500exercises,dividedintosixcategories.Completeanswersareprovidedforallexercises,exceptresearchproblems,makingthebookparticularlyvaluableforself-study.
來自《具體數學（第二版）》英文版
《具體數學》第二版暫無中文，但第一版中文版在網上可以找到pdg的，清晰完全可以接受。本書可以作為研究高德納(DonalE.Knuth)的另一部著作《電腦程式設計藝術》的前期數學準備，亦是第一章的擴充。
本書討論範圍有遞歸、和、整函式、數論、二項係數、特殊數、母函式、離散機率、漸進，這些都是程式設計中所要涉及的基礎數學知識，掌握好對今後的程式設計有莫大的幫助。
圖書作者
RonaldL.GrahamischiefScientistatAt&TLabresearch.DonalE.KnuthisProfessorEmeritusoftheArtofComputerprogrammingatStanfordUniversity.OrenPatashnikisamemberoftheresearthstaffatthecentorforCommunitcationResearch,Lajolla.DonaldE.Knuthisknownthroughouttheworldforhispioneeringworkonalgorithmsandprogrammingtechniques,forhisinventionoftheTexandMetafontsystemsforcomputertypesetting,andforhisprolificandinfluentialwriting.ProfessorEmeritusofTheArtofComputerProgrammingatStanfordUniversity,hecurrentlydevotesfulltimetothecompletionofthesefasciclesandthesevenvolumestowhichtheybelong.
圖書目錄
1RecurrentProblems1
1.1TheTowerofHanoi11.2LinesinthePlane41.3TheJosephusProblem8Exercises17
2Sums21
2.1Notation212.2SumsandRecurrences252.3ManipulationofSums302.4MultipleSums342.5GeneralMethods412.6FiniteandInfiniteCalculus472.7InfiniteSums56Exercises62
3IntegerFunctions67
3.1FloorsandCeilings673.2Floor/CeilingApplications703.3Floor/CeilingRecurrences783.4!(R)mod!TheBinaryOperation813.5Floor/CeilingSums86Exercises95
4NumberTheory102
4.1Divisibility1024.2Primes1054.3PrimeExamples1074.4factorialFactors1114.5RelativePrimality1154.6!(R)mod!ˉ:TheCongruenceRelati1234.7IndependentResidues1264.8AdditionalApplications1294.9PhiandMu133Exercises144
5BinomialCoefficients153
5.1BasicIdentities1535.2BasicPractice1725.3TricksoftheTrade1865.4GeneratingFunctions1965.5HypergeometricFunctions2045.6HypergeometricTransformations2165.7PartialHypergeometricSums223Exercises230
6SpecialNumbers
6.1StirlingNumbers2436.2eulerianNumbers2536.3HarmonicNumbers2586.4HarmonicSummation2656.5BernoulliNumbers2696.6FibonacciNumbers2766.7Continuants287Exercises295
7GeneratingFunctions7.1DominoTheoryandChange3067.2BasicManeuvers3177.3SolvingRecurrences3237.4SpecialGeneratingFunctions3367.5Convolutions3397.6ExponentialGeneratingFunctions3507.7DirichletGeneratingFunctions356Exercises357
8DiscreteProbability
8.1Definitions3678.2MeanandVariance3738.3ProbabilityGeneratingFunctions3808.4flippingCoins3878.5Hashing397Exercises413
9Asymptotics
9.1AHierarchy4269.20Notation4299.30Manipulation4369.4TwoAsymptoticTricks4499.5Euler!ˉsSummationFormul4559.6FinalSummations462Exercises475AAnswerstoExercisesBBibliographyCCreditsforExercisesIndexListofTables
盤點有關算法書籍
| 算法可以理解為有基本運算及規定的運算順序所構成的完整的解題步驟。或者看成按照要求設計好的有限的確切的計算序列，並且這樣的步驟和序列可以解決一類問題。 |
