Mathematics: A Discrete Introduction PDF
Preview Mathematics: A Discrete Introduction
Scheinerman-5059 49421 February03,2012 18:41 ii Scheinerman-5059 49421 February03,2012 18:41 ii Scheinerman-5059 49421 February03,2012 18:41 i Mathematics Scheinerman-5059 49421 February03,2012 18:41 ii Scheinerman-5059 49421 February03,2012 18:41 iii Mathematics A Discrete Introduction ThirdEdition Edward R. Scheinerman Department ofAppliedMathematicsand Statistics TheJohnsHopkinsUniversity Australia Brazil Japan Korea Mexico Singapore Spain UnitedKingdom UnitedStates Scheinerman-5059 49421 February03,2012 18:41 iv Mathematics:ADiscreteIntroduction, ©2013,2006,2000Brooks/Cole,CengageLearning ThirdEdition EdwardR.Scheinerman ALLRIGHTSRESERVED.Nopartofthisworkcoveredbythecopyrighthereinmay bereproduced,transmitted,stored,orusedinanyformorbyanymeansgraphic, Publisher/ExecutiveEditor:RichardStratton electronic,ormechanical,includingbutnotlimitedtophotocopying,recording, scanning,digitizing,taping,Webdistribution,informationnetworks, AcquisitionsEditor:MollyTaylor orinformationstorageandretrievalsystems,exceptaspermittedunder AssistantEditor:WalshShaylin Section107or108ofthe1976UnitedStatesCopyrightAct,withouttheprior EditorialAssistant:AlexanderGontar writtenpermissionofthepublisher. MediaEditor:AndrewCoppola Forproductinformationandtechnologyassistance,contactus MarketingManager:JenniferP.Jones atCengageLearningCustomer&SalesSupport,1-800-354-9706 MarketingCommunicationsManager: Forpermissiontousematerialfromthistextorproduct, MaryAnnePayumo submitallrequestsonlineatwww.cengage.com/permissions. CoverDirection,ProductionManagement, Furtherpermissionsquestionscanbeemailedto andComposition:PreMediaGlobal [email protected]. ManufacturingPlanner:DougBertke RightsAcquisitionSpecialist: LibraryofCongressControlNumber:2012931870 MeyerDareJennifer StudentEdition: CoverImage:JonahScheinerman ISBN-13:978-0-8400-4942-1 ISBN-10:0-8400-4942-0 Brooks/Cole 20ChannelCenterStreet Boston,MA02210 USA CengageLearningisaleadingproviderofcustomizedlearningsolutionswithoffice locationsaroundtheglobe,includingSingapore,theUnitedKingdom,Australia, Mexico,BrazilandJapan.Locateyourlocalofficeat international.cengage.com/region CengageLearningproductsarerepresentedinCanadabyNelsonEducation,Ltd. Foryourcourseandlearningsolutions,visitwww.cengage.com. Purchaseanyofourproductsatyourlocalcollegestoreoratourpreferredonline storewww.cengagebrain.com. Instructors:Pleasevisitlogin.cengage.comandlogintoaccess instructor-specificresources. PrintedintheUnitedStatesofAmerica 1 2 3 4 5 6 7 16 15 14 13 12 Scheinerman-5059 49421 February03,2012 18:41 v To Leora and Danny Scheinerman-5059 49421 February03,2012 18:41 vi Scheinerman-5059 49421 February03,2012 18:41 vii Contents TotheStudent xvii HowtoReadaMathematicsBook xviii Exercises xviii TotheInstructor xix AudienceandPrerequisites xix TopicsCoveredandNavigatingtheSections xix SampleCourseOutlines xx SpecialFeatures xx What’sNewinthisThirdEdition xxiii Acknowledgments xxv ThisNewEdition xxv FromtheSecondEdition xxv FromtheFirstEdition xxv 1 Fundamentals 1 1 Joy 1 Why? 1 TheAgonyandtheEcstasy 1 Exercise 2 2 Speaking(andWriting)ofMathematics 2 Precisely! 2 ABitofHelp 2 Exercise 3 3 Definition 4 Recap 6 Exercises 6 4 Theorem 8 TheNatureofTruth 8 If-Then 9 IfandOnlyIf 11 And,Or,andNot 12 WhatTheoremsAreCalled 12 VacuousTruth 13 Recap 13 Exercises 13 5 Proof 15 AMoreInvolvedProof 18 ProvingIf-and-Only-IfTheorems 20 ProvingEquationsandInequalities 22 Recap 22 Exercises 22 6 Counterexample 23 Recap 24 Exercises 24 vii Scheinerman-5059 49421 February03,2012 18:41 viii viii Contents 7 BooleanAlgebra 25 MoreOperations 27 Recap 28 Exercises 28 Chapter1 SelfTest 30 2 Collections 33 8 Lists 33 CountingTwo-ElementLists 33 LongerLists 35 Recap 38 Exercises 38 9 Factorial 40 MuchAdoAbout0! 40 ProductNotation 41 Recap 42 Exercises 42 10 SetsI:Introduction,Subsets 43 EqualityofSets 45 Subset 46 CountingSubsets 48 PowerSet 49 Recap 49 Exercises 50 11 Quantifiers 51 ThereIs 51 ForAll 52 NegatingQuantifiedStatements 53 CombiningQuantifiers 53 Recap 54 Exercises 54 12 SetsII:Operations 56 UnionandIntersection 56 TheSizeofaUnion 58 DifferenceandSymmetricDifference 60 CartesianProduct 64 Recap 64 Exercises 64 13 CombinatorialProof:TwoExamples 66 Recap 69 Exercises 69 Chapter2 SelfTest 70 3 Counting and Relations 73 14 Relations 73 PropertiesofRelations 75 Recap 76 Exercises 76
The list of books you might like
