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《Kevin Houston-How to Think Like a Mathematician_ A Companion to Undergraduate Mathematics-Cambridge University Press (2009)》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。
1、ThispageintentionallyleftblankHowtoThinkLikeaMathematicianLookingforaheadstartinyourundergraduatedegreeinmathematics?Maybeyouvealreadystartedyourdegreeandfeelbewilderedbythesubjectyoupreviouslyloved?Dontpanic!Thisfriendlycompanionwilleaseyourtransitiontore
2、almathematicalthinking.Workingthroughthebookyouwilldevelopanarsenaloftechniquestohelpyouunlockthemeaningofdefinitions,theoremsandproofs,solveproblems,andwritemathematicseffectively.Allthemajormethodsofproofdirectmethod,cases,induction,contradictionandcontra
3、positivearefeatured.Concreteexamplesareusedthroughout,andyoullgetplentyofpracticeontopicscommontomanycoursessuchasdivisors,EuclideanAlgorithm,modulararithmetic,equivalencerelations,andinjectivityandsurjectivityoffunctions.Thematerialhasbeentestedbyrealstud
4、entsovermanyyearssoalltheessentialsarecovered.Withover300exercisestohelpyoutestyourprogress,youllsoonlearnhowtothinklikeamathematician.Essentialforanystartingundergraduateinmathematics,thisbookcanalsohelpifyourestudyingengineeringorphysicsandneedaccesstoun
5、dergraduatemathematicstopics,orifyouretakingasubjectthatrequireslogicsuchascomputerscience,philosophyorlinguistics.HowtoThinkLikeaMathematicianACompaniontoUndergraduateMathematicsKEVINHOUSTONUniversityofLeedsCAMBRIDGEUNIVERSITYPRESSCambridge,NewYork,Melbou
6、rne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,CambridgeCB28RU,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521895460©K.Houston2009T
7、hispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublishedinprintformat2009ISBN-13978-0-511-50645-1
8、eBook(EBL)ISBN-13978-0-521-89546-0hardbackISBN-13978-0-521-71978-0paperbackCambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofurlsforexternalorthird-partyinternetwebsitesreferredtointhisp
