how to study mathematics

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1、HowtoStudyMathematics页码，1/7HowtoStudyMathematicsLawrenceNeffStout,DepartmentofMathematics,IllinoisWesleyanUniversity,Bloomington,Il61702-2900Thisessaydescribesanumberofstrategiesforstudyingcollegelevelmathematics.Ithassectionsentitled1.Howiscollegemathematicsdifferent?2.Whatshouldyoudowithade

2、finition3.Theorems,Propositions,Lemmas,andCorollaries4.Fittingthesubjecttogether5.Howtomakesenseofaproof6.Developingtechnique7.AfewfinalsuggestionsReturntoL.N.Stout'shomepage.Howiscollegemathematicsdifferentfromhighschoolmath?Inhighschoolmathematicsmuchofyourtimewasspentlearningalgorithmsandm

3、anipulativetechniqueswhichyouwereexpectedtobeabletoapplyincertainwell-definedsituations.Thislimitationofmaterialandexpectationsforyourperformancehasprobablyledyoutodevelopstudyhabitswhichwereappropriateforhighschoolmathematicsbutmaybeinsufficientforcollegemathematics.Thiscanbeasourceofmuchfru

4、strationforyouandforyourinstructors.Myobjectinwritingthisessayistohelpeasethisfrustrationbydescribingsomestudystrategieswhichmayhelpyouchannelyourabilitiesandenergiesinaproductivedirection.Thefirstmajordifferencebetweenhighschoolmathematicsandcollegemathematicsistheamountofemphasisonwhatthest

5、udentwouldcalltheory---theprecisestatementofdefinitionsandtheoremsandthelogicalprocessesbywhichthosetheoremsareestablished.Tothemathematicianthismaterial,togetherwithexamplesshowingwhythedefinitionschosenarethecorrectonesandhowthetheoremscanbeputtopracticaluse,istheessenceofmathematics.Acours

6、edescriptionusingtheterm``rigorous''indicatesthatconsiderablecarewillbetakeninthestatementofdefinitionsandtheoremsandthatproofswillbegivenforthetheoremsratherthanjustplausibilityarguments.Ifyourapproachistogostraighttotheproblemswithonlycursoryreadingofthe``theory''thisaspectofcollegemathwill

7、causedifficultiesforyou.Theseconddifferencebetweencollegemathematicsandhighschoolmathematicscomesintheapproachtotechniqueandapplicationproblems.Inhighschoolyoustudiedonetechniqueatatime---aproblemsetorunitmightdeal,forinstance,withsolutionofq