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1、HowtoreadmathematicsAletRouxUniversityofHull18November2003Readingmathematicsisdifficult,becausemathematicsisdifficult.Sincemath-ematicsisasubjectthatbuildsuponitself,booksandpapersinmathematicsoftenpresupposedifferentknowledgethanwhataspecificreaderactuallypos-sesses.Moreover,duet
2、othesuccinct,densestyleofmathematicalwriting,readingamathematicaltextrequiresmoreinvolvementfromthereaderthanmosttextsinothersubjects.Consequently,readingmathematicstakeslongerthanothertypesoftexts;often,attemptingtoreadmathematicstoofastresultsinfrustrationwithoutcomprehens
3、ion.AccordingtoAdler(1967,p.119),ifatext“isworthreadingatall,itisworththreereadingsatleast”.By“reading”,heimpliesareadinginmanner,namelytheemphasisingofaparticularaspectofatextduringthereadingprocess.Inshort,thethreewaysofreadingabookcanbesummarisedasfollows.Inthefirstplace,y
4、oumustbeabletograspwhatisbeingofferedasknowledge.Inthesecondplace,youmustjudgewhetherwhatisbeingofferedisreallyacceptabletoyouasknowledge.Intheotherwords,thereisfirstthetaskofunderstandingthebook,andsecondthejobofcriticizingit....Theprocessofunderstandingcanbefurtherdivided.Tou
5、nderstandabook,youmustapproachit,first,asawhole,havingaunityandastructureofparts;and,second,intermsofitselements,itsunitsoflanguageandthought.(Adler,1967,pp.123–124)Thesereadingstendtocoalesce,especiallythefirsttwo.Inessence,thefirsttworeadingsleadthereaderonacircularroute,star
6、tingfromthewholeofthetext,dividingintoalltheparts,puttingthembacktogetheragain,endingwiththewhole.Thethirdreadingisaidedbyobservationsduringthefirsttworeadings;howeverthisreadingcanneverbecomeabsolutelysimultaneouswiththeothertwo,asunderstandingatextmustalwaysprecedeitscritic
7、ism.Wenowconsidereachofthesereadingsseparately.By“text”,wemeananypieceofmathematicalwriting,understoodastoincludebooks,papers,theorems,definitionsandproofs.1StructuraloranalyticreadingInthisreading,thereaderproceedsfromthewholeofthetexttoitsparts.Toaccomplishthefirstreading,yo
8、umustcompletethefollowingtasks(adaptedfromAdler,1967,pp.124,268):11.Findout
