How-to-Write-a-Paper-(PPT)

UNIVERSITYOFCAMBRIDGECENTREFORMATHEMATICALSCIENCESDEPARTMENTOFAPPLIEDMATHEMATICS&THEORETICALPHYSICSHOWTOWRITEAPAPER?AriehIserlesCambridge19thFebruary20071Whywriteapaper?Badreasons:•Everybodyelsedoesit:thisiswhatacademicsdoforliving;•Ihavebeenbusydoingresearch,havebeengettingresultsandnowIwanteverybodyelsetoknowaboutit;•ThisiscompetitiveworldandunlessIrushtorecordmyachievements,theywillberecognisedassomebodyelse’sachievements;•Iwantdissertation,postdoc,career,tenure,fame!Iwanttheworldtobeatmyfeet.2Agoodreason:(embarrassinginitssimplicity)•Iwanttocommunicateideastootherpeople.Whyisthisimportant?Becauseeverygoodtextmustbeconsideredfirstandforemostfromthepointofviewofitstargetaudience.TheBGMLholdsabout75000volumesofmorethan2100mathematicsandtheoreticalphysicsjournals.Thisisplentyofdeadtrees!Yourpaperneedstocompetewiththousandsofotherpapersinaverycrowdedmarketplaceofideasforthe(very)limitedattentionofbusyacademics.Itisyourdutytopersuadethemthattheyshouldexpandtimeandattentiononyourpaper.Agoodruleofathumbis:Askyourselfwhichsortofpaperwouldyouliketoread–andthenwriteit.3Goodreason1toreadapaper:GoodtitleandabstractAtitleandanabstractareyourshopwindow.Mostpotentialreadersbrowsejournals,whetherinalibraryoronInternet,likeshoppersonHighStreet.Bythisstagethepurposeoftheexerciseistograbtheirattentionsufficientlytomotivatethemtoreadon:1.Goodtitleusesfewwell-chosenwordstoplaceyourpaperattherightcornerofmathe-maticaluniverse.Goodabstractstatesclearlywhatisthesubjectareaofthepaperanditsmainresults.2.Usenon-technicallanguage.Yourabstractshouldbeunderstandablenotjusttofewexpertsbuttoeverybodyinitswiderconstituency.Thisisparticularlyimportantiftheresultsarerelevantbeyondyournarrowspecialism.3.Neveruseintheabstract(orthetitle!)conceptsthatyoudefinelaterinthepaper.4.Avoidcomplicatedmathematicalformulæandreferencestobibliography.Titlesandab-stractsshouldstandontheirown(hencenoreferences)andbeeasilytranslatabletoHTML(which,exceptinitsXMLmanifestation,ishopelesswithmathematicalsymbols).4Goodreason2toreadapaper:GoodintroductionOK,soyouhavetemptedunwarypunterstoentertheshop.Theybrowsearound,fingerthegoods,enterthemeasuringbooth:nowyouwantthemtosurrendertheplastic.1.Explainveryclearlywhatexactlyistheproblemthatyouareaddressinginthepaper–andwhy.Remember:youhaveworkedonthewretchedthingformonthsandmonths,foryouthemotivationisclear.Butyouaretryingtopersuadepeoplethatperhapsneverthoughtaboutyourproblem.Mathematicalresultsareworthwhilenotjustbecausetheyinterestyou.Itisagoodideatocommencewithbroad-brushcontext,explainingwhythethemeofpaperisrelevantandimportant.2.Sketchthemainresultsofthepaper.Noneedtoseekthegreatestgenerality,whichoftendependsonmathematicalmachinerythatyou’llintroducelater.Itisbettertoexplainclearlyandaccessiblyyourmainideasandmethodology.3.Useprofuselyexamples,toyproblemsandfigures.4.Placeeverythingintocontext.Youaren’tthefirsttoconsiderthisproblem,neitherthefirsttosaysomethingworthwhileaboutit.5.Providecontinuitywithrelevantpreviousworks.Noteverybodyrememberseverythinginpapersunderlyingyourargument.Andsendingthehaplessreadertoconsultfivedifferentreferencesineachparagraphisanti-social.5Goodreason3toreadapaper:GoodpresentationThereareanumberofissuesthatimprovepresentation:Structure.Planinadvancethestructureofthepaper:sections,subsectionsandtheircontent.Structureshouldbelogical.Itshouldnotfollowspecificpersonalmeanderingsofyourresearch(i.e.,yourpersonallogic)butthelogicofapersontryingtoassimilatethisinformation.Remember:Researchisnonlinear,presentationshouldbelinear.Sectionsshouldnotbetoolong:informationisabsorbedbetterindigestiblechunks.Yourargumentshouldbeillustratedbyexamples,tablesandfigures.Itissometimesagoodideatouseasingleexampletoillustratedifferentstagesofyourargument.Newconceptsshouldbeintroducedatthepointwheretheymakesenseandwheretheirrelevanceisclearfromthecontext.6Notation.Muchoftheclarityofyourargumentdependsonnotation.Itisagoodpolicytodecideonnotationinadvance(thinkhowmessyitistochangeitmid-stream)accordingtoanumberofgeneralrulesofthethumb:•Considertheuseofnotationasanopportunitytoclarifyyourargumentandinformthereader,notjustasatechnicalnecessity.•Don’tinventyourpersonalnotationifagreednotationalreadyexistsinyoursubject.•Keeptoconvention:thus,“foreveryε0thereisaδ0”(nottheotherwayaround),ε0issmallandRr.Cleverdickeryisasillydistraction.•Consistencyinnotationhelpsthereadertoorganiseinformation.Forexample,boldfaceforvectors,UPPERCASEformatrices,SHELLCAPITALsforsets.•Avoidaprofusionofsubscripts,superscripts,multipleindices,hats,invertedhats,tildes,doubletildes,....ThefactthatitcanbedonewithLATEXisnotasufficientreasontodoit!•Youmighthavedefinedsomething-or-otheronpage5.Thisdoesn’tmeanthatthereaderwillrememberitonpage27.Sometimesitisagoodpolicytorecalldefinitionsandnotation.•Never,butnever,overloadnotation!7Language.PapersarenotwritteninMathematese,theyarewritteninEnglish.Remember:languageisthemaintooltoconveyinformation.Endlessbrightideashavebeenrenderedobscureandimpenetrablebypoorlanguage.•Firstandforemost,evenifyournativelang