readinglist

October 10, 2014  |  By  | 


1INTRODUCTION Therangeofmathematicsbooksnowavailableisenormous.Thislistjustcontainsafewsuggestions whichyoushouldndhelpful.Theyaredividedintothreegroups:historicalandgeneral(whichaim togiveabroadideaofthescopeanddevelopmentofthesubject);recreational,fromproblembooks (whichaimtokeepyourbrainworking)totechnicalbooks(whichgiveyouinsightintoaspecicarea ofmathematicsandincludemathematicaldiscussion);andtetbooks(whichcoveratopicinadvanced mathematicsofthekindthatyouwillencounterinyourrstyearatuniversity).Donotfeelthatyou shouldonlyreadthedicultones:medicineisonlygoodforyouifitishardtotake,butthisisnottrue formathematicsbooks.Anyreadingyoudowillcertainlyproveuseful. Allthebooksonthelistshouldbeobtainablefromyourlocallibrary,thoughyoumayhavetoorder them.ostareavailable(relatively)cheaplyinpaperbackandsowouldmakegoodadditionstoyour Christmaslist.Somemaybeoutofprint,butstillobtainablefromlibraries. Youmightalsoliketolookonthewebformathematicssites.Goodstartingpointsare: NRICH (http://nrich.maths.org.uk)whichisaweb-basedinteractivemathematicsclub; Plus (http://plus.maths.org.uk),whichisaweb-basedmathematicsjournal. BoththesesitesarebasedinCambridge. 2STUDYINGMATHEMATICS Howtostudyforamathsdegree LaraAlcock(OUP,2013) Thissoundslikethesortofbookthatcouldbeterrible,butitturnsouttoberathergood.Whatis writtenonthecovertellsyouaccuratelywhatisinside,sothereisnoneedtosayanymore.Denitely worthalook. 3HISTORICALANDGENERAL Oneofthemostfrequentcomplaintsofmathematicsundergraduatesisthattheydidnotrealiseuntil toolatewhatwasbehindallthematerialtheywrotedowninlectures:Whywasitimportant?What weretheproblemswhichdemandedthisnewapproach?Whodidit?Thereismuchtobelearntfroma historicalapproach,evenifitisfairlynon-mathematical. MakersofMathematics S.Hollingdale(Penguin,1989) Therearenotmanybooksonthehistoryofmathematicswhicharepitchedatasuitablelevel.Hollingdale givesabiographicalapproachwhichisbothreadableandmathematical.YoumightalsotryE.T.Bell MenofMathematics (TouchstoneBooks,SimonandSchuster,1986).Historiansofmathematicshavea lottosayaboutthis(verylittleofitcomplimentary)butitisfullofgoodstorieswhichhaveinspired generationsofmathematicians. ARussianChildhood S.Kovalevskaya(trans.B.Stillman)(Springer,1978,nowout ofprint) SonyaKovalevskayawastherstwomaninmoderntimestoholdalectureshipataEuropeanuniversity: in1889,inspiteofthefactthatshewasawoman(withanunconventionalprivatelife),aforeigner,a socialist(orworse)andapractitionerofthenewWeierstrassiantheoryofanalysis,shewasappointed aprofessorattheUniversityofStockholm.Hermemoriesofchildhoodarenon-mathematicalbutfasci- nating.Shediscoveredinhernurserythetheoryofinnitesimals:timesbeinghard,thewallshadbeen paperedwithpagesofmathematicalnotes. AlanTuring,theEnigma A.Hodges(Vintage,1992) AgreatbiographyofAlanTuring,apioneerofmoderncomputing.Thetitlehasadoublemeaning: themanwasanenigma,committingsuicidein1954byeatingapoisonedapple,andtheGermancode thathewasinstrumentalincrackingwasgeneratedbytheEnigmamachine.Thebookislargelynon- mathematical,buttherearenoholdsbarredwhenitcomestodescribinghismajorachievement,now calledaTuringmachine,withwhichhedemonstratedthatafamousconjecturebyHilbertisfalse. 1

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