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50年国际数学奥林匹克50th IMO:50 Years of International Mathematical Olympiads(2011)

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50年国际数学奥林匹克50th IMO:50 Years of International Mathematical Olympiads(2011)

50THIMO–50YEARSOFINTERNATIONALMATHEMATICALOLYMPIADS−HANSDIETRICHGRONAUHANNSHEINRICHLANGMANNDIERKSCHLEICHEREDITORS50THIMO–50YEARSOFINTERNATIONALMATHEMATICALOLYMPIADS123EDITORSHANSDIETRICHGRONAUUNIVERSITTROSTOCKINSTITUTFRMATHEMATIKULMENSTR6918051ROSTOCKGERMANYGRONAUUNIROSTOCKDEDIERKSCHLEICHERJACOBSUNIVERSITYRESEARCHICAMPUSRING128759BREMENGERMANYDIERKJACOBSUNIVERSITYDEHANNSHEINRICHLANGMANNBILDUNGBEGABUNGGEMEINNTZIGEGMBHBUNDESWETTBEWERBMATHEMATIKKORTRIJKERSTR153177BONNGERMANYLANGMANNBUNDESWETTBEWERBMATHEMATIKDEISBN9783642145643EISBN9783642145650DOI101007/9783642145650SPRINGERHEIDELBERGDORDRECHTLONDONNEWYORKMATHEMATICSSUBJECTCLASSIFICATION201000A09CSPRINGERVERLAGBERLINHEIDELBERG2011THISWORKISSUBJECTTOCOPYRIGHTALLRIGHTSARERESERVED,WHETHERTHEWHOLEORPARTOFTHEMATERIALISCONCERNED,SPECIFICALLYTHERIGHTSOFTRANSLATION,REPRINTING,REUSEOFILLUSTRATIONS,RECITATION,BROADCASTING,REPRODUCTIONONMICROFILMORINANYOTHERWAY,ANDSTORAGEINDATABANKSDUPLICATIONOFTHISPUBLICATIONORPARTSTHEREOFISPERMITTEDONLYUNDERTHEPROVISIONSOFTHEGERMANCOPYRIGHTLAWOFSEPTEMBER9,1965,INITSCURRENTVERSION,ANDPERMISSIONFORUSEMUSTALWAYSBEOBTAINEDFROMSPRINGERVIOLATIONSARELIABLETOPROSECUTIONUNDERTHEGERMANCOPYRIGHTLAWTHEUSEOFGENERALDESCRIPTIVENAMES,REGISTEREDNAMES,TRADEMARKS,ETCINTHISPUBLICATIONDOESNOTIMPLY,EVENINTHEABSENCEOFASPECIFICSTATEMENT,THATSUCHNAMESAREEXEMPTFROMTHERELEVANTPROTECTIVELAWSANDREGULATIONSANDTHEREFOREFREEFORGENERALUSECOVERDESIGNWMXDESIGNGMBH,HEIDELBERGPRINTEDONACIDFREEPAPERSPRINGERISPARTOFSPRINGERSCIENCEBUSINESSMEDIAWWWSPRINGERCOMPREFACEFROM10TO22JULY2009GERMANYHOSTEDTHE50THINTERNATIONALMATHEMATICALOLYMPIADIMOTHISJUBILEEANNIVERSARYEVENTTOOKPLACEONTHECAMPUSOFJACOBSUNIVERSITYBREMENFORTHEFIRSTTIMETHENUMBEROFPARTICIPATINGCOUNTRIESEXCEEDED100,WITH104COUNTRIESFROMALLCONTINENTSSENDINGADELEGATIONCONSISTINGOFSIXSTUDENTS,ALEADERANDADEPUTYLEADERCELEBRATINGTHE50THANNIVERSARYOFTHEIMOPROVIDESANIDEALOPPORTUNITYTOLOOKBACKOVERTHEPASTFIVEDECADESANDTOREVIEWITSDEVELOPMENTFROMMODESTBEGINNINGSTOBECOMEAWORLDWIDEEVENTTHISBOOKISAIMEDATSTUDENTSINTHEIMOAGEGROUPANDSEEKSTODEMONSTRATETHATMATHEMATICSISANACTIVEANDLIVELYSUBJECT,THOUSANDSOFYEARSOLDANDYETYOUNGANDFRESHASEVERWEHAVEINVITEDSEVERALIMOPIONEERSTOTELLUSABOUTTHEDEVELOPMENTOFIMOSINCEITFIRSTBEGANTHEYREVEALTHATINITIALLYNOBODYTHOUGHTITWOULDDEVELOPINTOANANNUALEVENT,LETALONEGROWASBIGASITISTODAYWEINCLUDETHREEACCOUNTSFROMIMOPIONEERSMIRCEABECHEANUFROMROMANIA,SPEAKINGONBEHALFOFTHECOUNTRYTHATCREATEDTHEIMOANDHOSTEDTHEINITIALOLYMPIADEVENT;ISTVNREIMANFROMHUNGARYWHOPERSONALLYEXPERIENCEDTHEEARLYYEARS;ANDWOLFGANGENGELFROMTHENEASTGERMANYWHOWITNESSEDTHEIMPACTTHEOLYMPIADSHAVEHADFROMTHEOUTSETONMATHEMATICALACTIVITIESFORSTUDENTS,PARTICULARLYINGERMANYTHESEREPORTSGIVEAVIVIDANDPERSONALDESCRIPTIONOFWHATGRADUALLYBECAMEANINTERNATIONALSUCCESSSTORYALSOINCLUDEDISDATAABOUTTHE50ANNUALOLYMPIADSWHICHILLUSTRATESTHEDEVELOPMENTOFTHECOMPETITIONFROMJUSTSEVENCOUNTRIESIN1959TO104COUNTRIES,WITH565PARTICIPANTS,IN2009WELISTTHEMOSTSUCCESSFULCONTESTANTS,THERESULTSOFTHE50OLYMPIADSANDTHENAMESOFALL112COUNTRIESTHATHAVEEVERTAKENPARTINMATHEMATICS,TALENTISOFTENDEVELOPEDANDDEMONSTRATEDATANEARLYAGETHUSITISIMPRESSIVETOSEETHATMANYOFTHEWORLD’SLEADINGRESEARCHMATHEMATICIANSWEREAMONGTHEMOSTSUCCESSFULIMOPARTICIPANTSINTHEIRYOUTHTOILLUSTRATETHISWEINCLUDEALISTSHOWINGWINNERSOFPRESTIGIOUSRESEARCHAWARDSWHOPARTICIPATEDINTHEIMOWHENTHEYWEREYOUNGINADDITIONTOTHEMATHEMATICSCOMPETITIONANIMPORTANTASPECTOFTHEOLYMPIADSISTHATSTUDENTSFROMALLOVERTHEWORLDMEETANDEXCHANGEIDEASITISBOTHAPERSONALVVIPREFACEHIGHLIGHTOFTHEIRLIVESTHATTHEYTREASUREFORALONGTIMEANDAPLACEWHEREINTERNATIONALFRIENDSHIPSDEVELOPSOMEOFTHEPERSONALORAMUSINGANECDOTESOFPREVIOUSIMOSAREINCLUDEDINTHELASTCHAPTEROFTHEBOOKTHEOUTSTANDINGEVENTOFTHE2009OLYMPIADWASTHECELEBRATIONOFTHEIMO’S50THANNIVERSARYSIXOFTHEWORLD’SLEADINGMATHEMATICIANS,ALLOFTHEMHIGHLYSUCCESSFULFORMERIMOPARTICIPANTS,WEREINVITEDASGUESTSOFHONOURTOGIVEPRESENTATIONSBLABOLLOBS,TIMOTHYGOWERS,LSZLLOVSZ,STANISLAVSMIRNOV,TERENCETAOANDJEANCHRISTOPHEYOCCOZTHEIRCONTRIBUTIONSAREALSOINCLUDEDINTHISBOOKWEWOULDLIKETOEXPRESSOURSINCEREGRATITUDETOALLTHOSEWHOSUPPORTEDTHEORGANISATIONOFTHE50THIMO,MAKINGITAMEMORABLEANDUNIQUEEVENTFORALLPARTICIPANTSFINALLY,WEWISHTOTHANKTHESPRINGERVERLAGFORPUBLISHINGTHISBOOKWEAREINDEBTEDTOCLEMENSHEINEFORHISSUPPORTANDCOLLABORATIONROSTOCK,BONN,BREMENHANSDIETRICHGRONAUMAY2010HANNSHEINRICHLANGMANNDIERKSCHLEICHERWELCOMEMESSAGEDEARIMOPARTICIPANTS,THISYEAR’SIMOHASASPECIALSIGNIFICANCEWECELEBRATETHE50THANNIVERSARYOFTHEIMOINTHEBEGINNINGSITSTARTEDASAONETIMEEVENTFORSTUDENTSFROMTHECOUNTRIESWHICHATTHETIMEWERESAIDTOFORMTHE“SOCIALISTBLOCK”OR“SOVIETBLOCK”,TOWITBULGARIA,CZECHOSLOVAKIA,GERMANDEMOCRATICREPUBLIC,HUNGARY,POLAND,ROMANIAANDTHESOVIETUNIONITISREMARKABLETHATOFTHOSE7COUNTRIES,3DONOTEXISTANYMOREBUTTHEIMO,WHICH,ENCOURAGEDBYTHESUCCESSOFTHEFIRSTCOMPETITIONBECAMEAYEARLYEVENT,FLOURISHESSOMEKEYDATES1967THEFIRSTWESTEUROPEANCOUNTRIESUNITEDKINGDOM,FRANCE,ITALY,SWEDENTAKEPARTINTHE9THIMOINCETINJE,YUGOSLAVIAFINLAND’SONETIMEPARTICIPATIONIN1965HADNOIMMEDIATECONTINUATIONTHENETHERLANDSFOLLOWEDSUITIN1969,AUST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