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MathematicsSubjectClassification2000MathematicsSubjectClassification2000(MSC2000)ThisisacompletelyrevisedversionoftheMSC,preparedcollaborativelyintheeditorialofficesofMRandZentralblattMATH.Itreplacesthe1991MSCandiseffective(inMR)withtheJanuary2000issue(2000a).WhileinmanyareasintheMSCthereareonlyverysmallchanges,othershavebeenexpandedsignificantly,andinsomeareasthereisanaltogethernewclassification.Themajorchangesareasfollows:Section04hasbeeneliminated;03Ewillnowbeusedforitemspreviouslyclassifiedin04.Anewsection,37,hasbeencreatedforDynamicalsystemsandergodictheory;asaresultSection58Fhasbeeneliminated.AlsoinSection58,58Ghasbeencompletelyrevisedandnowappearsas58J.ThenewSection74,Mechanicsofdeformablesolids,isacompletelyrevisedversionofSection73,whichhasbeeneliminated.TheareascoveredbySections90and92havebeenreorganizedintoSections90,91and92.Sections90Band90Cremainessentiallyunchanged.ThenewSection91Areplaces90Dand91Breplaces90A.Theothersubsectionsof91replacetheoldsubsections92G,H,JandK.Sections92B,C,D,andEremainessentiallyunchanged.MSC2000containsanewsection,97,forMathematicseducation.ThiswillbeusedonlyasasecondaryclassificationinMR.Othersectionswithsignificantadditionsorreorganizationinclude14,22,32,34,46,47,53,and65.TohelpusersoftheMSC,conversiontableshavebeencon-structedandareavailableontheAMSwebsite,ficationthatdoesnotappearinMSC2000,theclassification(s)inMSC2000thataremostlikelytobeusedforitemsthatwouldpreviouslyhavebeenclassifiedusingtheoldclassification,and,foreachnewclassificationinMSC2000,theclassification(s)inthe1991MSCthataremostlikelytohavebeenusedearlierforitemsclassifiedusingthenewclassification.InstructionsforusingtheMathematicsSubjectClassification2000Theseinstructionsapplyuniformlytoallfieldslisted.Themainpurposeoftheclassificationistohelpreadersfindtheitemsofpresentorpotentialinteresttothemasreadilyaspossible—inMR,inZbl,oranywhereelsewherethisclassificationsystemisused.Apaperorbookshouldbelistedundertheclassificationwhereitwillreceivethebroadestattentionfromreaderspossiblyinterestedinit—theseincludebothpeopleworkinginthatareaandpeoplewhoarefamiliarwiththatareaandapplyitsresultsandmethodselsewhere(insideoroutsidemathematics).Itwillbeextremelyusefulforbothreadersandclassifierstofamiliarizethemselveswiththeentireclassificationsystemandthustobecomeawareofalltheclassificationsofpossibleinteresttothem.Foreverypaperorbooklisted,MRchoosespreciselyone“primary”classification,whichissimplythecodeforthesection(MSCentry)inwhichtheitemwillbelocated.Thissectionshouldbetheonethatcoverstheprincipalcontribution.Whenanitemcontainsseveralprincipalcontributionsindifferentareas,theprimaryclassificationshouldcoverthe“mostimportant”amongthem.Apaperorbookmayreceiveoneorseveral“secondary”classifications(or“cross-references”)tocoveranyremainingprincipalcontributions,ancillaryresults,motivationororiginoftheproblemsdiscussed,intendedorpotentialfieldofapplication,orothersignificantaspectsworthyofnotice.The“primary”principalcontributionismeanttobetheoneincludingthemostimportantpartoftheworkactuallydoneintheitemunderconsideration.Forexample,apaperwhosemainoverallcontentisthesolutionofaproblemingraphtheory,whicharoseincomputerscienceandwhosesolutionis,say,atpresentonlyofinteresttocomputerscientists,belongsprimarilyin05Cwithacross-referencein68;conversely,apaperwhoseoverallcontentliesmainlyincomputerscienceshouldreceiveaprimaryclassificationin68,evenifitmakesheavyuseofgraphtheoryandprovesseveralnewgraph-theoreticresultsalongtheway.Therearetwotypesofcross-referencesgivenaftermanyclassificationsinthelist.Thefirsttypeisoftheform“{ForA,seeX}”;ifthisappearsinsectionY,itmeansthatforcontributionsdescribedbyAoneshouldusuallyassigntheclassificationX,notY.Theothertypeofcross-referencemerelypointsoutrelatedclassifications;itisoftheform“[Seealso...]”,“[Seemainly...]”,etc.,andtheclassificationslistedinthebracketsmay,butneednot,beaddedtotheclassificationofapaper,ortheymaybeusedinplaceoftheclassificationwherethecross-referenceisgiven.Theclassifierwillhavetojudgewhichclassificationisthemostappropriatefortheitemathand.00–XXGENERAL00–01Instructionalexposition(textbooks,tutorialpapers,etc.)00–02Researchexposition(monographs,surveyarticles)00AxxGeneralandmiscellaneousspecifictopics00A05Generalmathematics00A06Mathematicsfornonmathematicians(engineering,socialsciences,etc.)00A07Problembooks00A08Recreationalmathematics[Seealso97A20]00A15Bibliographies00A17Externalbookreviews00A20Dictionariesandothergeneralreferenceworks00A22Formularies00A30Philosophyofmathematics[Seealso03A05]00A35Methodologyofmathematics,didactics[Seealso97Cxx,97Dxx]00A69Generalappliedmathematics{Forphysics,see00A79andSections70through86}00A71Theoryofmathematicalmodeling00A72Generalmethodsofsimulation00A73Dimensionalanalysis00A79Physics(usemorespecificentriesfromSections70through86whenpossible)MATHEMATICSSUBJECTCLASSIFICATION200000Axx200A99Miscellaneoustopics00BxxConferenceproceedingsandcollectionsofpapers00B05Collectionsofabstractsoflectures00B10Collectionsofarticlesofgeneralintere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