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8
I
Secondly,weincludedpreciseinformationaboutthesourceswehad
used.Thisturnedouttobeadifficultanddauntingtask.Itrequired
keepingtrackofwherewetookeverythingfrom(andsometimes
franticallysearchingthroughourlibrarieswhenweforgottotake
noteofthat!).Aftercompilingthem,wefeltmorerespecttothejob
ofhistorians,whodealwithsuchissuesonadailybasis.(Andwe
didnoteventrytoestablishpriorityifseveralpeopleappearedto
provethesamethingaroundthesametime,althoughsometimeswe
includedareferencetotheoriginalworkontheissuesdiscussed.)
Understandably,thesesectionsareratherboring,sowesometimes
includedsomechocolatecoatingtomakethemgodowneasier.Read
themforyourselftoseewhatwemean.(Anoteonforeignwords:
whencitingworksinlanguagesotherthanEnglish,wegenerallyleft
thenameslikefltheorem”intheoriginallanguage,sincethegoalof
citationsistohelpthereaderfindtherelevantplaceinthebook–an
additionaltranslationstepwouldaccomplishnothing.Wemadean
exception,though,forliteratureusingnon-Latinscripts,sinceeither
includinge.g.theCyrilliclettersorromanizingthempresentaunique
setofchallenges.Inthatcase,wedecidedtojusttranslatethewords
fltheorem”,fldefinition”andsoon,anduseversionsofpeople’snames
commoninEnglish-languageliterature.)
Webelievethatthebook(orsomeofitsparts)canbeusedasabasis
foraseriesoflectures.Sincetheoryisbesttaught(andlearned)when
thestudenthastheopportunitytoactivelyengagewiththematerial,
thereisaneedforexercises.Weincludedasetofthemattheendof
eachchapter,too.However,sinceweareawarethatourbookmaybe
alsousedtoself-teachtheconceptswepresented,wewerehesitant
torelegateideasimportantfortherestoftexttotheexercises,and
preferredtoe.g.writeoutmostexamplesinfull.(Manyofthemcanbe
turnedtoexercisesinclassroomsetting.)Wealsoconsideredadding
hintstomoredifficultproblems,butafterawhiledecidedagainstit–
instead,weprovidesourcesfortheexercises,soifyouarestuck,going
totheplacetheexercisecomesfrommaybeofhelp.
Speakingofexamples–thisisoneoftheareaswepushedreally
strongin.Wethinkthateverysingledefinitioninanybookonmathe-
