資源描述：
《discrete mathematics》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫(kù)。
1、PrefaceFormoststudents,the?rstandoftenonlycourseincollegemathematicsiscalculus.Itistruethatcalculusisthesinglemostimportant?eldofmathematics,whoseemergenceintheseventeenthcenturysignaledthebirthofmodernmathematicsandwasthekeytothesuccessfulapplicationsofmathematicsinthesciencesandengineering.
2、Butcalculus(oranalysis)isalsoverytechnical.Ittakesalotofworkeventointroduceitsfundamentalnotionslikecontinuityandthederivative(afterall,ittooktwocenturiesjusttodeveloptheproperde?nitionofthesenotions).Togetafeelingforthepowerofitsmethods,saybydescribingoneofitsimportantapplicationsindetail,ta
3、kesyearsofstudy.Ifyouwanttobecomeamathematician,computerscientist,orengineer,thisinvestmentisnecessary.Butifyourgoalistodevelopafeelingforwhatmathematicsisallabout,wheremathematicalmethodscanbehelpful,andwhatkindsofquestionsdomathematiciansworkon,youmaywanttolookfortheanswerinsomeother?eldsof
4、mathematics.Therearemanysuccessstoriesofappliedmathematicsoutsidecalculus.Arecenthottopicismathematicalcryptography,whichisbasedonnumbertheory(thestudyofthepositiveintegers1,2,3,...),andiswidelyapplied,forexample,incomputersecurityandelectronicbanking.Otherimportantareasinappliedmathematicsar
5、elinearprogramming,codingtheory,andthetheoryofcomputing.Themathematicalcontentintheseapplicationsiscollectivelycalleddiscretemathematics.(Theword“discrete”isusedinthesenseof“separatedfromeachother,”theoppositeof“continuous;”itisalsooftenusedinthemorerestrictivesenseof“?nite.”Themoreeverydayve
6、rsionofthisword,meaning“circumspect,”isspelled“discreet.”)viPrefaceTheaimofthisbookisnottocover“discretemathematics”indepth(itshouldbeclearfromthedescriptionabovethatsuchataskwouldbeill-de?nedandimpossibleanyway).Rather,wediscussanumberofselectedresultsandmethods,mostlyfromtheareasofcombinato
7、ricsandgraphthe-ory,withalittleelementarynumbertheory,probability,andcombinatorialgeometry.Itisimportanttorealizethatthereisnomathematicswithoutproofs.Merelystatingthefacts,withoutsayingsomethingaboutwhythesefactsarevalid,wouldbeterriblyfarfr
