内容简介
Thisisagenuineintroductiontoplanealgebraiccurvesfromageometricviewpoint,designedasafirsttextforundergraduatesinmathematics,orforpostgraduateandresearchworkersintheengineeringandphysicalsciences.Thebookcontainsseveralhundredworkedexamplesandexercises,makingitsuitableforadoptionasacoursetext.Fromthelinesandconicsofelementarygeometrythereaderproceedstogeneralcurvesintherealaffineplane,withexcursionstomoregeneralfieldstoillustrateapplications,suchasnumbertheory.Byaddingpointsatinfinitytheaffineplaneisextendedtotheprojectiveplane,yieldinganaturalsettingforcurvesandprovidingafloodofilluminationintotheunderlyinggeometry.AminimalamountofalgebraleadstothefamoustheoremofBezout,whilsttheideasoflinearsystemsareusedtodiscusstheclassicalgroupstructureonthecubic.
作者简介
ChrisGibsonreceivedanhonoursdegreeinMathematicsfromStAndrewsUniversityin1963,andlaterthedegreesofDrsMathandDrMathfromtheUniversityofAmsterdam,returningtoEnglandin1967tobeginhis35yearmathematicscareerattheUniversityofLiverpool.Hisintereststurnedtowardsthegeometricareas,andhewasafoundermemberoftheLiverpoolSingularitiesGroupuntilhisretirementin2002asReaderinPureMathematics,withover60publishedpapersinthatarea.In1974heco-authoredthesignificant'TopologicalStabilityofSmoothMappings'(publishedbySpringerVerlag)presentingthefirstdetailedproofofThom'sTopologicalStabilityTheorem.Inadditiontopurelytheoreticalworkinsingularitytheory,hejointlyappliedsingularmethodstospecificquestionsaboutcausticsarisinginthephysicalsciences.Hislaterinterestslaylargelyintheapplicationstotheoreticalkinematics,andtoproblemsarisingintheoreticalrobotics.ThisinterestgaverisetoasubstantialcollaborationwithProfessorK.H.HuntintheUniversitiesofMonashandMelbourne,andproducedaformalclassificationofscrewsystems.Attheteachinglevelhismajorcontributionwastopioneerthere-introductionofundergraduategeometryteaching.ThepracticalexperienceofmanyyearsofundergraduateteachingwasdistilledintothreeundergraduatetextspublishedbyCambridgeUniversityPress,nowwidelyadoptedinternationallyforundergraduate(andgraduate)teaching.
