A History of Vector Analysis The Evolution of t

OnOctober16，1843，SirWilliamRowanHamiltondiscoveredquaternionsand，ontheverysameday，presentedhisbreakthroughtotheRoyalIrishAcademy.Meanwhile，inalessdramaticstyle，aGermanhighschoolteacher，HermannGrassmann，wasdevelopinganothervectorialsysteminvolvinghypercomplexnumberscomparabletoquaternions.Thecreationsofthesetwomathematiciansledtoothervectorialsystems，mostnotablythesystemofvectoranalysisformulatedbyJosiahWillardGibbsandOliverHeavisideandnowalmostuniversallyemployedinmathematics，physicsandengineering.YettheGibbs-Heavisidesystemwonacceptanceonlyafterdecadesofdebateandcontroversyinthelatterhalfofthenineteenthcenturyconcerningwhichofthecompetingsystemsofferedthegreatestadvantagesformathematicalpedagogyandpractice.
Thisvolume，thefirstlarge-scalestudyofthedevelopmentofvectorialsystems，tracesheriseofthevectorconceptfromthediscoveryofcomplexnumbersthroughthesystemsofhypercomplexnumberscreatedbyHamiltonandGrassmanntothefinalacceptancearound1910ofthemodernsystemofvectoranalysis.ProfessorMichaelJ.Crowe(UniversityofNotreDame)discusseseachmajorvectorialsystemaswellasthemotivationsthatledtotheircreation，development，andacceptanceorrejection.
Thevectorialapproachrevolutionizedmathematicalmethodsandteachinginalgebra，geometry，andphysicalscience.AsProfessorCroweexplains，intheseareastraditionalCartesianmethodswerereplacedbyvectorialapproaches.Healsopresentsthehistoryofideasofvectoraddition，subtraction，multiplication，division(inthosesystemswhereitoccurs)anddifferentiation.Hisbookalsocontainsrefreshingportraitsofthepersonalitiesinvolvedinthecompetitionamongthevarioussystems.
Teachers，students，andpractitionersofmathematics，physics，andengineeringaswellasanyoneinterestedinthehistoryofscientificideaswillfindthisvolumetobewellwritten，solidlyargued，andexcellentlydocumented.Reviewershavedescribeditas"afascinatingvolume，""anengagingandpenetratinghistoricalstudy"and"anoutstandingbook(that)willdoubtlesslongremainthestandardworkonthesubject."In1992itwonanawardforexcellencefromtheJeanScottFoundationofFrance.