Chinese Roots of Linear Algebra

Inbunden, Engelska, 2011

939 kr

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A monumental accomplishment in the history of non-Western mathematics, The Chinese Roots of Linear Algebra explains the fundamentally visual way Chinese mathematicians understood and solved mathematical problems. It argues convincingly that what the West "discovered" in the sixteenth and seventeenth centuries had already been known to the Chinese for 1,000 years. Accomplished historian and Chinese-language scholar Roger Hart examines Nine Chapters of Mathematical Arts-the classic ancient Chinese mathematics text-and the arcane art of fangcheng, one of the most significant branches of mathematics in Imperial China. Practiced between the first and seventeenth centuries by anonymous and most likely illiterate adepts, fangcheng involves manipulating counting rods on a counting board. It is essentially equivalent to the solution of systems of N equations in N unknowns in modern algebra, and its practice, Hart reveals, was visual and algorithmic. Fangcheng practitioners viewed problems in two dimensions as an array of numbers across counting boards.By "cross multiplying" these, they derived solutions of systems of linear equations that are not found in ancient Greek or early European mathematics. Doing so within a column equates to Gaussian elimination, while the same operation among individual entries produces determinantal-style solutions. Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra.

Produktinformation

Utgivningsdatum2011-02-26
Mått156 x 235 x 25 mm
Vikt567 g
FormatInbunden
SpråkEngelska
Antal sidor304
FörlagJohns Hopkins University Press
ISBN9780801897559

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Preface1. IntroductionOverview of This BookHistoriographic IssuesOutline of the Chapters2. PreliminariesChinese ConventionsChinese MathematicsModern Mathematical Terminology3. The Sources: Written Records of Early Chinese MathematicsPractices and Texts in Early Chinese MathematicsThe Book of ComputationThe Nine Chapters on the Mathematical Arts4. Excess and DeficitExcess and Deficit Problems in the Book of Computation"Excess and Deficit," Chapter 7 of the Nine Chapters5. Fangcheng, Chapter 8 of the Nine ChaptersThe Fangcheng ProcedureProcedure for Positive and Negative NumbersConclusions6. The Fangcheng Procedure in Modern Mathematical TermsConspectus of Fangcheng Problems in the Nine ChaptersEliminationBack SubstitutionIs the Fangcheng Procedure Integer-Preserving?Conclusions7. The Well ProblemTraditional Solutions to the Well ProblemThe Earliest Extant Record of a Determinantal CalculationThe Earliest Extant Record of a Determinantal SolutionConclusions8. Evidence of Early Determinantal SolutionsThe Classification of ProblemsFive Problems from the Nine ChaptersConclusions9. ConclusionsThe Early History of Linear AlgebraQuestions for Further ResearchMethodological IssuesSignificance and ImplicationsAppendix A: Examples of Similar ProblemsExamples from Diophantus's ArithmeticaExamples from ModernWorks on Linear AlgebraAppendix B: Chinese Mathematical TreatisesBibliographies of Chinese Mathematical TreatisesMathematical Treatises Listed in Chinese BibliographiesAppendix C: Outlines of ProofsBibliography of Primary and Secondary SourcesIndex