The Chinese Roots of Linear Algebra

Preface
1. Introduction
Overview of This Book
Historiographic Issues
Outline of the Chapters
2. Preliminaries
Chinese Conventions
Chinese Mathematics
Modern Mathematical Terminology
3. The Sources: Written Records of Early Chinese Mathematics
Practices and Texts in Early Chinese Mathematics
The Book of Computation
The Nine Chapters on the Mathematical Arts
4. Excess and Deficit
Excess and Deficit Problems in the Book of Computation
"Excess and Deficit," Chapter 7 of the Nine Chapters
5. Fangcheng, Chapter 8 of the Nine Chapters
The Fangcheng Procedure
Procedure for Positive and Negative Numbers
Conclusions
6. The Fangcheng Procedure in Modern Mathematical Terms
Conspectus of Fangcheng Problems in the Nine Chapters
Elimination
Back Substitution
Is the Fangcheng Procedure Integer-Preserving?
Conclusions
7. The Well Problem
Traditional Solutions to the Well Problem
The Earliest Extant Record of a Determinantal Calculation
The Earliest Extant Record of a Determinantal Solution
Conclusions
8. Evidence of Early Determinantal Solutions
The Classification of Problems
Five Problems from the Nine Chapters
Conclusions
9. Conclusions
The Early History of Linear Algebra
Questions for Further Research
Methodological Issues
Significance and Implications
Appendix A: Examples of Similar Problems
Examples from Diophantus's Arithmetica
Examples from ModernWorks on Linear Algebra
Appendix B: Chinese Mathematical Treatises
Bibliographies of Chinese Mathematical Treatises
Mathematical Treatises Listed in Chinese Bibliographies
Appendix C: Outlines of Proofs
Bibliography of Primary and Secondary Sources
Index