Book Review
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MathSciNet review:
2985956
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Book Information:
Author:
Roger Hart
Title:
The Chinese roots of linear algebra
Additional book information:
Johns Hopkins University Press,
Baltimore, Maryland,
2011,
xiv+286 pp.,
ISBN 978-0-8018-9755-9,
US $65.00
David E. Rowe, New trends and old images in the history of mathematics, Vita mathematica (Toronto, ON, 1992; Quebec City, PQ, 1992) MAA Notes, vol. 40, Math. Assoc. America, Washington, DC, 1996, pp. 3–16. MR 1391731
John von Neumann, The mathematician, The Works of the Mind, University of Chicago Press, Chicago, Ill., 1947, pp. 180–196. Edited for the Committee on Social Thought by Robert B. Heywood. MR 0021929
I. Grattan-Guinness, The mathematics of the past: distinguishing its history from our heritage, Historia Math. 31 (2004), no. 2, 163–185 (English, with English and Portuguese summaries). MR 2055640, DOI 10.1016/S0315-0860(03)00032-6
Joseph W. Dauben, Chinese mathematics, The mathematics of Egypt, Mesopotamia, China, India, and Islam, Princeton Univ. Press, Princeton, NJ, 2007, pp. 187–384. MR 2368472
Yan Li and Shi Ran Du, Chinese mathematics, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1987. A concise history; Translated from the Chinese and with a preface by John N. Crossley and Anthony W.-C. Lun; With a foreword by Joseph Needham. MR 932966
J.-C. Martzloff, Histoire des mathématiques chinoise, Masson, Paris, 1987, A History of Chinese Mathematics (Translated by S. S. Wilson). Springer, Berlin, 1997.
Carl Meyer, Matrix analysis and applied linear algebra, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000. With 1 CD-ROM (Windows, Macintosh and UNIX) and a solutions manual (iv+171 pp.). MR 1777382, DOI 10.1137/1.9780898719512
Karine Chemla and Shuchun Guo, Les neuf chapitres, Dunod, Paris, 2004 (French). Le classique mathématique de la Chine ancienne et ses commentaires. [The mathematical classic of ancient China and its commentaries]; With a preface by Geoffrey Lloyd. MR 2111394
Kangshen Shen, John N. Crossley, and Anthony W.-C. Lun, The nine chapters on the mathematical art, Oxford University Press, New York; Science Press Beijing, Beijing, 1999. Companion and commentary; With forewords by Wentsün Wu and Ho Peng Yoke. MR 1740507
J. Brennan, NSF proposal preparation, Notices Amer. Math. Soc. 54 (2007), no. 9, 1153–1157.
D. A. Grier, When computers were humans, Princeton Univ. Press, 2005.
J. Buteo, Logistica, Paris, 1560.
A. Heeffer, From the second unknown to the symbolic equation, Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics (A. Heeffer and M. Van Dyck, eds.), College Publications, London, 2011, pp. 57–101.
J. F. Grcar, How ordinary elimination became Gaussian elimination, Historia Math. 38 (2011), no. 2, 163–218.
—, Mathematicians of Gaussian ellimination, Notices Amer. Math. Soc. 58 (2011), no. 6.
I. Newton, Universal arithmetick, Senex, Taylor, et al., London, 1720.
F. Chiò, Mémoire sur les fonctions connues sous le nom de résultantes ou de déterminants, Turin, 1853.
L. E. Fuller and J. D. Logan, On the evaluation of determinants by Chiò’s method, College Math. J. 6 (1975), no. 1, 8–10.
Erwin H. Bareiss, Sylvester’s identity and multistep integer-preserving Gaussian elimination, Math. Comp. 22 (1968), 565–578. MR 226829, DOI 10.1090/S0025-5718-1968-0226829-0
Steven C. Althoen and Renate McLaughlin, Gauss-Jordan reduction: a brief history, Amer. Math. Monthly 94 (1987), no. 2, 130–142. MR 874013, DOI 10.2307/2322413
Victor J. Katz, Who is the Jordan of Gauss-Jordan?, Math. Mag. 61 (1988), no. 2, 99–100. MR 934825, DOI 10.2307/2690039
References
- D. E. Rowe, New trends and old images in the history of mathematics, Vita mathematica: historical research and integration with teaching (R. Calinger, ed.), Cambridge Univ. Press, 1996, pp. 3–16. MR 1391731 (97d:01002)
- J. von Neumann, The mathematician, The Works of the Mind (R. B. Heywood, ed.), Univ. of Chicago Press, 1947, pp. 180–196. MR 0021929 (9:130f)
- I. Grattan-Guinness, The mathematics of the past: distinguishing its history from our heritage, Historia Math. 31 (2004), no. 2, 163–185. MR 2055640 (2005e:01029)
- J. W. Dauben, Chinese mathematics, The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook (V. J. Katz, ed.), Princeton Univ. Press, 2007, pp. 187–384. MR 2368472
- Y. Lĭ and S. Dù, Chinese mathematics (Translated from the Chinese by J. N. Crossley and A. W.-C. Lun), Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1987. MR 932966 (90m:01003)
- J.-C. Martzloff, Histoire des mathématiques chinoise, Masson, Paris, 1987, A History of Chinese Mathematics (Translated by S. S. Wilson). Springer, Berlin, 1997.
- C. Meyer, Matrix analysis and applied linear algebra, SIAM, Philadelphia, 2000. MR 1777382
- K. Chemla and G. Shuchun, Les neuf chapitres, Dunod, Paris, 2005. MR 2111394 (2005h:01004)
- K. Shen, J. N. Crossley, and A. W.-C. Lun, The nine chapters of the mathematical art companion and commentary, Oxford Univ. Press, New York, 1999. MR 1740507 (2001g:01012)
- J. Brennan, NSF proposal preparation, Notices Amer. Math. Soc. 54 (2007), no. 9, 1153–1157.
- D. A. Grier, When computers were humans, Princeton Univ. Press, 2005.
- J. Buteo, Logistica, Paris, 1560.
- A. Heeffer, From the second unknown to the symbolic equation, Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics (A. Heeffer and M. Van Dyck, eds.), College Publications, London, 2011, pp. 57–101.
- J. F. Grcar, How ordinary elimination became Gaussian elimination, Historia Math. 38 (2011), no. 2, 163–218.
- —, Mathematicians of Gaussian ellimination, Notices Amer. Math. Soc. 58 (2011), no. 6.
- I. Newton, Universal arithmetick, Senex, Taylor, et al., London, 1720.
- F. Chiò, Mémoire sur les fonctions connues sous le nom de résultantes ou de déterminants, Turin, 1853.
- L. E. Fuller and J. D. Logan, On the evaluation of determinants by Chiò’s method, College Math. J. 6 (1975), no. 1, 8–10.
- E. H. Bareiss, Sylvester’s identity and multistep integer-preserving Gaussian elimination, Math. Comp. 22 (1968), no. 103, 565–578. MR 0226829 (37:2416)
- S. C. Althoen and R. McLaughlin, Gauss-Jordan Reduction: A Brief History, Amer. Math. Monthly 94 (1987), 130–142. MR 874013 (88d:01017)
- V. J. Katz, Who is the Jordan of Gauss-Jordan?, Math. Mag. 61 (1988), no. 2, 99–100. MR 934825 (89f:01034)
Review Information:
Reviewer:
Joseph F. Grcar
Affiliation:
6059 Castlebrook Drive; Castro Valley, California 94552-1645
Email:
jfgrcar@gmail.com
Journal:
Bull. Amer. Math. Soc.
49 (2012), 585-590
DOI:
https://doi.org/10.1090/S0273-0979-2011-01341-6
Published electronically:
June 7, 2011
Review copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
