And in the source

Date of publication:2012-11   Press: Shanghai Jiao Tong University press   Author:Xu Zelin   Pages:366   Words:361000  
Summary

"And in the source (and algorithm and its numerical origin)" by Xu Zelin, this book from the viewpoint of the algorithm, through the analysis of historical textual research and mathematical, introduced traditional Japanese mathematics (and counting) in the numerical solution of nonlinear equation and the equation of higher degree elimination algorithm, interpolation method, the arithmetic progression of higher order summation algorithm, congruence group method, Diophantine approximation, function accelerated approximation method, and calculus algorithm's achievements, and traces of these algorithms and traditional Chinese mathematical (numerical) origin of the corresponding algorithm of.
"and is in the source (and algorithm and its numerical origin)" reveals the spirit of Traditional East Asian algorithm and achievement of mathematics, which demonstrates the traditional Chinese mathematics to the evolution of the modern mathematics.
Author brief introduction

Xu Zelin, born in 1963, Anhui Province, Wuwei County, majoring in history of science and technology, Inner Mongolia Normal University in 1994 to study the history of science and the master of Science in Mathematics Department of Northwestern University, in 1998 won the science and history of science doctorate, the same year in Tianjin Normal University school discipline school teaching, is a professor of Donghua University Humanities Institute, director of Chinese society the history of science and technology, a member of the Japanese Society for the history of science. The main research interest for East Asian history of mathematics, mathematics communication history and the history of mathematics, mathematical astronomy in China. Author of "and" and other selected.
Catalogue of books

The first chapter "play" and the evolution of the East Asia algebraic approach for the development of
1.1 mathematics history on "play" concept different interpretation of
1.2 of song in mathematics "play" the
1.3 on the math "play" the
1.4 and is "play" review the meaning of
1.5 "play" concept and evolution of
1.6 from the "play" the evolution of the concept of the East Asian algebra calculation way development and significance of
second chapter numerical solution of algebraic equation: open organization
2.1 ancient Chinese square root operation and increase by evolution of
2.2 Guan Xiaohe square root operation and is home to open art of
2.3 day equation theory achievement "
2.4 Kurujima Yoshita iterative method of
2.5 Kurujima Yoshita holds the French
this chapter summary of
third chapter solution of nonlinear equations, geometric algebra traditional kaifukudai
3.1 China with the elimination of
3.2" Chinese enlightenment "in communications and Tianyuan operation by the capacity of
3.3 Guan Xiaohe kaifukudai and mathematics mechanization characteristics of
3.4 and an improved
Home expansion method of determinant 3.5 Wu's method and geometric study of

summary of this chapter fourth chapter polynomial interpolation method: chaos zhaocha method
4.1 function interpolation principle of
4.2 ancient Chinese interpolation
4.3 Guan Xiaohe tired cut zhaocha method
4.4 Guan Xiaohe zhaocha method
4.5 "into by" equation in bidding difference method
4.6 Guan Xiaohe chaos Zhao thought source of
difference 4.7 and various applications of
move method this chapter summary of
fifth chapter series summation algorithm: stack accumulation of
5.1 ancient Chinese duo product of
5.2 Guan Xiaohe stack accumulation method
5.3, other and home stack accumulation of

summary of this chapter sixth chapter congruence group and indefinite equation solution: cut and remaining tube with a
6.1 Chinese Remainder Theorem and Dayan zongshushu
6.2 and for a period of between
6.3 Guan Xiaohe's all about art, one postoperative
and shear tube 6.4 Qing Dynasty mathematician uncertainty analysis of
seventh chapter Diophantine approximation algorithm: rational zero was
7.1 real approximation method
7.2 ancient Chinese through the rate of operation and adjustment method
7.3 filial piety and the Zero about operation and interpolation method
7.4 Jianbu wise zero about operation and continued fraction expansion method
7.5 Takebe Hhiro tired about operation and weighs about
7.6 Kurujima Yoshita square zero about operation and periodic continued fraction expansion of
7.7 and Diophantine approximation algorithm is the origin of
eighth chapter Extreme algorithm: extreme concept germination
pole number
8.1 Takebe Hhiro very numerology and long island pole number 15 asked
8.2 traditional Chinese calendar in the summary of this chapter ninth chapter numerical acceleration
approximation algorithm: tired times increase about operation and Romberg algorithm of
9.1 on the Richardson extrapolation and Romberg algorithm
9.2 Takebe Hhiro tired times increase about operation and Romberg algorithm of
9.3 Guan Xiaohe again by about
9.4 Liu Hui's "Twelve Gu power-law message of
tenth chapter geometric quadrature and infinite series expansion method: circle theory circle theory zhuishu
10.1 in ancient Chinese mathematics.
10.2 early Edo round
10.3 Guan Xiaohe circle theory research of
10.4 Takebe Hhiro circle theory zhuishu
10.5 house flow round of
10.6 Kurujima Yoshita and Matsunaga Ryo. Back arc of circle of
10.7 Ajima Naodo and two round physical zhuishu
10.8 and Tian Ning circle theory open operation and numerical integral table
the summary of this chapter
Chapter excerpt

The copyright page: illustration: in addition to 5 of the two equations can be used in section method for direct field play and won the Tianyuan type, the method section equation were without Liu Yi and Li Ye are playing period. In fact, Zhu Shijie here in Tianyuan were playing, playing process using volume premiere algebraic relations and polynomial formula chart reflects. This suggests that the transcendence of Zhu Shijie Li Ye and get rid of the geometric intuition, the segment is more abstract and formal, algebraic calculus on the general equation of higher degree. In addition to the "four Yuan Yu Jian", "Chinese enlightenment" (1299) is also used in the forward section, and also has a section of text of the play. The volume under the "open release lock" eighth under the title Zhu Shijie note to self: the ancient law to play, and step, eight thousand four hundred and sixty-four step, four, but direct product, is also a power. Column product, four, eight thousand two hundred and eight, the reduction of more than two hundred and fifty-six, more power, for the real, in a low, square opening, more sixteen steps, and, half, long, long a reduction, that is also. Today to Tianyuan play, open source, life and times. Fake a count from Tai Chi, the best for the square, low-cost, Yu from the positive and the negative, but the virtual product modeling, destructive constructive, and the real product. To reason on by asking, preparation made fine grass, drawing its aspect, the positive and negative, so that scholars to be too bright. Zhu said "by ancient act" and "ancient law", when referring to "section", said "today to Tianyuan play", when referring to the Tianyuan operation. So, Zhu Shijie notes that section method (the method) and Tianyuan were all speech segment method. Here, in his "Yigu Yanduan" in practice and Li Ye, the Tianyuan operation was compared with section. And Takebe Hhiro of the Tianyuan operation according to the order, in the "zhuishu Suan Jing" (1722) by direct Tian of Tianyuan operation application, also pointed out: as the ancient law, will be surrounded by four direct product, the central content of Changping difference power made long and power of square first for long flat and. To this question, it is also, if the total so to the problem is less than existing heart observation, not into the cable number operation. Element method today, its physical and although you the hermit, but speed method for God, but not the straight, pure for multiplication, addition and subtraction of the theoretical exploration, exploration and its degree also. Notable is, what Zhu Shijie called the "false a count in Taiji, the best for the square, low-cost, Yu from positive and negative", clear, current goal is to obtain the "party, low-cost, Yu from the positive and the negative" (equation), the "segments" meaning is no longer the ichnography geometry of quantifiers, as "open release lock" Fifteenth ask the said: "the one hundred and twenty-two Duan Ping, to take, for the one hundred and twenty-two volume", here the "section" is not only one segment of the quantifier, and 2D graphics quantifiers, such as "three party TSMC, four sections of cone product, four cubic volume three-dimensional graphics classifiers also appear and the topic. "Section" meaning is no longer limited to planar graph, geometric significance in desalination, algebraic significance in enhancing the gradual abstraction for multiple, various mathematical quantity (coefficient), but also for the polynomial coefficients. To sum up, Zhu Shijie's "speech" is not limited to the section method, but the widespread use of operation in Tianyuan and four elements, is the algebraic calculations with polynomial calculus as a center, equations for target.
Editor recommends

"And in the source: and numerical algorithm and its numerical origin" is a research and development and the origin is considered a masterpiece. Professor Xu Zelin is one of the few and an expert on the history of.
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