The Sino-foreign Analysis Of Symbolic Processes In The Solution Of Equation

The equation theories are the important parts of elementary algebra,and the key content of the mathematics education of middle school,which play a significant role in the Chinese traditional mathematics history and Chinese and foreign exchange history.For solving the ancient Chinese equations,some mathematical historian have carefully collated and studied the Chinese classical ancient books,published lots of mathematical history and research papers.However,there are a few literatures,concerning.The appearance of mathematical symbols is a sign of the birth and development of mathematics.The use of standardized unified mathematical symbols makes the exchange of different countries,regions and ethnic very convenient.Symbols are the basis of the development of Algebra,which have a variety of classification.The German Mathematical historian,Selman gave three phases for the introduction and development of Algebra symbols:rhetorical algebras,syncopated algebras(or semi-group algebra),symbolic algebras.For these phases,the Chinese and foreign equations solvers have their own characteristics.However,the corresponding algebraic symbol development is not balanced,Each have focus on.In the history of the development of mathematics,Both Chinese and foreign,rhetorical algebras have gone through a long period of time.The syncopated algebra experiences the shortest time,To the ancient Greek Diophantu’s symbol and the Chinese Song and Yuan Dynasties semi-symbol algebra as the representative.The symbolic algebra of Veda and Descartes in France,marks the highest stage of the development of algebraic symbols.Medieval China,made the greatest contribution to the algebraic phase;Modern Europe,made the greatest contribution to the establishment of symbolic algebra.In this thesis,the authors focus on the time from the 3rd century to the 17 th century,using the method of the classification of the Salmon in algebraic notation and taking the mian line for the study of the evolution of the symbols in the equation solving,the mainly work on the following analsis and research:First,the definition of “equation”and the classification of “algebraic notation”.The authors explain the evolution of “equation ”and distinguish the definition as it has been developing.By the thchnique of the classification of the Salmon in algebraic notations,they analyse the characteristics of the rhetorical algebras,syncopated algebras(or semi-group algebra),symbolic algebras.Second,the contribution of China to word algebra.there are two phases that mathematicians reviewed the word rhetorical algebras,syncopated algebras respectively.Ancient chinese mathematics had reached to its peak around the time of 3rd century.Through the researches of Hui Liu、Shuang Zhao in the Three Kingdoms period and Xian Jia、Yi Liu、Jiuzhao Qin in Song and Yuan Dynasties,the method of euation solving can work out the high-order equation.“Tianyuan operation”brought by Zhi Li and “Siyuan operation”brought by Shijie Zhu had made a great contribution to the development of qeuation theory and also reached to the climax of ancient chinese mathematics.Hui Liu、Shuang Zhao、Xian Jia、Yi Liu had made use of rhetorical algebrasa”when they worked out the equations.Also,there was a germination of “syncopated algebras”in the way of Jiuzhao Qin’s equation solving.“Tianyuan operation”brought by Zhi Li would be the representative of a complete system of “syncopated algebras”.From the period of Hui Liu’s to Zhi Li’s,the development of quation solving was actually the evolutio of rhetorical algebrasa” to “semi symbloic algebra” in China,which had went through for more than one thousand years,“syncopated algebras” in China had reached its peak and “Tianyuan operation”also had a directly effect on the “Dianchuan operation”in Japan.Third,the contribution of Europe to symbolic algebra.Therer were also two phases for mathematicians to reorganise the work of Diophantine in the “reduced word algebra”period and the work of Weida and Descartes in the “symbolic algebra”period,respectively.Different from the traditional pursuit of equation’s numerical solution in China,foreigners are aim at the radical solution of equation.,Based on the cluses of the solution of quadratic equation with one variable、cubic equation with one variable and quartic equation in this paper,the authors analyse the evolution of `the notations and the development of the solutions of equations and mainly focus on Diophantine reduced word algebra in the 3rd century.However,the ideology of reduced notation did not come along with the time period.India mathematician Brahmagupta in the 7th century and Arabia mathematician Hua La Semi in the 9th century all took the method of “word algebra”when it comes to the equation solving.In the 16 th century,french mathematicians had established a complete algebraic symbolic theory.Weber’s work marked the establishment of symbolic algebr and the work of Descartes,a French mathematician,represented the maturity of symbolic algebra.The characteristics and defects of semi-symbolic algebra "Tian yuan operation" in chinese and foreign comparison.After the song and yuan dynasties,Chinese traditional mathematics failed to complete the transition from semi-algebra to symbol algebra.After the 17 th century,The introduction of European symbolic algebra making modern algebra flourish.From the above Chinese and foreign equations evolved,from following the two angles,Comparaing and analysis the Chinese and foreign。First,comparing the Chinese and foreign’semi-symbolic algebra,a comparative study of the of "Tian yuan operation" and Diophantine’s Semi-symbolic,The second is to compare the semi-algebraic period with the establishment of foreign symbolic algebra,A comparative study of “Tianyuan operation"and Viète’s symbolic algebra.From the Comparative Study,analysis the characteristics of Chinese symbols and shortcomings.Finally,the author thought introduce the equation symbolic history into the middle school equation teaching,inspires the students to understand the equation from the mathematic symbol,promote students’ understanding of mathematics.