A Research Of The History Of The Vector Theory

As an indispensable tool in modern physics, the vector theory has many applications in various mathematics branches as well as in other scientific fields. The purpose of this dissertation is to analyze the development of the vector theory according to three clues based on analysis of original materials and investigation of previous researches in this field. The main results gained in this dissertation are as follows:1. The vector theory which originates from parallelogram rule of velocity and force is inspected in detail. Until the first half of the 19th century, the vector theory is merely associated with mechanical application, and the vector appears mainly in form of Cartesian coordinates and at the same time supplies mechanical application with a useful tool. Although the vector was used in mechanics at that time, its exact importance was not realized completely and had not been abstracted and studied in a higher lever.2. The vector theory related to situation geometry is elaborated. This theory stems from Leibniz's concept of situation geometry. The most important work is Grassmann's Ausdehnungslehre published in 1880's. However, Grassmann's system is so abstract and far away from the tradition as not to be understood. Its influence on the foundation of modern vector analysis is not as it should have impacted although it does affect on the axiomatization of vector theory. Mobius' barycentric calculus and Bellavitis' calculus of equipollences related to geometrical tradition are introduced briefly as well.3. The third clue of the development of vector theory is elaborated in view of the geometrical representation of complex numbers, which modern vector theory develops on. We discuss and compare the work of Hamilton, Tait, Maxwell, Gibbs and Heaviside, and sort out the clue : the geometrical representation of complex numbers — Hamilton's discovery of quaternion — Tait's development to quaternion — Maxwell's critical acceptance of quaternion — Gibbs-Heaviside's creation of modern vector theory.4. The latter development of vector theory is discussed. After created by Gibbs and Heaviside, modern vector theory is applied to branches of physics and mathematics, especially electromagnetics. The process of axiomatization of vector theory is also studied. The modern concept of vector is defined as an element of a vector space, and its connotation is much richer and profounder than when it is originally created.5. The spread of vector theory in China is inspected. On basis of firsthand materials of the Republic of China, the spread of vector theory in teaching and study in China are discussed in detail. In the 19th century, Chinese scholars begin realizing the directed quantities accompanied with Western learning coming to China. At the beginning of the 20th century, Chinese scholars study and translate a great deal of works, which plays important role on the spread and introduction of vector theory inChina. The development of higher education in China after the Revolution of 1911 leads to the golden period of vector theory in the 1930's and 1940's. After liberation, vector theory becomes one part of content of mathematics and physics course. At the end of the 20th century, vector theory is set in senior high school courses.