Mathematical Abstraction Degree Theory And Its Applications

The methods of mathematical abstraction degree analysis were first introduced by Professor L. C. Hsu et al. in the eighties of the 20th century, and have further developed later. The methods quantitatively analyze the mathematical abstraction and can help revealing the inner construction of mathematical theory with rich connotation by means of the theory of partial order set and graph theory, and so on.In chapter 1 we give a survey of the previous works relating to the thesis and make them systematic. Some minor faults in the reference are pointed out and corrected.Professor L. C. Hsu et al. put forward some open problems on the study of mathematical abstraction degree analysis which contained the suggestions that a set of formalized theory should be established on mathematical abstraction degree by graph theory and it should be applied to analyze the abstraction within some mathematical structure. We are in chapter 2 and chapter 3 working along the line on the basis of the results obtained. The concepts of relative relation degree and semi-kernel are introduced to the theory of mathematical abstraction degree analysis and algebraical algorithms are given by means of Boolean matrix. Meanwhile the final parts in each chapter are intended to apply our results in the absolute geometry system.