The Analysis Of The Origin And Culture Of The Limit Concept

Limit is an important concept in mathematics that transforms from constants to variable, from finite to the infinite, and from approximate to precise, which occupies an important place in the history of mathematics development. Limit is the fundamental concept of calculus in university mathematics curriculum. With the new curriculum reform, the derivative (a special kind of limit) has entered the high school mathematics teaching materials. Limit, as an important mathematical thought method in university and high school mathematics, is also one of the most essential ways of thinking in mathematics learning. Therefore, the author attempts to explore systematically the development process of the concept of limit to give teachers and students a thorough knowledge of the history and current situation of limit. However, mathematics historians have already done the work of studying from the perspective of the history of mathematics, so it is of little value and dull. And mathematical culture is a new perspective to analyze the concept of limit from the origin, development, the improvement of the mathematics and its applications to the person’s ideas, thoughts, and different ways of thinking. This article tries to discuss from the angle of mathematical culture development of the concept of limit, observe the set limit of the high school mathematics curriculum content, and analyze the implication of culture. The author gives the teaching advice in order to bring benefit to high school mathematics teachers’ teaching and students’learning.This article mainly uses literature research and the method of historical retrospection. It first summarizes the meaning and characteristics of culture and mathematics culture, analyzes the research perspective of the concept of limit, which is the theoretical foundation to study the concept of limit. Then it discusses the process of development of the limit concept in Chinese and western mathematics, which contains the limits of culture, and the most important thing is to show its influence on the change of human thoughts and ideas and the enterprising spirit. In the understanding of the limit concept, Chinese mathematics mainly traces the ancient cultural traditions, as well as the influence on other mathematical problem solutions. The limit development of Western mathematics is opposed to it. In the West the concept of limit gets the final close and formal development, so the author will explore from the perspective of symbolic level, and divide limit development into four stages in western mathematics, that is the emerging stage, the mysterious stage, the unified stage and extension stage. Finally, this thesis discusses the culture of limits in educational form from the perspective of the standard of mathematics curriculum, teaching material and teaching.Through the analysis process of the culture of limit concept, it gets to the main conclusions and suggestions:1 In the high school mathematics the content basically reflects the ultimate cultural development for arrangement.2 While senior high school students feel hard to understand the definition of formal limits, descriptive definition of limit should be given in the textbooks as it is the basic content of "derivative and its application".3 Mathematics curriculum should be more active and conscious penetration of the essence of limit—endless thoughts. Infinite ideas can be appropriately penetrated before the concept of limit, such as the experience of the infinitude of the number of natural numbers and the understanding of the limitlessness of decimal fraction of irrational numbers.