Mathematical Manuscripts: Evolution of Western Mathematical Knowledge

The evolution of mathematics can be regarded as the continuous development of abstraction and the extension of subject matter. Eastern and western cultures have also adopted different angles. European civilization developed geometry, and China developed arithmetic. The first abstract concept is probably number (China's arithmetic), and its cognition that two apples and two oranges have something in common is a great breakthrough in human thought. Besides knowing how to calculate the number of real objects, prehistoric humans also knew how to calculate the number of abstract concepts, such as time. Day, season and year. Arithmetic (addition, subtraction, multiplication and division) will naturally occur.

In addition, you need writing or other systems that can record numbers, such as Mu Fu or chips used by the Incas. There are many different counting systems in history.

In ancient times, the main principles in mathematics were the study of astronomy, the rational distribution of land and grain, taxation and trade. Mathematics is formed to understand the relationship between numbers, measure land and predict astronomical events. These needs can be simply summarized as the study of quantity, structure, space and time in mathematics.

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Western Europe experienced the Renaissance from ancient Greece to16th century, and elementary mathematics such as elementary algebra and trigonometry were basically complete. But the concept of limit has not yet appeared.

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/kloc-the emergence of the concept of European variables in the 0/7th century made people begin to study the relationship between variation and the mutual transformation between graphs. In the process of establishing classical mechanics, the method of combining calculus with geometric accuracy was invented. With the further development of natural science and technology, the fields of set theory, mathematical logic and so on, which are produced for studying the basis of mathematics, have also begun to develop slowly.

Mathematics manuscript content: high school mathematics learning skills 1. The thinking method of combining numbers and shapes.

The combination of number and shape is to fully investigate the internal relationship between the conditions and conclusions of mathematical problems, not only analyze its algebraic significance but also reveal its geometric significance, skillfully combine the quantitative relationship with the spatial form, and find and solve the problem. Make the problem difficult and simple, so as to be solved. For example, in some algebraic expressions whose numerator and denominator are trigonometric functions or linear functions, it is required to convert the range of values into the linear distance between two points to solve them; Or in some algebraic problems with radical signs, the structure has no obvious geometric significance, and the distance formula between two points may not be used at this time. If we can use method of substitution and the thinking method of combining numbers and shapes, the problem can be solved quickly. Therefore, the combination of mathematics and thinking method is a very important method to solve mathematical problems.

2. Discuss ways of thinking by category

The thinking method of classified discussion means that when solving some mathematical problems, according to certain principles or standards, on the basis of comparison, the mathematical objects are divided into several parts that are both related and different, and then discussed one by one, and then the conclusions of these categories are summarized to get the answers to the questions. For example, solving inequality ax >；; 2. We divide it into & gt0, a=0 and a.

3. Thought method of function and equation

The idea of functional equation refers to the idea of constructing appropriate functions and equations when solving some mathematical problems, and transforming the problems into the idea of studying the properties of auxiliary functions and auxiliary equations. For example, when solving the distribution problem of equation roots, of course, it can be solved step by step, but it is very complicated. If we solve it from the viewpoint of function, the process of reasoning and proving inequality will be much simpler and clearer. Students who don't believe can work out this problem below:

4. Equivalent transformation of thinking methods

Equivalence transformation is an important thinking method to transform the problem of unknown solution into a problem that can be solved within the scope of existing knowledge. When students encounter problems that are difficult to make directly, they can deal with them by turning them into familiar problems, or turning more complicated problems into simpler ones, such as from transcendence to algebra, from unreasonable to rational, from fractions to algebraic expressions. For example, when it is difficult to directly construct an inequality with parameters as elements in the problem of exploring the range of parameters, we can often introduce a correlation coefficient A and transform the problem equivalently with the help of A.