Pocket ebook: Moscow and Beijing

What is the relationship between a pocket ebook and "Moscow and Beijing? Is it crazy in your mind? None. Why?

First, let's clarify some basic concepts: Russia's current primary and secondary school system is 11 years old, so their 10-11 grades are equivalent to China's high school. In grade 10-11, Russian students have two required Mathematics Courses: ry and preliminary analysis of algebra and mathematics. That is to say, Russia's high school students require calculus (this step has been popularized since 1975 ). It can be seen that Moscow and Beijing have opened a distance. (Note: we do not need to talk about the situation in China .)

As we all know, the importance of middle school textbooks is related to the growth of a large number of social forces. The textbook preliminary analysis of algebra and mathematics used by Russian middle school is edited by Academician A. kolmogrov of the former Soviet Union, and has been published more than 13 times. It can be seen that the authority and influence of this teaching material have influenced the formation of world outlook in the minds of tens of millions of Russian students. For children in Moscow and Beijing (high school students), the difference is obvious because they do not understand what calculus is (except for individuals ).

What is the level of Russian middle school Calculus Teaching materials? Related materials show that the textbook uses the concept of function increment and intuitively gives a descriptive definition of the concept of derivative. The specific definition is as follows: "When incremental delta x tends to be zero, the derivative of function f at point A is the Increment Ratio of the function to the independent variable ." However, it is unclear what the meaning of "incremental delta x tends to be zero" (the actual situation is that the author intentionally avoids it ).

According to the relevant information, the function knowledge in China's high school is to first learn the set knowledge, use the set, correspondence, and ing viewpoint to elaborate the function concept, and then focus on all kinds of elementary functions. In this context, how should we catch up with Russia's middle-school calculus? What should we do?

According to the "Modern Mathematics Curriculum Theory" prepared by Mr. Ding Ersheng (Jiangsu Education Press, published in 1997): "Chinese Middle School Mathematics Textbooks use a set of languages as the basis of research functions, in Russia, the textbook "completely gave up the set theory point of view, and the terminologies related to the" set "will no longer appear ". This is the gap between the two, and this is our opportunity. In terms of set theory, we have some advantages (or advantages ). What should we do? There are two ways to choose from: one is the old path of traditional calculus, and the other is the new path of Infinitely small calculus.

The "pocket ebook" published yesterday: what is infinite closeness? "In this article, we propose an idea: In the middle school stage, we should introduce the concept of an infinitely small super real number as early as possible. With the help of the power of the" St "operation, we should open up complicated extreme theories and reconstruct elementary calculus, beijing surpassed Moscow.

Note: I especially like "old Soviet nostalgia Songs", for example, "Moscow-Beijing" (Baidu music), sung by Russian female choir. While listening to this song, I waved my hands up and down to cheer for them. I hope that our country's "little hair" (or "Little Girl") will be able to compare with Russia's "little hair" in the near future, to see who has a higher level of calculus. In general, it is still the following sentence: the infinite small method PK (ε, Delta) dogma, to see who will laugh at the end ?!