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为了使数学更好地为我国的社会主义与共产主义建设服务,目前的迫切問題是要求数学教材联系实际和現代化。数学中的現代內容,一般地說,与現代的社会实践联系較紧,因而具有較广泛的发展前途。只有抓住数学中新生的进步的东西,才能迅速攀登世界数学的高峯。人們在实际中,經常碰到的現象大致可分为两类:必然現象与偶然現象,亦卽在一定条件下,必然出現(或不出現)的現象与可能出现也可能不出現的現象。如果說,微分方程是研究必然現象的有力工具,那么,研究偶然現象的有力武器便是概率論与数理統計(以下簡称概率統計)。正是由于在实际中存在大量的偶然現象,所以必須在中学讲授它,使它为广大羣众所掌握,为我国的建设服务。也只有这样,才能使这門学科在我国迅速发展。这里一个基本问题是可能性問題,就是說,中学同学是否可能学好这門課程。現在我們从下列三方面,較仔細地考察一下。
In order to make mathematics better serve our country’s socialist and communist construction, the urgent problem at present is to require mathematics textbooks to link reality with modernization. The modern content of mathematics, generally speaking, has a tighter connection with modern social practice and therefore has a broader development prospect. Only by grasping the new things in mathematics can we quickly climb the peak of mathematics in the world. In practice, people often encounter phenomena that can be roughly divided into two categories: inevitable phenomena and accidental phenomena, and also under certain conditions, phenomena that must (or do not occur) occur and may or may not occur. If we say that differential equations are powerful tools for studying inevitable phenomena, then the powerful weapons for studying accidental phenomena are probability theory and mathematical statistics (hereinafter referred to as probability statistics). It is precisely because there are a large number of accidental phenomena in practice, so it must be taught in secondary schools so that it can be mastered by the masses and serve the construction of our country. Only in this way can this discipline develop rapidly in our country. One of the basic issues here is the question of possibility, that is, whether the secondary school classmates may learn this course. Now we will examine the following three aspects in more detail.