Well-planned, organized, and infinitely small

History has proved that in the late autumn of 1960, German mathematician. for the first time in human history, Robinson joined infinitesimal with a hyperreal number, making it a rigorous mathematical concept and getting rid of embarrassment.

An infinitely small is not a separate mathematical entity (or concept). It is integrated into the entire calculus system. The reform of calculus must be thorough, and improvement will not work. In recent years, the foreign media has had a lot of research materials in this area, and the content is quite rich, relatively speaking, it seems relatively poor. Especially for beginners of mathematics, it is difficult for them to find formal teaching materials and popular books on the analysis of Infinitely small. This situation needs to change.

Frankly speaking, Chinese people generally have low mathematical literacy, and calculus are not widely used as the basic knowledge of modern science and technology. When it comes to calculus, someone has a headache. This phenomenon is closely related to the current practice of mathematics education in Chinese universities. We certainly know that changing the current situation of mathematics education in colleges and universities is not a simple task.

The 6.18 infinitely small Internet release plan is in progress. The team is responsible for the specific implementation of the plan. At present, text transcription has become a "bottleneck", limiting the progress of other related work. Fortunately, a Shanghai entrepreneur expressed his willingness to support the acceleration of the plan. Recently, the power of text transcription is expected to be significantly enhanced.

Why speed up the transcription of J. Keisler's books (electronic textbooks )? Because this book is the "Source" of everything related to the infinitely small calculus, both at home and abroad. Without this teaching material, there is no way to talk about calculus reform. This mathematics teaching material is extremely important to further improve the mathematical literacy of the majority of Chinese students. It can expand students' scientific horizons, understand the history of mathematics development in the world, and help establish scientific historical materialism.

In fact, calculus is a very interesting discipline, not a rigid dogma. The traditional (ε, Delta) limit-defined quantifiers are reversed. The game should end and exit the historical stage (leaving the classroom ). For beginners of mathematics, the current (ε, Delta) limit ∀ ∃ ∀ definition mode is obviously not suitable, and it is difficult for students to grasp its essence.

In fact, the original intention of the 6.18 infinitely small release Internet plan is to change the above situation and protect the majority of students from the spirit of the limit definition of the traditional (ε, Delta) (for example: it also reduces the teaching burden of mathematics teachers. The introduction of the concept of Infinitely small improves the intuition and interest of calculus. We believe that the phenomenon that raises calculus will gradually disappear and become a historical relic.