September 1 is a big day in China and in the United States, and that is the first day of school. The difference is that there are not many procedures on the American side, and basically the admission procedures have been completed at the time of the report, so the start of school means that the official course has begun.

Mathematics, which is the core course of Princeton, is naturally the top priority, so from the first day, the formal curriculum of the mathematics department has begun.

The sophomore mathematics course focuses on the mathematical analysis course, that is, the differential and partial differential courses, which are the core computational methods and the most important research tools for modern mathematical problems.

Princeton's mathematical analysis program is world-renowned, and along with differential geometry at Caltech's and topology at Harvard University, it is one of the top math programs in the United States.

Mathematical analysis is very important to Junxin, even with his current mathematical attainments, he is very concerned about this course. You know, if you look at mathematics from the Hilbert problem, mathematics is divided into four parts, the first part is the foundation of mathematics, the second part is algebra, the third part is geometry, and the fourth part is mathematical analysis.

In mathematical analysis, the most important method of calculation and research, which runs through almost all branches of higher mathematics, is calculus. How important calculus is is to show how general.

From other perspectives, calculus is also the most important means and tool for the study of chemistry and physics. Of course, in the process of studying physics and chemistry, although the more important is partial differentiation, but calculus is the basis of all mathematical analysis, if you do not understand calculus, or more harshly, if you do not have a solid foundation in calculus, then it is impossible to achieve achievements in mathematics and chemistry.

Therefore, for the discipline of mathematical analysis, Junxin really attaches great importance to it and cannot pay attention to it anymore.

Princeton's mathematics professors never read textbooks and textbooks to teach, which is most similar to high school mathematics teachers in China, and they never read textbooks and lecture notes according to the textbooks, and the content of their lectures is always based on the textbook and diverged as the real content of the lecture.

It's the same with professors at Princeton, who never look at textbooks when they give lectures, because they think the content of the textbooks is too superficial. In his previous life, Professor William Timothy Gowers, a professor of mathematics at Princeton University, often said that the content in the textbook was so simple that the children at Harvard understood it at a glance and there was nothing to say.

Although the current Professor Gowers is about the same age as Junxin, he looks like he is about twenty years old, and he has not yet graduated from his supervisor, not even from his university, let alone won the Fields Medal, and then came to Princeton University as a professor in the Department of Mathematics.

However, Professor Gowers's statement does represent that the teaching methods of the mathematics department at Princeton University are indeed extensive, although not as exaggerated as the textbooks that Grothendieck wrote while studying at the Institut des Hautes Etudes in Paris, but it is indeed very different.

There are not many people in the mathematics department, all the sophomores plus Junxin about 100 people, a slightly larger classroom can fit in, but this is also a subject with more people in American universities.

Calculus was taught by a well-known and gifted mathematician, Charles Feverman, who completed calculus at the age of 12, graduated from the University of Maryland at the age of 17, received a Ph.D. from Princeton at the age of 20, was promoted to full professor at the University of Chicago at the age of 22, and won the Fields Medal at the age of 29 (1978). He currently teaches in the Department of Mathematics at Princeton University and also works at the Institute for Advanced Study in Princeton. He had an outstanding record of work on singular integral operators and partial differential equations, and was awarded the Fields Medal at the age of 29. Among the winners of the Fields Medal, the age is second only to Professor Jean-Pierre Serre. Professor Searle was 27 years old when he won the Fields Medal.

There is a clear difference between the master's lectures and those of others, which in Junxin's view is the difference between an artist and a craftsman, and the difference between the top artists and ordinary craftsmen. When an ordinary professor or lecturer talks about a course, he usually follows the textbook and does not have his own theory. However, when the top masters give lectures, they usually have a flash of inspiration and can inadvertently convey some scientific cutting-edge research methods and research results. They will even put forward their own opinions and questions on certain issues.

Junxin is crazy to absorb some of the thinking methods and research methods of mathematicians who are at the peak of research in this era, and he is a little dismissive of the results of the problems. In his opinion, the most important thing in mathematics is not the results, but the idea of studying the problem. Because the results are there, if you don't study them, they are still there, but not everyone can listen to the master's research ideas, and these ideas will pass and never appear again. In comparison, it is especially precious.

In fact, Charles Feverman's explanation is not necessarily clever for ordinary students, and it may not even be better than other ordinary lecturers in their opinion, and even adds some reasoning and calculation formulas that they can't understand and understand, making it more troublesome for them to learn.

However, the students of Princeton University are not the kind of mediocre students after all, they naturally understand the research results of Professor Charles Feverman, and naturally pay more attention to the research of the formulas he added to the reasoning, and even if there is something they don't understand, they will write it down first, and then find a time to ask.

“…… That's all for his answer to this question, and in about five minutes, I won't move on to the next question, and you can ask questions freely. ”

"Brush, brush!" In less than a second, everyone's hands were raised in the air, except for Junxin.

Of course, although Junxin didn't raise his hand to ask questions, no one looked at him, because he habitually sat in the corner and basically wouldn't be seen.

Of course, this is not to say that there are no problems with Junxin, but what Junxin wants to ask Professor Charles Feverman in private is to ask these questions in private, because these questions cannot be asked clearly in a few words. So Junxin is just waiting for the end of class.