During the period of suspension of classes for review, Zhao Xiancai successfully advanced the task of "Ten Books" to 7/10 and began to read "Lecture Notes on Mathematical Models".

The "Lecture Notes on Mathematical Models" that Zhao Xiancai read was written by Lei Gongyan and published by Peking University Press. It was supplemented and revised by Professor Lei based on the lecture notes used in his "Mathematical Model" course.

The whole book is divided into fifteen chapters.

Finally, at the end of the exam week and when he was about to leave school and go home, Zhao Xiancai specially borrowed a book "Real Variable Functions" so that after studying "Mathematical Models" at home, he could continue to study "Real Variable Function Theory".

It was okay when he first returned home, because New Year's Eve was not until February 18th, so from January 19th when he returned home to February 18th, Zhao Xiancai's life was still very stable. Apart from studying, he did nothing every day.

Some housework and nothing else to do.

After New Year's Eve, the Spring Festival came, and every household came and went to pay New Year's greetings. Except for the first day of the lunar month, from the second to the seventh day of the lunar month, Zhao Xiancai only had lunch and dinner at his own home these days.

After the seventh day of the Lunar New Year, the activities of walking around to pay New Year greetings became much less frequent. Except for the occasional meal out, Zhao Xiancai went out less often.

However, because the holiday started early, Zhao Xiancai went back to school on March 1, the eleventh day of the first lunar month, and did not even celebrate the Lantern Festival at home.

During this period of time at home, Zhao Xiancai also gained something. He not only finished studying "Mathematical Models", but also "Theory of Real Variable Functions". When he returned to school, he had "ten books"

There are only 1/10 left in the mission.

Now, I only have to study the textbook "Preliminary Differential Geometry" that will be used in the "Differential Geometry" course.

On the first day of registration, after returning "Lecture Notes on Mathematical Models" and "Real Variable Functions", Zhao Xiancai borrowed "Preliminary Differential Geometry".

However, the semester started on March 2nd, and on the 7th and 8th, Zhao Xiancai took all the exams for which he wanted to apply for exemptions.

And Zhao Xiancai naturally passed these exemption examinations without any surprise.

Now he has become a member of the top-notch program, and his thesis is about to begin. In the end, the thesis direction Zhao Xiancai chose was differential equations.

Zhao Xiancai has just begun to learn the content of the junior professional courses, and he has not learned much. It is not easy to write an article on his own that can be published in a decent mathematics journal. It is almost impossible.

Not too possible.

Therefore, Zhao Xiancai finally sought help from the system.

After Zhao Xiancai described some issues, the system gave him several articles to choose from.

Finally, Zhao Xiancai chose a paper titled "Solubility of Singular Integral Differential Equations in the Riemann-Hilbert Problem".

This paper cost Zhao Xiancai 1,564 points, which were the points he determined after bargaining with the system, otherwise it would have cost him even more points.

The bargaining between Zhao Xiancai and the system was not the kind of bargaining that ordinary people would do when buying things. Instead, Zhao Xiancai only wanted one paper and did not need supporting explanations, doubt-solving and other services, so the price was lowered.

After Zhao Xiancai read this paper, he found that there were indeed some places in the paper that touched on his blind spots in knowledge.

However, this was a situation that Zhao Xiancai had long expected to encounter. He had no choice but to save points. He could only find relevant books and materials to study one by one based on the knowledge points in the paper that he did not understand.

No matter what, he must first understand the parts of this paper that he does not understand, otherwise he will not understand the paper he published. If this is known to others, others will definitely know that this paper was not written by him.

However, Zhao Xiancai estimates that if he understands all the knowledge points involved in this paper, and he has studied this problem for a period of time, and only looks for system solutions when he encounters problems, then the points he spent must not be more than one thousand.

More than five hundred.

After all, in Zhao Xiancai's view, this system is more about letting him learn and study on his own, rather than letting him sit there and casually obtain research results and scientific technologies that have not yet been developed from the system.

But no matter how Zhao Xiancai estimated it, it was just his guess. He could only verify it after he had completed his studies and started to actually do research.

After that, the time Zhao Xiancai spent studying "Preliminary Differential Geometry" was greatly reduced. He spent most of his time studying "Solvability of Singular Integral Differential Equations in the Riemann-Hilbert Problem"

I have learned something about sex that I don’t understand.

After half a month like this, the time came to the end of March. Except for a few points that he still didn't understand, Zhao Xiancai finally solved most of his knowledge blind spots in this paper.

"There are still a few questions that I need to consult with the professors at the school."

When he came out of the library in the evening, Zhao Xiancai thought to himself and began to check the information of professors on the official website of the School of Mathematics at Beijing University.

After that, he specifically consulted the dean.

Finally, Zhao Xiancai found Professor Liu Shan, who had taught undergraduate courses such as "Ordinary Differential Equations", "Selected Lectures on Dynamical Systems", "Selected Lectures on Geometry Theory of Differential Equations" in the School of Mathematics at Peking University, and "Advanced Mathematics (b)" in the School of Non-Mathematics.

.

The introduction to Professor Liu on the official website of Peking University states that his main research directions are "ordinary differential equations" and "Kam theory and its application in nonlinear vibrations."

That night, Zhao Xiancai found the professor's class schedule. He planned to go to the professor when he was in class tomorrow, just in time to listen to his lectures and use his spare time to ask him some questions of his own.

In this way, the next day soon came.

In the third and fourth classes this morning, Professor Liu was teaching "Ordinary Differential Equations" in a classroom to sophomores who were in the next semester.

Zhao Xiancai walked into the classroom before class and sat in an inconspicuous place in the back row. In addition, the ordinary differential equations class was a big class. There were several classes of students in one classroom, so there was no one there.

It was obvious that Zhao Xiancai was a newbie, but it was also not obvious that he was not a sophomore at all.

"...This Liouville formula is actually the Wronski determinant composed of any n solutions of the seventh-order equation, one of its forms... This is the content of this section. Okay, you can take a break after class. We will go to the next section later.

Let’s talk about it later in class.”

After Professor Liu finished speaking, he was about to go back to the lounge to take a rest. At this time, Zhao Xiancai ran out with a notebook and a pen, following Professor Liu.

"Hello, Teacher Liu, I have some questions I would like to ask you."

After catching up with Professor Liu who had already walked out of the classroom, Zhao Xiancai said to him.

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