Midday.

Chen Zhou and Yang Yiyi returned to Yanda and settled lunch in the cafeteria.

After that, I went back to the dormitory.

Chen Zhou glanced at the time, it was half past twelve.

Exams start at 2:30 p.m., but just like the team competition, the individual competition also requires half an hour in advance for each subject.

In such a short period of time, Chen Zhou didn't want to do anything else.

Simply lay down in bed and prepared to take a nap to recuperate for the afternoon and evening exams.

He didn't have to worry about Zhao Qiqi waking him up when they came back.

Because, he had already called the three of them, and all three of them did not submit their papers until 12 o'clock.

By the time they walked out of the math center, it was already 12:15.

They didn't plan to go back to school, so they found a nearby restaurant to solve the problem.

Until the alarm clock rang, Chen Zhou opened his eyes, turned over and got out of bed.

I looked at the time and slept for about half an hour.

Just right.

Half an hour of napping is enough, and sleeping more and less is not good.

went to wash his face, and Chen Zhou called Yang Yiyi.

The two met and went to the math center.

At half past two in the afternoon, the chousse continued.

The first course of the individual competition is analysis and partial differential equations.

Chen Zhou roughly skimmed through the entire test paper.

The first question focuses on questions about measurable functions.

What does a measurable function mean by definition?? t∈R, E[f>t] is the measurable set, then the function f is the measurable function.

Therefore, combined with the question information fn∈L?? (R) is the sequence of measurable functions, and fn→f are continuous everywhere.

Chen Zhou can basically determine the solution to this problem.

Reuse the assumptions given at the end, ║fn║L?? →║f║L??。

Chen Zhou quickly wrote out his answers on the test paper.

After I finished writing, I took a look at it.

After confirming that there were no detailed errors, Chen Zhou moved on to the next question.

The second problem is the problem of continuous functions and definite integrals.

It didn't take much effort, Chen Zhou got it done.

The difficulty of this question is about the same as that of the first question.

Then comes the third question.

Seeing this question, Chen Zhou raised his eyebrows.

It's kind of interesting.

The question information for this question is an inequality.

【|f(z)|≤|z|??|Im(z)|?? 】

What is then required is the maximum "z" value for the inequality to satisfy the condition.

Often, the less information there is about this kind of question, the easier it is to lose your head.

But Chen Zhou wouldn't, and after a little thought, he understood the meaning of this question.

Immediately, I began to write.

Swap out the thoughts in your head for the steps to disintegrate.

Write it out one formula at a time, step by step.

The fourth problem is the problem of pure functions.

When Chen Zhou first browsed, he felt that it was really a coincidence.

He has just completed a paper on a topic related to pure functions.

This brings us to the problem of pure functions.

Send sub-questions.

Question 5.

Questions about Hilbert space.

This is also an issue that Chen Zhou is interested in.

The main reason for interest is the Hilbert space.

Although this question is simple after all, it also provides Chen Zhou with some ideas.

For the next step, the direction of his research topic.

After this question was completed, Chen Zhou completed the task of this exam in order.

Back to the fifth question to the first question.

Chen Zhou checked again.

After all, what Yang Yiyi instructed them also applied to himself.

People tend to overlook obvious mistakes.

After carefully checking the steps and details of the five questions, Chen Zhou had to get up and hand in the papers.

To his surprise, Professor Shang, whom he met in the morning, was standing beside him again this time.

Seeing that he was about to hand in the paper, Professor Shang directly stretched out his hand.

Chen Zhou handed the test paper to Professor Shang and smiled at him.

After Chen Zhou walked out of Professor 1308, it didn't take long for him to see Yang Yiyi also come out.

Chen Zhou glanced at the time, and a smile appeared on the corner of his mouth: "Analysis and partial differential equations are worthy of what this girl is good at......"

and Yang Yiyi went to the Morningside Mathematics Center of the Chinese Academy of Sciences, and when the exam was over, Zhao Qiqi and the three came out.

Chen Zhou and the five of them found a restaurant together.

After dinner, because Yang Yiyi did not register for the probability and statistics exam, she went back to Yan University first.

The four of Chen Zhou were left, returning to the mathematics center and silently waiting for the entrance exam.

There is a tacit understanding, Zhao Qiqi and the three of them never mentioned the exam in front of Chen Zhou.

Even if they made all the test papers, they didn't say a word.

After all, the past is vivid......

Wait until half past six in the evening.

The second subject of the individual competition, Probability and Statistics, begins the exam.

How to say it, Chen Zhou felt that the test paper of this subject must not have been taken seriously.

Whether it is an individual competition or a team competition, the test paper of this subject is very simple.

For example, the question of coin toss can appear in it.

The title means:

[Toss an even coin until the flowered side of the coin appears twice in a row, and ask how many times the coin is flipped?]

There are many solutions to this problem that Chen Zhou can think of.

The most common is the probability formula.

Then there is the method of forking the tree recursive column equations.

In general, the difficulty of the probability and statistics test paper is not even as difficult as the final exam of the probability theory course that Chen Zhou took last year.

Of course, the reason for this situation, Chen Zhou can also guess.

After all, this is only a preliminary round, and the crowd facing is college students from all regions of China.

After the probability and statistics test, Chen Zhou waited outside for a long time before he saw Li Li hand in the papers.

Then there was Zhu Mingli, and finally Zhao Qiqi.

Chen Zhou asked with a smile, "Don't wait until the end?"

Zhao Qiqi also replied with a smile: "Aren't you afraid that Brother Chen will wait too long?"

Zhu Mingli also said: "Submit the papers early, go back early." ”

Only Li Li said silently: "The topic is too simple, I'm embarrassed to waste ......."

When Chen Zhou heard this, he looked at Li Li with a smile.

That's the truth......

Chen Zhou and the others took the bus back to Yan University, and when they walked into the dormitory, it was just 9 o'clock in the evening.

Chen Zhou sent a message to Yang Yiyi, telling him that he had returned to the dormitory.

This is the minimum respect between lovers.

It didn't take long for Yang Yiyi to reply to the message.

[Uh-huh, then you can read a book, so you can almost wash and sleep. 】

Chen Zhou replied with an "OK" expression.

Speaking of which, if you look at the book, Chen Zhou doesn't really want to read physics textbooks now.

But he has already finished the textbooks for the undergraduate courses of the Department of Mathematics.

And the topic has not yet been decided, and he has no direction for the time being.

After thinking about it, Chen Zhou turned on the computer and searched for "Hilbert 23 Questions".

Hilbert's words have a magical charm in the world of mathematics.

He was one of the greatest mathematicians of the 19th and 20th centuries.

This man is almost a perfect mathematical person, his footprints are all the frontiers of modern mathematics, and his mathematical ideas have also deeply penetrated into the entire modern mathematics.

Hilbert's 23 questions are the 23 most important mathematical problems proposed by Hilbert at the Congress of Mathematicians in Paris in 1900.

In a sense, Hilbert's 23 questions have guided the direction of mathematical research since the twentieth century, and its influence continues to this day.

In 1976, among the top ten achievements of mathematics in the United States since 1940, Hilbert's first question, fifth question, and tenth question accounted for three of them.

Including the seven millennial problems proposed by the Clay Institute of Mathematics in the United States, they also echo the 23 questions proposed by Hilbert in 1900.

Its influence can be seen from this.

Chen Zhou looked at the information he found.

Although more than a century has passed, the discipline of mathematics has also come a long way.

However, of these 23 questions, a total of 17 have been recognized and all resolved.

There are still 6 remaining issues, which have not been fully resolved.

It can be seen that time is not a sufficient condition for solving the problem, it is only a necessary factor.

It's like Fermat's theorem, but after more than 300 years of precipitation, it was finally solved by Wiles in 1995.

Chen Zhou looked at the discussion behind these questions with some emotion.

In fact, the existence of these problems has long gone beyond the meaning of the problem itself.

In the process of studying these problems, new mathematical tools and research methods are born that are even more important than some problems.

Like the question of "proof of the transcendence of certain numbers".

As early as 1929 and 1935, it was independently proven correct by several mathematicians.

However, the research on the theory of transcendental numbers is far from complete.

The study of this problem has also become part of the theory of transcendental numbers.

There is also the problem of "prime-number separation".

The Riemann conjecture, the Goldbach conjecture, and the twin prime problem.

These are all unresolved issues.

However, in the process of solving these conjectures, both the obtained three-prime theorem and the important improvement of the sieve method are extremely important and rare results.

Holding the mouse and sliding the scroll wheel, Chen Zhou sorted out the 6 unsolved problems in the 23 questions again.

It's not that he plans to pick one of these six questions as a topic for study.

Rather, he hopes to get some direction out of it.

Then, get closer to the real puzzles.

Moreover, the system task only guides one direction every time, and everything has to rely on Chen Zhou himself.

Therefore, Chen Zhou plans to establish a systematic research idea.

Starting with the topic selection of the topic, and continuing with every step after that.

He intends to develop his own research style gradually, or rather to develop it.

This is also Chen Zhou's decision after careful consideration.

After all, judging from the last task, the experience rewarded by the system is ultimately the value of the subject.

Of course, you have to go deeper and deeper.

After Chen Zhou finished taking notes, he searched for some related literature and similar content.

After doing all this, Chen Zhou stretched.

Glancing at the time, it was already past 10 o'clock.

I just wondered, why didn't Yang Yiyi come to urge the news.

I heard my phone vibrate.

Chen Zhou picked it up and took a look, Yang Yiyi sent it.

[Happy, it's time to sleep, be good, hee-hee. 】

Looking at the message, Chen Zhou smiled slightly, clicked his finger quickly, and replied.

[Well, that happy Yiyi, let's sleep......]

As soon as it was sent, Yang Yiyi came back.

[Uh-huh, good night.] 】

Chen Zhou: [Good night. 】

The next day, Sunday, March 22.

Admission at 9 a.m. and exams at 9:30 a.m.

The third subject in the individual competition is Geometry and Topology.

After Yang Yiyi finished taking this subject, her entire written test stage was over.

She didn't report the last two subjects in the afternoon.

For the geometry and topology test papers, Chen Zhou's eyes were bright.

This test paper is produced by a good person, the paper is neat, and the questions are very short.

It's very pleasant to look at......

The first question is about the product of a sphere.

Chen Zhou raised his pen to calculate, with clear thinking and rigorous calculation.

It didn't take much time to solve the first question.

Then comes the second question.

Proof of three-dimensional manifolds.

Manifolds are described in mathematics as geometric shapes.

The second question is solved, and the third question is reached.

Questions about borderless smooth manifolds and vector fields.

It was not much difficulty, after Chen Zhou finalized his ideas, he wrote down the problem-solving process on the test paper.

The fourth problem returns to the surface problem, where the standard sphere is proved according to the average curvature.

Soon, you're done!

The fifth question is about Riemannian manifolds, that is, Riemannian geometry.

Chen Zhou looked at this question a little more.

It's not because of the title.

Rather, he was interested in Riemannian geometry in the same way that he was interested in Hilbert spaces in yesterday's analysis and partial differential equations.

It's the same as last night, when Chen Zhou searched for literature and searched in the same direction.

With the release of new missions in the system, his goal of participating in the Qiusai is more to find direction.

In the morning, after Chen Zhou and Yang Yiyi submitted the papers in advance, like yesterday, the two returned to Yanda together.

In the afternoon, Yang Yiyi planned to go to the professor and follow up on the topic of mechanics.

Chen Zhou took a nap in the dormitory and then rushed to the Morningside Math Center.

At half past two in the afternoon, the fourth exam of the individual competition, algebra and number theory, began.

Chen Zhou complained a lot about this test paper.

First of all, unlike other subjects, this paper is not 5 out of 6 questions.

It has only 5 questions.

It is also different from the test paper of the team competition.

However, each of its 5 major questions consists of at least 4 small questions.

Well, the third question is 3 questions, but in the third question, there are 4 more questions......

Therefore, this test paper is the most of so many subjects that Chen Zhou has taken.

5 questions, 3 sheets of A4 paper were printed......

Another point, which Chen Zhou couldn't help but complain about, was that the beginning of this test paper was also different from other test papers.

At the beginning of this paper, there is a sentence to dissuade you from quitting.

[This 160-point test paper is just to test how much you know, not how much you don't know, you don't need to complete all the questions, you just need to do your best.] 】

Chen Zhou feels that there are at least two meanings.

One layer is that we produce this test paper, just to pull it up, it's normal that you won't do it, just do your best.

The other layer is that you need to make sure that you know the problem and then solve it.

If you can't, don't scribble, we have so many questions, don't delay our grading time......

Chen Zhou shook his head slightly, the candidates who came to participate in the competition must want to score as much as possible.

The passage at the beginning of this test paper is really unfriendly......

Chen Zhou didn't quite understand the meaning of this passage, so he could only classify it as, maybe this is also a way to take the exam......

Looking left and right, Chen Zhou really saw a few candidates whose emotions had changed.

Retracting his gaze, Chen Zhou sorted out his thoughts and began to answer the questions.

This paper mainly focuses on commutative groups, orthogonal complex matrices, complex matrix spaces, prime number problems, unique factorization domains, etc.

It may be difficult for others, but for Chen Zhou, these are just a general test of what he has learned.

The best response to the sentence at the beginning of the test paper is to get a full score on this test paper!

Wait until Chen Zhou hands in the papers and leaves classroom 1308.

In the classroom, I thought I was used to having someone who always turned in their papers in advance.

At this moment, I have mixed feelings.

This test paper is the most difficult one they have had since the exam in the past two days.

At 5 p.m., the exam ends.

Chen Zhou and Zhao Qiqi met and went to yesterday's restaurant again.

It's just that, except for Chen Zhou, the appetite of Zhao Qiqi and the three seems to have been affected by the afternoon exam.

Chen Zhou thought about it, but he didn't say anything to comfort him.

This kind of thing that is affected by the exam, comfort is the most useless.

At half past six in the afternoon, the last exam of the individual competition and the last exam of the written test stage of the Qiu competition.

Applied and Computational Mathematics, start the exam.

In fact, this paper is mainly an assessment of the application of mathematics.

Including linear models, numerical fitting problems, etc.

Although it is not something that Chen Zhou is good at, he has the experience accumulated in the last UPC competition, and he is very easy to deal with.

9 p.m.

Chen Zhou, who had been waiting for a while, finally saw the figures of Zhao Qiqi, Zhu Mingli, and Li Li.