Volume 1: Student Life Chapter 171 The written test is over
noon.
Chen Zhou and Yang Yiyi returned to Yanda and had lunch in the cafeteria.
Then, I returned to the dormitory.
Chen Zhou looked at the time. It was a little past 12:30.
The exam starts at 2:30 p.m., but just like the team competition, candidates are also required to enter the exam venue half an hour in advance for each subject of the individual competition.
In such a short time, Chen Zhou didn't want to do anything else.
I simply lay down on the bed and prepared to take a nap to conserve my energy for the exams in the afternoon and evening.
He also didn't have to worry about Zhao Qiqi and the others waking him up when they came back.
Because he had already called three people, and all of them handed in their papers at 12 o'clock.
It was already 12:15 by the time they walked out of the math center .
They decided not to go back to school and just found a nearby restaurant to eat.
It was not until the alarm clock rang that Chen Zhou opened his eyes and got out of bed.
I looked at the time and realized I had slept for about half an hour.
Just right.
A half-hour nap is enough. Sleeping too much or too little is not good.
After washing his face, Chen Zhou called Yang Yiyi.
The two met and went to the mathematics center.
At 2:30 pm, the Qiu race continued.
The first subject in the individual competition is analysis and partial differential equations.
Chen Zhou took a quick look at the entire test paper.
The focus of the first question is on issues related to measurable functions.
A measurable function means that if At∈R, E［f＞t］ is defined as a measurable set, then the function f is a measurable function.
Therefore, combined with the question information, fn∈L2(R) is a sequence of measurable functions , and fn→f is continuous everywhere.
Chen Zhou can basically determine the solution to this problem.
Reusing the last assumption given above, ║fn║L2→║f║L2.
Chen Zhou quickly wrote down 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 started on the next question.
The second question is about continuous functions and definite integrals.
It didn't take much effort for Chen Zhou to get it done.
The difficulty of this question is similar to the first question.
Then comes the third question.
Seeing this question, Chen Zhou raised his eyebrows.
Quite interesting.
The title information of this question is just an inequality.
【|f（z）|≤|z|2|Im（z）|2】
What is then required is the maximum value of "z" for which the inequality satisfies the condition.
Often the less information there is in a question of this type, the easier it is to lose a clue.
But Chen Zhou didn’t know how to do that. After a little thought, he understood the meaning of the question.
Then, he began to write.
Replace the thoughts in your mind with the steps of disintegration.
Write it out formula by formula, step by step.
The fourth question is about holomorphic functions.
When Chen Zhou started browsing, he thought it was a coincidence.
He has just completed a paper on the topic of holomorphic functions.
This brings us to the question of holomorphic functions.
Easy points question.
Question 5.
Question about Hilbert space.
This is also the question that Chen Zhou is interested in.
The main reason for my interest is Hilbert space.
Although this question is simple after all, it also provides Chen Zhou with some ideas.
As for the future direction of his research project.
After finishing this question, Chen Zhou completed the tasks of this exam in order.
Let’s go back to question 5 to question 1.
Chen Zhou checked it again.
After all, what he told Yang Yiyi and the others also applied to himself.
People tend to ignore obvious mistakes.
After carefully checking the solution steps and details of the five questions, Chen Zhou was about to stand up and hand in the paper.
To his surprise, Professor Shang, whom he met in the morning, stood next to him again this time.
Seeing that he was about to hand in the paper, Professor Shang simply extended his hand.
Chen Zhou handed the test paper to Professor Shang and smiled at him.
Not long after Chen Zhou walked out of Room 1308, he saw Yang Yiyi coming out.
Chen Zhou glanced at the time and smiled: "Analysis and partial differential equations, this girl is indeed good at it..."
I wandered around the Morningside Mathematics Center of the Chinese Academy of Sciences with Yang Yiyi for a while, and when the exam was over, Zhao Qiqi and the other two came out.
Chen Zhou and his five companions found a restaurant together.
After dinner, because Yang Yiyi did not sign up for the probability and statistics exam, she returned to Yanda first.
Chen Zhou and four others were left, and they returned to the Mathematics Center and waited silently for the exam.
As if in tacit agreement, Zhao Qiqi and the other two never mentioned anything about the exam in front of Chen Zhou.
Even if they finished all the test papers, they didn't say a word more.
After all, the past is still fresh in our minds...
Wait until 6:30 pm.
The second subject of the individual competition, Probability and Statistics, began the exam.
How to say it, Chen Zhou felt that the person who wrote the test paper for this subject must not have been serious.
Whether it is an individual or team competition, the test paper for this subject is very simple.
For example, questions about tossing a coin can appear here.
The title means:
[Toss a fair coin until the flowered side of the coin appears twice in a row. How many times does the coin flip? ]
Chen Zhou can think of many solutions to this problem.
The most common one is the probability formula.
Secondly, there is the method of recursively listing equations using a bifurcation tree.
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, Chen Zhou could also guess the reason for this situation.
After all, this is just the preliminary round, and the audience is college students from all over China.
After finishing the probability and statistics exam, Chen Zhou waited outside for a short while before he saw Li Li handing in his paper.
Then came Zhu Mingli, and finally Zhao Qiqi.
Chen Zhou smiled and asked, "Aren't you waiting until the end?"
Zhao Qiqi also smiled and replied: "Isn't it because I'm afraid that you'll wait too long, Brother Chen?"
Zhu Mingli also said: "Hand in the paper early and go home early."
Only Li Li said silently: "The question is too simple, I'm sorry to waste my time..."
Upon hearing this, Chen Zhou looked at Li Li with a smile.
This is the truth...
Chen Zhou and his friends took the bus back to Yanda University. When they walked into the dormitory, it was exactly 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.
Not long after, Yang Yiyi replied.
[Okay, then you can read for a while, then you can go to bed.]
Chen Zhou replied with an "OK" expression.
Speaking of reading books, Chen Zhou doesn't really want to read physics textbooks right now.
However, he has already finished reading the textbooks for the undergraduate courses in the Department of Mathematics.
The topic has not been determined yet and he has no direction yet.
After thinking about it, Chen Zhou turned on his computer and searched for "Hilbert's 23 Questions".
These words "Hilbert" have a magical charm in the mathematical world.
He was one of the greatest mathematicians of the 19th and 20th centuries.
This man is almost a perfect mathematician. His footprints are spread across all frontier fields of modern mathematics, and his mathematical ideas have deeply penetrated into the entire modern mathematics.
Hilbert's 23 questions are the 23 most important mathematical problems proposed by Hilbert at the Paris Congress of Mathematicians in 1900.
In a sense, Hilbert's 23 questions guided the direction of mathematical research after the 20th century, and its influence continues to this day.
In 1976, American mathematicians selected the top ten achievements in American mathematics since 1940, and Hilbert's first, fifth, and tenth questions accounted for three of them respectively.
Including the seven millennium problems proposed by the Clay Mathematics Institute in the United States, they also echoed the 23 questions raised 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 subject of mathematics has made great progress.
But out of these 23 questions, 17 were acknowledged and fully resolved.
There are still 6 issues left that have not been fully resolved.
From this we can see that time is not a sufficient condition for solving problems, it is only a necessary factor.
Just like Fermat's Last Theorem, it took more than 300 years to be solved, and was finally solved by Wiles in 1995.
Chen Zhou looked at the discussion behind these questions with some emotion.
The existence of these problems has actually surpassed the significance of the problems themselves.
In the process of studying these problems, new mathematical tools and research methods are born, which are even more important than some of the problems.
Like the question "Proof of the transcendence of certain numbers".
Its correctness was independently proved by several mathematicians as early as 1929 and 1935.
However, the research on transcendental number theory is far from complete.
The study of this problem has also become a part of transcendental number theory.
There is also the problem of "prime number distinction".
Riemann hypothesis, Goldbach conjecture, and the twin prime problem.
These are all unresolved issues.
But in the process of solving these conjectures, both the three prime number theorem and the important improvements to the sieve method were extremely important and rare results.
Holding the mouse and sliding the scroll wheel, Chen Zhou sorted out the six unresolved problems among the 23 questions again.
It’s not that he intends to pick one of these six questions as a research topic.
Rather, he hoped to gain some direction from it.
Then, move on to the real challenges.
Moreover, the system tasks only point in one direction each time, and Chen Zhou has to do everything by himself.
Therefore, Chen Zhou planned to establish a systematic research idea for the topic.
Starting from the selection of the topic to every step thereafter.
He intends to gradually develop, or form, his own research style.
This was also a decision Chen Zhou made after careful consideration.
After all, judging from the last mission, the experience rewarded by the system ultimately depends on the value of the subject.
Of course, we have to go deeper step by step.
After taking notes, Chen Zhou searched for some related literature and similar content.
After finishing all this, Chen Zhou stretched.
I glanced at the time and it was already past 10 o'clock.
I was just wondering why Yang Yiyi didn't come to remind me of the news.
Then I heard my phone vibrate.
Chen Zhou picked it up and took a look. It was sent by Yang Yiyi.
[Happy, time to go to bed, be good, hehe. ]
Looking at the message, Chen Zhou smiled slightly, tapped quickly with his fingers, and replied.
[Well, happy Yiyi, let’s go to sleep…]
As soon as I sent it, Yang Yiyi replied.
【Yeah, good night. 】
Chen Zhou: [Good night.]
The next day, March 22, Sunday.
Enter the venue at 9:00 am and take the exam at 9:30 am.
The third subject of the individual competition is geometry and topology.
After Yang Yiyi finished this subject, her entire written test phase was over.
She did not sign up for the last two subjects in the afternoon.
Chen Zhou's eyes lit up when it came to the geometry and topology test papers.
The person who prepared this test paper is good, the paper is neat and the questions are very short.
It's so comfortable to look at...
The first question is about the area of a sphere.
Chen Zhou picked up his pen and started calculating. His thinking was clear and his calculations were rigorous.
It didn't take much time to finish the first question.
Then comes the second question.
Proof questions on three-dimensional manifolds.
Manifolds in mathematics describe geometric shapes.
The second question is solved, and now it’s time for the third question.
On problems with unbounded smooth manifolds and vector fields.
It was not difficult. After Chen Zhou finalized his idea, he wrote the solution process on the test paper.
The fourth question returns to the surface problem and proves the standard sphere based on the mean curvature.
Quick, done!
The fifth question is about Riemannian manifolds, which is a Riemannian geometry problem.
Chen Zhou took a closer look at this question.
It’s not because of the topic.
Instead, just like the Hilbert space in analysis and partial differential equations in yesterday's test, he was interested in Riemannian geometry.
Just like Chen Zhou searched for literature last night, the search direction was the same.
With the release of new tasks in the system, his goal in participating in the Qiu race was more to find direction.
In the morning, after Chen Zhou and Yang Yiyi handed in their papers early, they returned to Yanda together, just like yesterday.
In the afternoon, Yang Yiyi planned to see the professor to follow up on the mechanics topic.
Chen Zhou took a nap in the dormitory and then rushed to the Morningside Mathematics Center.
At 2:30 p.m., the fourth individual exam, Algebra and Number Theory, began.
Chen Zhou complained a lot about this test paper.
First of all, unlike other subjects, this test paper does not have 6 questions and you have to choose 5 from them.
It has only 5 big questions in total.
The test paper is also different from the team competition.
However, each of its 5 main questions consists of at least 4 small questions.
Well, question 3 does have 3 sub-questions, but within sub-question 3, there are 4 sub-questions...
Therefore, this test paper has the most questions among all the subjects Chen Zhou took.
5 questions, 3 A4 sheets of paper were printed...
Another point that made Chen Zhou couldn't help but complain was that the beginning of this test paper was different from other test papers.
There is a word of dissuasion at the beginning of this test paper.
【This 160-point test 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 felt that there were at least two meanings.
First, we make this test paper to raise the level. It is normal if you can't do it. Just try your best.
Another level is that you need to make sure you know how to solve the problem before you solve it.
Don’t write down the answers you don’t know. We have given so many questions, so don’t waste our time marking the papers…
Chen Zhou shook his head slightly. All the candidates who came to participate in the competition must want to get as many points as possible.
The words at the beginning of this test paper are really unfriendly...
Chen Zhou didn't quite understand the meaning of this sentence, and could only classify it as, maybe this is also a form of examination...
Looking around, Chen Zhou indeed saw several candidates whose emotions changed.
Chen Zhou retracted his gaze, sorted out his thoughts, and began to answer the questions.
This test paper mainly covers issues such as commutative groups, orthogonal complex matrices, complex matrix spaces, prime number problems, and unique factor decomposition domains.
It may be difficult for others, but for Chen Zhou, it is just an ordinary test of what he has learned.
The best response to the sentence at the beginning of the test paper is to get full marks on this test paper!
When Chen Zhou handed in his paper and left classroom 1308.
In the classroom, the candidates thought they had gotten used to someone always handing in their papers early.
At this moment, my mood became complicated again.
This test paper was the most difficult one they had taken in the past two days.
The exam ended at 5 pm.
Chen Zhou, Zhao Qiqi and the other two met up and went to the same restaurant as yesterday.
However, except for Chen Zhou, Zhao Qiqi and the other two seemed to have their appetite affected by the afternoon exam.
Chen Zhou thought about it but didn't say anything to comfort her.
When your mood is affected by exams, comfort is of no use.
At 6:30 pm, the last exam of the individual competition was held, which was also the last exam of the written examination stage of the Qiu competition.
Applied and Computational Mathematics, start exam.
This test paper is actually mainly an assessment of the application of mathematics.
Including linear models, numerical fitting problems, etc.
Although it was not something Chen Zhou was good at, with the experience accumulated from the last UPC competition, he was able to handle it with ease.
9pm.
Chen Zhou, who had been waiting for a while, finally saw the figures of Zhao Qiqi, Zhu Mingli and Li Li.
