From small town scholar to chief scientist

Chapter 9 Are You Zhou Yi?
It was not until ten o'clock in the evening, when the library was about to close, that Zhou Yi was woken up by the library staff from the sea of ​​books.

Zhou Yi looked around, and besides the staff, Xia Xue was here.

"Why are you still here?"

Zhou Yi asked with some doubts.

"Study duck, our major also has a lot of books to read, and many books that are not covered in the textbooks also need to be read. Seniors, you work so hard, and I can't fall behind."

Xia Xue blinked her lively eyes and said sweetly.

The staff on the side said:

"Okay, okay, the museum is closed, come back tomorrow."

Only then did Zhou Yi leave the library with Xia Xue.

"I'm going back to the bedroom first."

Zhou Yi dropped a sentence and ran away. This Xia Xue has impure goals, and I must not let a woman break my Dao heart!
Everyone who has not completed mathematics must not break the heart of Dao.

Xia Xue looked at Zhou Yi who fled in the wilderness, a smile appeared on the corner of her mouth, and then she also walked quickly to the dormitory.

Zhou Yi, who returned to the dormitory, continued to read after washing at an extremely fast speed.

Luo Yun and Yang Shuai are also busy with their own affairs.

Luo Yun was busy with class work, and Yang Shuai was busy with coding.

As for what happened in the large group during the day, everyone tacitly did not mention it.

From 10 pm to [-] pm, except for half an hour for dinner, Zhou Yi stayed in the library and never went out.

I saw the foreign textbook "Vladimir A. Zorich Mathematical Analysis" from the domestic textbooks on mathematics, and I also saw foreign textbooks from the domestic textbooks on analytic geometry.
There are only two foreign advanced algebra textbooks left.

Originally, Zhou Yi wanted to read domestic textbooks to do the task, but thinking that this was a solid foundation, he took the initiative to choose foreign textbooks with a higher degree of difficulty.

If you want to build a tall building, you must have a solid foundation.

Until two o'clock in the morning, Zhou Yi still had most of one book left unfinished.

Thinking that there was still class the next day, I fell asleep.

At six o'clock the next day, Zhou Yi quietly got up to wash up.

Then I bought two buns and hurried outside the library to start reciting English.

"I still need to memorize English for about three days, even if I have fully mastered the language of English."

Zhou Yi murmured.

Gained 200% comprehension since yesterday, and he has almost no memory of writing subjects.

In addition to the subject of English, compared with science, it is very simple.

I recite it for two hours every morning, and the time for three days is about the same.

Teaching Building 3301 of the Chinese Academy of Sciences.

"Old Zhou is here."

Seeing Zhou Yi entering the classroom, Yang Shuai yelled loudly.

After Zhou Yi walked over and sat down, he only heard the No.1 Xu Zihan in the class say:

"The first class is to count the points, but it is not Teacher Ma who counts us, but Professor Tang."

The boy on the side is No.3 in the class and said:

"I know it's him, but I heard that this professor is a bit ruthless. He lectures very quickly in class. Some theorems that are not proved in the book are even used as homework for the students."

"Isn't it possible for the equivalence theorem of the accumulation point theorem to become our homework?"

"Hey, you still previewed? As expected of the first grade point, there is something."

"I previewed it, but I don't know how to prove it. It's so difficult to score."

Xu Zihan complained.

Many people around were whispering and discussing matters related to study.

The completeness of real numbers is the most difficult part of counting. It is normal for many people to be afraid.

Many people don't even understand it.

Not long after, under the eyes of everyone, the old professor walked into the classroom and started teaching the first class.

Originally, Tang Ping wanted to trouble a 20th-level student named Zhou Yi, but he was busy with various things and was delayed, and he still didn't know which class Zhou Yi belonged to.

Then he shook his head and started to attend class.

"In fact, a multivariate function is the generalization of a one-variable function. It retains many properties of a one-variable function, but also produces many new properties due to the increase from one variable to many. We need to have a new understanding of these properties. "

The old professor said slowly, and the PPT was flipping page by page.

"If the domain of a function of one variable is the set of points on the real number axis, then the domain of the function of two variables is the set of points on the coordinate plane."

A class progressed slowly, and many people felt drowsy after listening to it. The previous point collection was okay and easy to understand, but when it came to the proof of completeness and theorem,
Everyone is impatient and distracted.

Moreover, the professor speaks quickly, and although he speaks thoroughly, very few people can keep up.

"Let's talk about the equivalence theorem of the accumulation point theorem. There is no proof in the book, and I don't want to prove it for you. I will keep it as homework.

The finite covering theorem is also similar to the proof process of unary. You are all excellent students of Yuda University, and these are not difficult for you, so hand them in as homework. "

Seeing that the lecture was almost done, Professor Tang began to assign homework.

"Or if someone proves any question on the blackboard right now, I can consider +10 points for the normal score of the final assessment."

Countless people in a class are silent, who would do that.

No.1 Xu Zihan doesn't even know it, let alone them.

You can only go down to find information, or think a little more, to prove it. Who can figure it out in such a short time in class?

Zhao Lili wanted to go, but she couldn't, neither did the study committee, and no one said anything.

Xu Zihan also wanted to try it. It was related to the final grades and even grade points. One step at a time, one step at a time.

But Xu Zihan can't either.

"Is there no one? Then you will miss the chance to add points."

At this time, Zhou Yi raised his hand and said:

"Professor Tang, I will."

"Huh? Which question do you know?"

Tang Ping didn't expect that someone would, it seems that some students still previewed in advance.

The students in the classroom also looked at Zhou Yi in amazement, how could he?
The mere No.10 will also do this?
Yesterday it was rumored that Zhouyi was a little spirited, but now it seems that it is true?
Zhou Yi said calmly:
"All will, add 20 points?"

"All of them? They will give you 20 points."

Professor Tang glanced at Zhou Yi and found that it looked familiar, but he still said it affirmatively.

Not long after, Zhou Yi walked up to the podium under the eyes of everyone, picked up the chalk, and began to write the process of solving the problem.

The first question is the one I read in Zhouyi,

A bounded infinite point sequence {Pn} contained in R must have a convergent subsequence {Pnk}.

At that time, Zhou Yi could deduce the writing on the blackboard in his mind, not to mention him who has thoroughly understood several textbooks now.

After a while, the only sound in the classroom was the sound of Zhouyi's chalk writing.

Those present, Yang Shuai was shocked, some classmates who watched the play were shocked, and those who just thought that Zhou Yi had mental problems were also shocked.

You, Zhou Yi, are so silent and strong.

Xu Zihan suddenly felt a sense of crisis, and his number one was in jeopardy.

Zhou Yi's mathematics level is actually similar to his. The reason why his grade point is the first is because Zhou Yi's grade point in the rest of the subjects is low, and the time spent on those subjects is used to do part-time jobs.

Otherwise, how to buy a computer.

In fact, there are too many ways to prove this theorem, and three or four methods come to Zhou Yi's mind now.

The simplest is the analogy of a one-dimensional bounded sequence proof,

Use the Bolzano-Weierstrass theorem of R1 to get the convergent subsequence {xm} of {xn}, and then examine the subsequence of {ym}, there is also a convergent subsequence {yk}, so that {(xk, yk)} is {pn} Convergent sub-columns.

Of course, you can also use the closed-field theorem learned today to prove it. There are many methods.

Zhou Yi wrote on the blackboard the simplest one.

Then, under the surprised eyes of everyone, the proof of the second question began.

Proof of the Finite Covering Theorem.

There are too many methods, Zhou Yi wrote one casually, and then respectfully said to Professor Tang Ping:

"Professor Tang, I have finished writing."

After Tang Ping finished reading it, he praised it without hesitation:

"Yes, the basic skills are good, there is no extra math language, and there are no extra steps. Unexpectedly, there is a seedling with a good foundation in class 20. What's your name?"

"My name is Zhou Yi."

"Well, you are Zhou Yi?"

Tang Ping was a little surprised, with an expression of disbelief.

(End of this chapter)