The top student must be diligent

At this moment, a hearty laugh came from their side.

The person who laughed was Hu Guangde.

Now, he really had a strong interest in this student named Xiao Yi.

If it was just because of Liu Bin at the beginning, then now, it was completely because of the feeling that Xiao Yi in the video gave him in just a few minutes.

If what this student said was true, then perhaps, he really met a genius who could set off a wave in the mathematics world?

Academician Hu's laughter brought Liu Bin back to his senses, and then he coughed twice and said, "Okay, Xiao Yi, let's not talk about these things for now, I'll introduce you."

He moved his phone to let Hu Guangde enter the camera, and said, "This is Academician Hu Guangde of our University of Science and Technology, and also an academician of our School of Mathematics. Academician Hu is very interested in you."

Xiao Yi was immediately shocked.

What?

Academician?

He actually met an academician?

Next to Xiao Yi, Luo Penghua also widened his eyes.

Just now Liu Bin told him that there was a great thing for Xiao Yi, and it turned out that there was an academician!

Wow, if he was favored by an academician before entering university, Luo Penghua couldn't imagine Xiao Yi's future.

"Young man, your name is Xiao Yi, right?" At this time, Hu Guangde spoke first.

Xiao Yi nodded quickly: "Hello, Academician Hu, I am Xiao Yi."

"Don't be nervous, just treat me as a mathematics teacher at the University of Science and Technology." Hu Guangde smiled and said, "You just said that you have read so many books in a few days, so I will test you."

Soon, Hu Guangde sent a word document.

The title is "Convergence of Riemann Integral and Lebesgue Integrability", and there is also an author named Zeng Ang.

Obviously, this is a paper.

"This paper is less than 6 pages long, so it shouldn't take you much time. Take a look and then talk about your views on this paper."

Chapter 22 Expectations for Xiao Yi

"Paper?"

Hearing the request from Academician Hu, Xiao Yi's eyes lit up. As a high school student, he had never come into contact with such a thing as a paper in the past.

Hmm... He had only come into contact with "argumentative essays" in Chinese composition.

And now Academician Hu actually sent him a paper directly and asked him to take a look, which immediately aroused his interest.

"Okay, I'll take a look."

Then he downloaded the paper sent by Academician Hu and started reading it.

First, he saw the relevant information of the author named Zeng Ang, who was actually a graduate student of the School of Mathematics of the University of Science and Technology, and his supervisor was not Hu Guangde, but another name.

Of course, Xiao Yi didn't read much of these contents. After all, studying other people's information is not a good habit. Then he turned to the next page.

"The convergence of Riemann integral and Lebesgue integrability are closely related. First, the convergence theorem of Riemann integral is proved in detail, then it is explained... and finally an application is given."

This part is the abstract, which mainly explains what this paper is about.

Then it goes into the main text.

Although he had only read the book for a few days, Xiao Yi did not feel any difficulty in reading after he really started reading the main text. Basically, he had seen the things mentioned in the paper in the book, and even if he had not seen it, he could understand it with a little deduction in his mind.

This paper is probably a paper written by the graduate student named Zeng Ang for practice. It is not deep. At least the theoretical derivation in the first half is completely fine.

Soon, Xiao Yi saw the last part of the paper, which is the application of the conclusions derived earlier.

But after a few glances, his brows slightly frowned.

Because he found an error in this application process.

"Using the Dirichlet criterion, under the current conditions, it is not possible to directly determine whether the Riemann integral (R) converges."

He couldn't help wondering if he was wrong. After all, this paper was written by a graduate student who could become his senior in the future. How could it be wrong?

There must be an explanation or a patch at the end.

So he continued to read on, but as he turned the page again, he found that the graduate student had directly concluded that "in summary, the conclusion is valid."

Then there was a summary.

"This..."

Xiao Yi was in trouble.

He turned back and read it again, and the final conclusion was still the same, that is, it was wrong!

However, after all, this paper was asked to be read by Academician Hu. Although the tutor of this student named Zeng Ang was not Academician Hu, he must have a certain relationship.

If the error is pointed out directly, wouldn't it be a bit bad?

But soon, he stopped struggling. Mathematics is a science of "right is right, wrong is wrong".

So, he finally spoke: "Academician Hu, I have finished reading it."

Hu Guangde smiled and said: "Okay, tell me what you think."

"Okay." Xiao Yi nodded: "The first three parts of this paper are correct and there are no mistakes, and the inferences in it should also belong to the relatively basic content of "Real Variable Function Theory", but it has also been studied to a certain extent."

"However, there is an error in the fourth part, the application of inference."

"There is an error in the part of using the Drichlet criterion to judge the convergence of the Riemann integral (R). Under the current known conditions, this judgment cannot be made directly."

Hearing Xiao Yi's words, Hu Guangde raised his eyebrows, and then said: "So, how do you think this error should be corrected?"

Xiao Yi was stunned. He didn't expect Hu Guangde to ask him how to correct this error instead of asking him how he found it.

But he said directly: "We need to start from the beginning."

"Let α∈R, and f(x)=sin1/x/x^α, x∈(0,1], then the following conclusion holds, (i) when α≤0, f∈R[0,1] and f belongs to L[0,1]..."

Xiao Yi began his narration, and on the other side of the video, in addition to Hu Guangde's increasingly brilliant smile, the other professors, including Liu Bin, opened their mouths wider and wider.

This paper is really nothing for these professors at the level of master's and doctoral supervisors, but the problem is that the person on the other side is a high school sophomore who has just read the theory of real variable functions once, and it has not even been two days!

After just studying for less than two days, he was able to master the real variable functions that he had to study ten times to this extent, and even pointed out the mistakes in the paper after reading a paper written by a graduate student?

I remember this graduate student named Zeng Ang, who seemed to be a student of Academician Hu ’s student, right?

That is, he is Hu Guangde’s disciple, so he must have the ability.

After being amazed, several professors looked at each other, and finally, all of them focused their eyes on Liu Bin’s face.

Lao Liu, Lao Liu, where did you find such a student?

Liu Bin showed a sad face.

Before, he was thinking of bringing Xiao Yi to their school to calm down the other geniuses in the junior class, but he never thought of calming down the mathematics professors.

Self-confidence is almost gone.

He thought of the 40 books he gave Xiao Yi. According to this guy’s reading efficiency, so many... so few books, can he last for a month?

At most, only algebraic geometry, algebraic topology and other particularly difficult books, and those English textbooks can make Xiao Yi spend a little more time, right?

Really...

A desperate gap.

“…For the integral ∫2πk+π, 2πk |sint/t|dt as a variable to replace x=... We can easily prove the correctness of (16), and then fL[0,1], and finally according to the Cauchy criterion, (iv) is proved. "

"The proof is complete."

Xiao Yi's voice came from the phone, which also meant that he had corrected the mistakes in this paper.

"Very good."

Finally, Hu Guangde nodded and even gave a thumbs up. If Xiao Yi was right in front of him, he might have applauded directly.

"Very well said, and this is exactly the main purpose of letting you read this paper."

"This mistake The error is not particularly obvious in this paper, because in the discussion of Riemann integral and Lebesgue integrability in section 3.2, it gives people an illusion that the condition that was originally missing is included, but in fact it is not. "

"Such an error may be difficult to prevent even for some skilled people."

"Only those who can truly master this part of real variable function theory can avoid such problems."

"In addition, the Cauchy criterion you used at the end also makes this part of the content more exciting."

The academician of mathematics made a final comment: "In short, I am now looking forward to seeing you in the School of Mathematics of our University of Science and Technology."

Chapter 23 Academician's Requirements

Science Class 3 classroom.

The Chinese class has ended, and it happened to be a break. Xiao Yi walked out of the office and returned to the classroom.

Soon, a group of classmates surrounded him and began to chatter in his ears.

"Wow, Xiao brother, what did the class leader call you to do just now? "