Chapter 357

Following.

The atmosphere of graduation season is still spreading on campus.

Cheng Nuo got up early to wash up, came to the outside of the defense classroom, and quietly looked forward to being flopped.

At a quarter past nine, Cheng Nuo was summoned to the defense classroom.

The defense team composed of four teachers was sitting in the first row of the classroom, quietly watching Cheng Nuo's every move from the beginning.

Cheng Nuo, the four teachers of the defense team, all knew each other, including Professor Fang and Dean Wei.

Both of them are leaders in the Chinese mathematics community.

In the face of such a big battle, Cheng Nuo's expression remained unchanged, and he walked up to the defense seat calmly, inserted the USB flash drive into the multimedia in the classroom, and then Cheng Nuo bowed slightly.

The first step is to introduce yourself.

Although the four people in the audience also know Cheng Nuo well, this link is still indispensable.

"Hello teachers, my name is Cheng Nuo, from the 2020 Mathematics and Applied Mathematics major, student number 2020XXXXXX,...... In the past two years, he has participated in the research work of four research projects, including a national key research project and an inter-university cooperation and exchange project. ”

"In terms of competition awards, he has won the first prize of the National College Student Mathematics Competition, the National College Student Mathematical Modeling Competition, and the O Award of the American College Student Mathematical Modeling Competition!"

"In terms of academic papers, three papers have been included in SCI journals, two of which are journals in Region 2 and one is the journal Nventiones mathematicae in Region 1. ”

"In terms of academic performance, out of a total of 54 courses in the Department of Mathematics, 32 subjects were obtained with perfect marks, with an average score of 97.52. Ranked first in the whole system. ”

In terms of extracurricular hobbies, he participated in intramural tennis tournaments and won the championship. He has participated in the Go group of the National College Chess Competition and won the championship!"

"In terms of scholarships, I have won the special scholarship three times, and I have won the scholarship 95 times in total!"

............

One by one, the reputations and awards were like worthless cabbages in Cheng Nuo's mouth, and he said them without any emotional fluctuations on his face.

After introducing himself, he was stunned by Cheng Nuo to make the feeling of the commendation conference.

“...... I'm done introducing myself, thank you!"

Finally, Cheng Nuo bent down to salute.

The four teachers in the defense team nodded with a smile and motioned for Cheng Nuo to continue.

Fortunately, they had done their homework on Cheng Nuo before they came, otherwise they might have been directly stunned on the spot in the face of Cheng Nuo, who was not at all like a normal person.

is worthy of being Professor Fang's most proud student, this strength really belongs to his peers.

Thinking like this, the other two professors in the defense team glanced at Professor Fang, who was smiling at the podium.

Seeing that his disciple has such a talent, this teacher must be happy!

On the defense table, Cheng Nuo, who finished introducing himself, opened the defense PPT that had been prepared a long time ago.

Officially enter the second part: the respondent's statement.

In this session, the respondent needs to explain the background of the topic, the reasons for choosing the topic, and the current development of the topic. the specific content of the topic; and the respondent's specific contribution to the topic.

The time limit is 20 minutes.

This is an extremely important part, second only to the next question from the defense teacher.

Cheng Nuo had already sent the specific graduation thesis to the teachers of the defense group half a month ago, so that he had enough time to read and prepare, and he did not have to worry about the teachers of the defense group not being able to keep up with his own ideas.

opened the first PPT, Cheng Nuo coughed lightly, and began his defense statement.

The title of this dissertation is "The Simple Proof of the Bertrand Hypothesis", which originated from the complexity of the Bertrand hypothesis proved by Chebyshev in the last century, and was born in order to simplify this proof step. ”

"In the paper, I used two proofs of the Bertrand hypothesis proposed by Mr. Chebyshev to derive twenty inferences, and then selected five inferences that were useful for proving the Bertrand hypothesis, and used the counter-proof method to prove the Bertrand hypothesis step by step. ”

Chebyshev's proof formula, a total of 185 lines, 3254 characters. After I simplified the proof step, it only takes 38 lines and 985 characters. ”

The five-fold reduction, especially for the Bertrand hypothesis, which was a well-known mathematical problem in the last world, can already be said to be a great leap forward in the historical sense.

The four people in the audience had already read Cheng Nuo's paper, so their faces could remain a little calm at this time.

You must know that when they first read the graduation thesis submitted by Cheng Nuo, the mouth seemed to be able to stuff their fists down.

On the defense seat, Cheng Nuo's statement continued.

In the hands of the four teachers of the defense team, there is a paper version of Cheng Nuo's graduation thesis.

Cheng Nuo smiled faintly, "Several teachers can directly turn the paper to the sixth page, and the previous part of the content can be skipped directly." ”

If we just paste the new method of proving the Bertrand hypothesis that Cheng Nuo has developed, the content of the paper may not even be able to fill two pages.

For academic papers, the simpler and clearer the content, the better.

But this is a graduation thesis, and it would be too insincere to throw a two-page paper directly!

Therefore, Cheng Nuo added additions and finally turned a dissertation with only two pages of actual content into a graduation thesis of more than 50 pages.

And from the sixth page of the paper, it is the core content of the paper.

Cheng Nuo continued, "Two lemmas, one let n be a natural number and p is a prime number, then the highest power of p divisible by n! is: s =Σi≥1floor(n/pi) (where floor(x) is the largest integer not greater than x), and if n is a natural number and p is a prime number, then Πp≤n p < 4n. ”

I have written down the specific proof methods of these two inferences below, and through the sum of the highest powers, the two are continuously superimposed, and then derived. ”

"My idea is to divide divisible by (2n)!/(n!n!) The highest power of p, set to an unknown inequality function. After a few series of derivations, we can get the value of s as: Σi≥1 [floor(2n/pi)- 2floor(n/pi)]. ”

"The existence of the counterproof method led Bertrand to hypothesize an alternative simple proof scheme, which I used ......"

"Also, I pass ......"

“......”

Cheng Nuo, who is familiar with every detail of the thesis, stood on the defense seat and danced with his eyebrows, and slowly said his thesis writing ideas, without any jams and language jams, which attracted frequent nods from the teachers of the defense team in the audience.

Let's not talk about anything else, but the quality of this paper is enough to meet the standard of papers included in SCI journals in the first district that they said to Cheng Nuo before.

There are even more than that.

After all, they were talking about those low-level SCI journals before, but just looking at this paper, even the midstream Zone 1 SCI journal may not refuse to include Cheng Nuo's paper.

Even if Bertrand's hypothesis has been proven once, there is an easier way to prove it.