universal data

Chapter 354 Graduation Defense
357 chapter

The next day.

The back atmosphere brought by the graduation season is still gradually permeating the campus.

Cheng Nuo got up early to wash up, and came outside the defense classroom, quietly expecting to be flopped.

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

The defense team composed of four teachers was sitting in the first row of the classroom. They had been silently watching Cheng Nuo's every move since the beginning.

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

Both of them are leading figures in Huaguo's mathematics circle.

In the face of such a big battle, Cheng Nuo's expression remained unchanged, and he walked to the defense table calmly, inserted the U disk 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 knew Cheng Nuo well, this link was still indispensable.

"Hello, teachers. My name is Cheng Nuo. I am from the 2020 Mathematics and Applied Mathematics Major. My student number is 2020XXXXXX. Since I entered the school two years ago, I have participated in four research projects, including a national key research project, and a cross-disciplinary research project. School cooperation and exchange projects.”

"In terms of competition awards, he has won the first prize in the National Undergraduate Mathematical Contest, the National Award in the National Undergraduate Mathematical Contest in Modeling, and the O Award in the American Undergraduate Mathematical Contest in Modeling!"

"In terms of academic papers, three papers have been included in SCI journals, two of which are journals in the second district, and one is the journal "Nventiones mathematicae" in the first district."

"In terms of academic performance, of the 54 courses in the Department of Mathematics, 32 subjects have received full marks, with an average score of 97.52. It ranks first in the department."

"In terms of extracurricular hobbies, I once participated in the school tennis competition and won the championship. I once participated in the Go group of the National College Student Chess Competition and won the championship!"

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

…………

The honors and awards were like worthless Chinese cabbage in Cheng Nuo's mouth, and he said them without any emotion on his face.

After some self-introduction, Cheng Nuo gave him the impression of a commendation conference.

"...My self-introduction is over, thank you!"

Finally, Cheng Nuo bowed down to pay tribute.

The four teachers in the defense team smiled and nodded, motioning for Cheng Nuo to continue.

Fortunately, they had done enough homework for Cheng Nuo before they came, otherwise, facing Cheng Nuo's pile of awards, which is not like a normal person at all, they might just stand there in a daze.

As expected of Professor Fang's most proud student, this strength really belongs to his peers.

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

Seeing that his disciple is so promising, the teacher must be very happy!

On the defense platform, Cheng Nuo finished his self-introduction and opened the defense ppt that he had prepared a long time ago.

Formally enter the second link: the respondent's statement.

In this link, the respondent needs to describe the background of the project, the reason for choosing this project, and the current development of the project; the specific content of the project; and the specific contribution of the respondent to this project.

The time limit is 20 minutes.

This is an extremely important link, second only to the following questions from the responding teacher.

Cheng Nuo sent the specific graduation thesis to the teachers of the defense team half a month ago, so he had enough time to read and prepare, and he didn't have to worry that the teachers of the defense team couldn't keep up with his thoughts.

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

"The title of this thesis is "A Simple Proof of the Bertrand Hypothesis". The background of the subject is derived from the complexity of the proof of the Bertrand Hypothesis proposed by Chebyshev in the last century. In order to simplify this proof step, this paper is here The Birth of the Paper.”

"In the thesis, I used the two proofs about Bertrand's hypothesis proposed by Mr. Chebyshev to deduce twenty inferences, and then screened out five inferences that are useful to prove Bertrand's hypothesis, and used the method of counter-evidence to step by step. Hypothetical proof."

"Chebyshev's proof formula has a total of 185 lines and 3254 characters. After my simplified proof steps, it only needs 38 lines and 985 characters."

The five-fold reduction, especially for Bertrand's assumption of such a well-known mathematical problem in the last world, can already be said to be a big leap in the historical sense.

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

You know, when they read the graduation thesis submitted by Cheng Nuo for the first time, their mouths were so big that they seemed to be able to stuff their fists.

At the defense table, Cheng Nuo's statement continued.

At the hands of the four teachers in the defense team, they all had a hard copy of Cheng Nuo's graduation thesis.

Cheng Nuo smiled faintly, "Teachers can turn to the sixth page of the thesis directly, and skip the first part of the content."

If you just paste the Bertrand Hypothesis proof method developed by Cheng Nuo, then the content of the thesis 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. It would be too dishonest to just throw a two-page thesis over!

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

And starting from the sixth page of the paper is the core content of the paper.

Cheng Nuo continued to talk, "Two lemmas, one assuming n is a natural number and p is a prime number, then the highest power of p that can divide n! is: s = Σi≥1floor(n/pi) (Formula where floor(x) is the largest integer not greater than x), and one sets n as a natural number and p as a prime number, then Πp≤np < 4n."

"I have written the specific proof methods of these two inferences below. Through the sum of the highest powers, the two are continuously superimposed, and then deduced."

"My idea is to set the highest power of p that can divide (2n)!/(n!n!) into an unknown inequality function. After some series of derivations, the value of s can be obtained: Σi ≥1 [floor(2n/pi) - 2floor(n/pi)]."

"The existence of the method of proof by contradiction makes Bertrand postulate another simple proof scheme, which I use..."

"Also, I passed..."

"..."

Cheng Nuo, who was familiar with every detail of the thesis, stood on the defense table with beaming eyebrows, and slowly introduced his thesis writing ideas, without any stuttering or choking on the key points, which caused the teachers in the defense group to nod frequently.

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

Even more than that.

After all, they were talking about the low-level SCI journals, but just looking at this paper, even the mid-level SCI journals would probably not refuse to include Cheng Nuo's paper.

Even if Bertrand's hypothesis has been proved once before, another simpler proof method is indeed capable of getting this kind of treatment.

(End of this chapter)