Great Country Academician

Staring at the calculations on the blackboard, Liu Jiaying frowned slightly. After thinking for a while, he hesitated and said, "Is this the derivative-free non-monotone smooth Newton method?"

She wasn't sure if it was because it was knowledge she had little exposure to.

But she can still understand the mathematical formulas and calculations on the blackboard.

Iterative sequence generation is performed through the derivative-free non-negative quadrant wCP, and then the function f is continuously differentiable and monotonic. This method saves at least two steps compared to the method she studied herself.

Xu Chuan smiled slightly, nodded and praised: "That's right."

"Iterative sequence generation through the derivative-free non-negative quadrant wCP can simplify many steps."

"And next, in the step of well-posed non-singular numbers, have you considered similar applications?"

Looking at the youngest student in front of him, Xu Chuan guided her thinking and expanded her thinking path.

Mathematics is a very magical field. Sometimes when a path doesn't work, you change it in a completely different direction, only to find that it can come back in the completely opposite direction.

For a student who has just entered the field of mathematics, he always believes that maintaining an active mind and accumulating enough knowledge are the two most important things.

The former represents sufficient imagination, logic and thinking power, while the latter is the cornerstone of the former.

Only by possessing both at the same time can we continue to advance on the road of mathematics.

Staring at the mathematical formulas on the blackboard, Liu Jiaying fell into deep thought.

"Convergence! Convergence, right? Professor!"

She didn't know how long had passed, but a flash of light flashed in her mind. She suddenly raised her head and looked at Xu Chuan, her eyes shining with a look for affirmation.

Xu Chuan nodded, nodded slightly, and said with a smile: "Yes, it can help you simplify calculations that exceed at least twenty lines. But this will happen after you go back. Let's continue."

In the office, Xu Chuan erased the mathematical formulas on the blackboard and continued to point out the flaws in the student's graduation thesis.

Although it was undeniable that her graduation thesis was far beyond the level of undergraduate mathematics students, in his eyes, it was still quite 'rough'.

Time passed like this, and the blackboard was re-covered with some inspiring calculations. More than an hour later, Xu Chuan put down the marker in his hand, looked at Liu Jiaying, and said with a smile.

"That's almost it. That's it for today. When you get back, you can reorganize the things I mentioned and optimize the paper."

He pointed out the areas in this graduation thesis that could be further optimized, but most of the problems were only briefly touched upon. He only gave or guided the direction of in-depth research, and the rest required him, a primary school student, to do it himself. Keep up the good work.

Liu Jiaying nodded subconsciously, with a thoughtful look on his face.

After capping the marker pen in his hand and throwing it back into the pen basket, Xu Chuan smiled and said, "When you optimize this paper, you can officially graduate."

"But then you should think about whether to choose to study as a graduate student or a doctoral student."

Hearing this, Liu Jiaying looked over subconsciously, with a puzzled look on his face: "Is there any choice?"

Xu Chuan smiled, moved back to the sofa and explained: "Of course, it is not uncommon to get a direct blog. Even if you follow me, you are not necessarily required to go through every learning stage."

"But the premise is that the knowledge and abilities you have mastered are enough to support you in leapfrog learning."

"Judging from your graduation thesis, even if my requirements are higher than those of other professors, I do not deny that you have the ability to skip graduate school and enter doctoral studies directly."

Liu Jiaying thought about it thoughtfully, pursed her lips and asked, "Professor, can I choose not to speak directly?"

Hearing this answer, Xu Chuan glanced at the student in surprise and asked curiously: "Do you want to study for a master's degree first? Can you tell me your reasons?"

Taking a deep breath, Liu Jiaying pursed her lips and said, "I want to study with you for a few more years."

Direct Ph.D. and postgraduate study first and then Ph.D. are two different concepts.

The former may be the choice for most people, but sometimes it will be more advantageous to choose the latter under special circumstances.

For example, now, if she gets a direct PhD, she can study with Xu Chuan for at most three or four years; but if she studies for a graduate degree first and then a PhD, she can double the time.

Although this mentor is often said to be 'unreliable', it is undeniable that his knowledge is as vast as the ocean, as vast as the universe.

For anyone who is interested in pursuing an academic career, being able to study with him may be the luckiest thing in life.

Looking at this student who looked more and more like her sister as he grew older, Xu Chuan nodded and said gently: "In this case, I'll do whatever you want."

"Thank you, Professor."

Xu Chuan: "Speaking of which, regarding your graduation thesis, there are actually some points that can be further optimized."

Hearing this, Liu Jiaying looked over subconsciously, with a puzzled look on his face: "Professor?"

Xu Chuan smiled and said: "Don't worry. Although there are still some points in your paper that can be further optimized, for now it has exceeded your knowledge and ability."

After thinking for a while, he continued: "Instead of telling them now, I think it's better to leave them to you as a homework or test."

"After you finish optimizing and revising the paper, you can try to continue to dig out the points that can be modified from it, and learn more deeply about differential geometry, differential topology and algebraic topology, differential equations and nonlinear analysis. "

"Sometimes, what I tell you is completely different from what you find yourself. The latter will only help you more in your academic path."

Liu Jiaying nodded seriously and said, "I know, professor, I will definitely revise this paper to the most perfect state!"

Hearing this, Xu Chuan laughed and encouraged: "Come on~"

"I will, professor." Liu Jiaying nodded like pounding garlic, with some excitement on his face.

Looking at this elementary school student who walked out with his graduation thesis, Xu Chuan smiled and shook his head gently.

Perfect?

Maybe.

But in his opinion, there may be no perfect thing in this world.

So-called science or truth, those seemingly perfect or indestructible things are actually just based on the current human observation and thinking of nature and the universe.

With the changes of the times, any existing science or truth may be broken.

Just like the observation of the universe by humans at the beginning, from the flat earth theory to the geocentric theory, to the heliocentric theory, and the Big Bang theory, everything is changing.

Perhaps mathematics is a little special. This discipline born based on high abstraction itself transcends specific science.

Its existence is more like a tool.

It is a tool to help humans explore, understand, and form the world, unlike other natural disciplines, which are "observation" disciplines.

After all, whether it is physics or chemistry, including biology, astronomy and other disciplines, they are actually observations and summaries of natural or experimental phenomena.

Only mathematics is not, it does not rely on the specific material world, but only describes and solves problems through symbols and formulas.

Just as something flashed through his mind, the door of the office was knocked twice gently.

"Professor, do you have time now?"

A head poked in at the door of the office. Xu Chuan came back to his senses and looked over. It was another student of his, Yin Shi.

Xu Chuan nodded and asked with a smile: "What's wrong?"

"I want to ask you to help me look at this paper."

Holding a stack of printed papers, Yin Shi walked in quickly.

"No problem, what is it about?"

Xu Chuan nodded with a smile, and asked casually after taking the paper.

Yin Shi: "Graduation thesis."

Hearing this, Xu Chuan looked up at her in surprise.

First there was Liu Jiaying, then Yin Shi. What happened today? They are all rushing to graduate. Have they discussed it?

But it's normal to think about it. It's time for Yin Shi to graduate.

She was the first batch of students he recruited after returning to Nanjing University to teach after the completion of controlled nuclear fusion technology. Now it has been about four years.

Before that, Doctor Tong Yang had already graduated, and another Doctor Ding Rui was still learning computational materials science with him, and now he has gone to the Sichuan Ocean Materials Research Institute for internship.

The only ones left were Yin Shi and Rong Xinji.

Although they were both graduate students, the latter was two years younger than her.

Of course, Rong Xinji was also about to graduate, after all, they were admitted in the same batch.

However, according to his previous understanding, Rong Xinji did not seem to have the idea of ​​graduating yet. He seemed to be trying to challenge a conjecture about analysis and number fields, and he had talked to him about this before.

Coming back to his senses, Xu Chuan opened the paper in his hand.

Unlike several other students, Yin Shi's learning direction is more focused on application fields, such as computational mathematics, graph theory, functions, analysis, etc.

These more applied mathematical fields are her main learning areas.

Although applied mathematics has always been despised by pure mathematics, without applied mathematics, there is no way to communicate the development between pure mathematics and technology.

For Xu Chuan, there is no difference between the two, and he will not look down on scholars who develop applied mathematics.

After all, his own development in the field of applied mathematics is not bad. Whether it is the mathematical model in computational materials science or the control model of high-temperature plasma turbulence, they are all part of applied mathematics.

And all of these have greatly promoted the development of the times.

His eyes glanced over Yin Shi's graduation thesis. The direction of her graduation thesis was the research in the field of graph theory.

The name is "Study on the Constructibility of Characterization and Homogeneous Factorization Based on Edge Transmission Graphs"

Graph theory is a branch of mathematics. It takes graphs as research objects and studies the mathematical theories and methods of graphs composed of vertices and edges. It originated from the famous Königsberg Seven Bridges Problem, and its research object is equivalent to one-dimensional topology.

Yin Shi's research direction is a mathematical conjecture in algebraic graph theory.

The original name of this conjecture is "Weiss's Finite Local Primitive Graph Conjecture".

The characterization and homogeneous factorization of edge-transmission graphs are one of the central topics of this conjecture, which has important theoretical significance and a broad application field.

As for whether Yin Shi can solve this problem, Xu Chuan's answer is that it is difficult.

He knows the level of this student, and he also knows that the difficulty of this problem is not something she can solve now.

However, it is also a very good choice to lay a solid foundation during the postgraduate period, make tentative breakthroughs to a certain extent, and then attack it after the doctoral period.

Even if this problem cannot be solved, some of the results obtained from it are widely used in information science, computer science and communications, especially in the design and optimization of the Internet.

In the office, after carefully reading Yin Shi's graduation thesis, Xu Chuan stood up and dragged out the mobile blackboard in the corner.

His attitude towards every student is the same. As long as they have problems, he will do his best to provide guidance.

In the office, after spending some time pointing out the problems and flaws in Yin Shi's thesis prepared for graduation, Xu Chuan said with a smile.

".Overall, this paper is quite good. The ideas in graph theory and structural research are very good. But relatively speaking, your knowledge is slightly lacking."

"For example, in areas such as algebra, multidimensional topology, numerical analysis, etc., my suggestion is to read more books and papers in these areas."

“Although they may not directly promote your research direction, they can enrich your thinking and logic and help your research from another perspective.”

After thinking for a while, Xu Chuan added: "I will make a catalog list for you later."

Yin Shi nodded and said, "Thank you, Professor."

Xu Chuan smiled and said: "Well, go ahead and optimize the paper."

Looking at Yin Shi's leaving figure, Xu Chuan also felt a little emotional.

Although he has never asked his students to solve many problems or advance in mathematics before they can graduate.

But the students he brought with him still worked very hard in their studies.

However, sometimes even if they work hard, not everyone can pick the ‘ideal’ ‘fruit’ on the academic path.

Even if the students he teaches are highly talented in mathematics, it is impossible for every one of them to grow into a mathematician.

For the subject of mathematics, genius is just the ticket.

Just because you have this ticket doesn't mean you can keep going.

In this world, there will always be people who are more talented than you and work harder than you.

PS: As I write this, I am reminded of the Olympiads I participated in in junior high school, and the math and physical competitions I participated in in high school. ε=(ο｀*))) Alas, there is a world out there, and there are people out there.

I thought I was awesome at that time, and I could get full marks in school and preliminaries. However, after entering the city competition and provincial competition, I couldn't solve many questions. I won't talk about it anymore. I can only say that I was always beaten. , Maomao sighed, life is not easy.

Also: More updates will be added tomorrow, please give me a monthly pass~, crab crab~(ov)ノ