Staring at the calculations on the blackboard, Liu Jiaying frowned slightly. After thinking for a while, he hesitated and said: "This is... the derivative-free non-monotone smooth Newton method?"
She wasn't sure if this was true 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 carried out 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.
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 inspiration 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 by 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 that could be further optimized in this graduation thesis, 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 finish optimizing this paper, you can officially graduate."
"But then you should consider 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 learn directly. 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 master are sufficient 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 studying for graduate school and then Ph.D. are two different concepts.
The former may be the choice of 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 this life.
Looking at this student who looked more and more like her sister as he got 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, it currently exceeds your knowledge and ability."
After thinking for a moment, he continued: "Rather than telling them about them now, I think it's better to leave them to you as a homework or investigation."
"After you complete the optimization and modification of the paper, you can try to continue to explore the points that can be modified, and learn more in-depth knowledge in the fields of differential geometry, differential topology and algebraic topology, differential equations and nonlinear analysis."
"Sometimes, what I tell you and what you are looking for yourself are two completely different meanings. The latter will only be more helpful to your academic path."
This chapter is not over yet, please click on the next page to continue reading! Liu Jiaying nodded seriously and said: "I understand, professor, I will definitely revise this paper to the most perfect state!"
Hearing this, Xu Chuan laughed and encouraged: "Come on~"
"I can, professor." Liu Jiaying nodded like she was pounding garlic, with some excitement on her face.
Looking at the primary school student walking out with his graduation thesis in hand, Xu Chuan had a smile on his face and shook his head gently.
Perfect?
Maybe.
But in his opinion, there may not be anything perfect in this world.
Whether it is so-called science or truth, things that seem perfect or indestructible are actually just based on current human observation and thinking about nature and the universe.
As times change, any existing science or truth may be broken.
Just like humankind's initial observation of the universe, from the flat earth theory, to the geocentric theory, to the heliocentric theory, to the big bang theory, everything is changing.
Perhaps mathematics is a bit special. This discipline, which was born based on a high degree of abstraction, itself transcends concrete science.
Its existence is more like a tool.
It is a tool to help humans explore, understand, and form the world. It is not an 'observation' discipline like other natural disciplines.
After all, whether it is physics, chemistry, biology, astronomy, etc., in the final analysis, they are all observations and summaries of natural or experimental phenomena.
Only mathematics is not, it does not rely on the specific material world, it only describes and solves problems through symbols and formulas.
Just when something flashed through his mind, there was a gentle knock on the office door twice.
"Professor, do you have time now?"
At the door of the office, a head popped in. Xu Chuan turned around and looked over. It was another student of his, Yin Shi.
Xu Chuan nodded, smiled and asked, "What's wrong?"
"I would like to ask your help to read this paper."
Holding a stack of printed papers, Yin Shi walked in quickly.
"No problem, what is it about?"
Xu Chuan smiled and nodded, reached out to take the paper and asked casually.
Yin Shi: "Graduation thesis."
Hearing this, Xu Chuan looked up at her in surprise.
First there was Liu Jiaying, and then there was Yin Shi. What happened today? They were all rushing to graduate. Have they discussed it?
But it’s normal to think about it, it’s indeed time for Yin Shi to graduate.
She was one of the first students he recruited after he returned to NTU to teach after the controllable nuclear fusion technology was completed. About four years have passed now.
Before that, Dr. Tong Yang had graduated, and another Dr. Ding Rui was still studying computational materials science with him, and now he has gone to the Sichuan-Hai Institute of Materials for an internship.
The only ones left are Yin Shi and Rong Xinji.
Although they are both graduate students, the latter is two years younger than her.
Of course, it's time for Rong Xinji to graduate. After all, he enrolled in the same batch.
However, according to his previous understanding, Rong Xinji seems to have not graduated yet. He seems to be trying to challenge a conjecture in the field of analysis and number fields. He has talked to him about this before.
After coming back to his senses, Xu Chuan opened the paper in his hand.
Unlike several other students, Yin Shi's learning direction focuses more on applied fields, such as computational mathematics, graph theory, functions, analysis, etc.
These areas of mathematics that are more involved in applications are her main areas of study.
Although applied mathematics has always been despised by pure mathematics, without applied mathematics, it is impossible 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 really good. Whether it is mathematical models in computational materials science or control models of high-temperature plasma turbulence, they are all part of applied mathematics.
And these have greatly promoted the development of the times.
...
I glanced at Yin Shi's graduation thesis. The direction she chose for her graduation thesis was research in the field of graph theory.
The name is "Research on the Constructability of Characterization and Homogeneous Factorization Based on Edge Transfer Graphs"
Graph theory is a branch of mathematics. It takes graphs as its research object 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 a
Dimensional topology.
Yin Shi’s research direction is a mathematical conjecture in algebraic graph theory.
The original name of this conjecture is the ‘Weiss finite local primitive graph conjecture’.
The characterization of the edge transfer graph and the homogeneous factor decomposition are one of the central topics of this conjecture, which have important theoretical significance and broad application fields.
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 Internet networks.
...
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, and the ideas in graph theory and structural research are very good. But relatively speaking, your knowledge is slightly lacking."
This chapter is not over, please click on the next page to continue reading! "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 led 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 to entry.
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. e=(′o｀*))) 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... Forget it, I won't say it anymore, just
It can be said that Maomao sighed after being hit all the time, life is not easy.
Also: There will be more updates tomorrow, please give me a monthly pass~, crab crab~(o?v?)ノ