In the dormitory, Xu Chuan rubbed his eyes and put down the "Linear Algebra" in his hand.
When he was studying the Weyl_Berry conjecture before, although he found some ideas, he was stuck on how to expand the domain and convert the function into a subgroup and establish a connection with the intermediate domain and collection during the verification process.
He was seriously lacking in mathematical knowledge in this area. He knew some functions, but he was not familiar with domain expansion.
But if you want to read a book, you have to start with algebra and number theory.
Because the field is related to algebraic number theory, and the expansion of the field evolved from the field theory of abstract algebra.
Simply put, everyone knows that 'addition, subtraction, multiplication and division' are the four most basic arithmetic operations, but these are all for a single number.
For example, 4396-3619=777.
On this basis, if there is a group of numbers, what should we do to be able to add, subtract, multiply and divide? Count them one by one? That would be too troublesome.
Therefore, mathematicians defined a "field". A "field" is a group of numbers that can be added, subtracted, multiplied and divided arbitrarily. A field is an algebraic structure with "addition", "subtraction", "multiplication" and "division" on it.
So if you want to completely understand the "domain" thing, you have to start learning from algebra.
As for algebra, Xu Chuan must have been exposed to it, but in order to understand mathematics more comprehensively, he read all the basic textbooks and algebra textbooks borrowed from the library from beginning to end.
For the past two days, he has been staying in his dormitory, rarely leaving the house except for three meals a day. Does this mean he has read one-fifth of the university's textbooks on line generation? Probably not. After all, algebra is a huge field and there are many textbooks.
However, this has accumulated some questions and doubts for him, which are all recorded in his notebook. Xu Chuan plans to go to Professor Zhou Hai this afternoon, or ask him to recommend personal communication to resolve them before continuing.
...
With his notebook in hand, Xu Chuan came to Zhou Hai's office.
For him, solving a mathematical problem or learning a little new knowledge brings him happiness like a game fan who shoots his head with one shot when playing CF or learns the blind man's handsome eye-touching maneuver in LoL. Kick and R five at a time in ranked, and there is an orphan rope next to him to take advantage of the situation and destroy the opponent.
When he stood in front of the office door and knocked twice, Xu Chuan suddenly remembered what he had forgotten in the past two days.
Professor Zhou Hai's student, the hot water bottle of the girl who brought him medicine seems to be still in his dormitory, and the money to buy cold medicine has not been given to him yet.
"Khan, why did I forget to do this?"
Xu Chuan slapped his head in annoyance. He had promised to return the girl's things the next day, but it had already been three days. If word got out, wouldn't people misunderstand that he had taken possession of other girls' things?
"Please come in."
In the office, a voice woke up Xu Chuan who was distracted. He opened the door and walked in.
"Huh? Xu Chuan is here. Your cold should be completely gone, right?"
In the office, Professor Zhou Hai glanced at the figure who walked in. When he saw the person, his face was immediately filled with smiles.
"It's fine now. Thank you teacher for your concern."
Xu Chuan gently closed the door and kept the heat in the office. In the office, there was not only Professor Zhou Hai, but also Cai Peng, who had accidentally wiped out his graduate thesis.
"Here comes the boss. What is he going to study next? Let me tell you first so that I can be mentally prepared, senior brother. At least the graduation thesis must avoid your research direction."
Cai Peng stood up, poured a glass of water for Xu Chuan and asked with a smile.
"Weyl_Berry guess, I want to try and see if I can develop something new."
Xu Chuan smiled sheepishly. Although it was not his fault, he was still a little embarrassed when facing his enemy.
"Phew, that's good, come on, I'm optimistic about you!"
Cai Peng breathed a sigh of relief. Fortunately, he changed his graduation thesis in time and did not continue to insist on the Weyl_Berry conjecture. Otherwise, he might not have even graduated with a Ph.D., and his research goals would have been lost.
Xu Chuan turned to Professor Zhou Hai and said, "Teacher, I encountered some problems while reading "Linear Algebra" and "Line Generation to the Right" in the past two days. Can you help me?"
"Huh? Aren't you studying the Weyl_Berry conjecture? Why did you suddenly switch to line generation?" Zhou Hai asked curiously.
"I want to take advantage of the time I have recently to read more books to enrich my brain." Xu Chuan said shyly, without telling the real reason.
Zhou Hai was stunned for a moment, then continued: "It's very good. Young people should read more books. What's the problem? Let me take a look."
As he spoke, he glanced at Cai Peng next to him. It would be great if this lazy guy could be so worry-free. No, even one-fifth of his efforts would not mean that he could not write a single word in his graduation thesis for three months. Write it down.
Feeling the teacher's gaze, the graduate student stood aside shivering, feeling that it was not a good time to go out today.
Xu Chuan took out a notebook from his school bag and handed it over. Zhou Hai took it and flipped it over, saying: "It's okay. These questions are quite difficult, but I can teach you a little. You bring a chair over and I'll explain it to you." .”
Before Xu Chuan could leave, Cai Peng moved the chair under his feet and looked at him expectantly:
"Boss, please sit down."
"Boss, can I listen in?"
Xu Chuan was a little dumbfounded, but he declined and sat down. On the other side, Cai Peng was listening, and the three of them formed a small classroom.
...
"This question is related to linear functionals. This course has not been taught in freshman year, but you should have learned it. It needs to be processed by Fourier transform. Let's take a look at the convolution theorem in Fourier transform. From it Start, then turn to the function, and then converge this line of formula to converge the exponent of L² to within the f norm..."
"...."
"This last problem is quite difficult. It mixes the knowledge of number theory field value calculation and Hilbert space. It needs to use domain expansion to turn it to commutative rings..."
...
In the small office, Xu Chuan eagerly absorbed new mathematical knowledge from Zhou Hai, asking some questions from time to time and calculating some formulas on the manuscript paper with a pen.
At this time, Zhou Hai would stop explaining and wait quietly for Xu Chuan to finish the calculations. After finishing the calculations, he would add some knowledge points to the calculations and answers.
This is a scene that is said not to happen in college classes. In college classes, when teachers explain knowledge points, they usually flip through the book faster than they turn around, and they basically don’t stop and wait for you to digest and understand.
Therefore, in the process of learning, it is really important to have a good teacher who can lead you forward and expand your knowledge boundaries.
...
