Great Country Academician

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 got stuck in the process of verifying the proof, how to expand the domain and convert the function into a subgroup and establish a connection with the intermediate domain and the set.

His lack of mathematical knowledge in this area is quite serious. He knows some functions, but he is not familiar with domain expansion.

But if you want to read books, you have to start with algebra and number theory.

Because the field is related to algebraic number theory, and the expansion of the field is evolved from the field theory of abstract algebra.

Simply put, everyone knows that 'addition, subtraction, multiplication and division' are the most basic four 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 I do to be able to add, subtract, multiply and divide? Count each one? That would be too much trouble.

Therefore, mathematicians have 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 on which there are "addition", "subtraction", "multiplication" and "division".

So if you want to thoroughly understand the 'field' 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 stayed in the dormitory, except for three meals a day, basically never going out. 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 already caused him to accumulate some questions and doubts. These things are recorded in the notebook. Xu Chuan is going to find Professor Zhou Hai this afternoon, or ask him to recommend a personal communication to solve them before continuing.

Bringing the notebook, Xu Chuan came to Zhou Hai's office.

For him, solving a math problem or learning a little new knowledge brings him happiness like a game fan who directly shoots his head while playing CF or learns the blind man's handsome eye-touching maneuver when lol Kicking and getting R five at a time in the rankings, and there is an orphan Suo next to him to take advantage of the situation to take advantage of the situation and destroy the opponent.

When he stood in front of the office door and knocked on the door 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 for cold medicine has not been given to him yet.

"Khan, why did I forget to do this?"

Xu Chuan patted his head annoyed. At the beginning, he agreed to return the other person's things the next day, but it has been three days. If it gets out, don't people misunderstand that he took other people's sister's 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, the cold should be completely cured, right?"

In the office, Professor Zhou Hai glanced at the figure walking in, and when he saw the person coming, his face was filled with a smile.

"It's done, thank you teacher for your concern."

Xu Chuan gently closed the door and kept the heating in the office. In the office, there were not only Professor Zhou Hai, but also Cai Peng, who had accidentally wiped out his graduate thesis.

"The boss is here, what is the boss going to study next? Tell me first, let me prepare myself a little bit, at least for my graduation thesis to avoid your research direction."

Cai Peng got up, poured a glass of water for Xu Chuan and asked with a smile.

"Weyl_Berry guesses, I want to try to see if I can develop something new."

Xu Chuan smiled embarrassedly. Although it wasn't his fault, it was still a bit embarrassing to face the culprit.

"Huh, that's good, come on, I like you!"

Cai Peng breathed a sigh of relief. Fortunately, he changed his graduation thesis in time and didn't continue to insist on Weyl_Berry's conjecture. Otherwise, he might not have graduated with a Ph.D., and his research goals would be gone.

Xu Chuan turned his head to look at Professor Zhou Hai, and said, "Teacher, I have encountered some problems while watching "Linear Algebra" and "Line Algebra to the Right" these two days. Can you help me?"

"Huh? Aren't you studying Weyl_Berry's conjecture? Why did you suddenly switch to wire generation?" Zhou Hai asked curiously.

"I want to take advantage of the recent time to read more books to enrich my brain." Xu Chuan said shyly, without revealing the real reason.

Zhou Hai was stunned for a moment, and then said: "It's good, young people should read more books, what's the problem? Let me see."

While talking, he also glanced at Cai Peng next to him. It would be great if this lazy guy can be so worry-free. No, with one-fifth of the effort, it won't take three months to write a graduation thesis without a single word. Write it down.

Sensing the teacher's gaze, the graduate student brother stood aside shivering, feeling that it was not suitable to go out today.

Xu Chuan took out the notebook from his schoolbag and handed it over. Zhou Hai took it and flipped through it, and said, "It's okay, these questions are quite difficult, but I can teach you a little bit. Bring a chair over here, and I'll explain it to you. .”

Before Xu Chuan left, Cai Peng moved the chair under his feet and looked at him expectantly:

"Boss, please sit down."

"Boss, can I listen in?"

Xu Chuan didn't know whether to laugh or cry, and sat down after a bit of refusal. On the other side, Cai Peng was listening, and the three of them formed a small classroom.

"This problem is related to linear functionals. I haven't taught this course in freshman year, but you should have learned it. It has 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 formulas, and converge the index of L to within the range of f."

"."

"The difficulty of this last problem is quite high. It mixes the knowledge of number theory field value calculation and Hilbert space. It needs to use field expansion to turn it to commutative rings."

In the small office, Xu Chuan eagerly absorbed new mathematical knowledge from Zhou Hai, asking some questions and calculating some formulas on the manuscript paper from time to time.

At this time, Zhou Hai would stop explaining and wait quietly for Xu Chuan to finish the calculations. After the calculations, he would add some knowledge points to these calculation formulas and answers.

This is a scene that is said to never appear in a university classroom. In a university classroom, the teacher generally turns over the book faster than turning over the face when explaining knowledge points, and basically does not stop to wait for you to digest and understand.

So in the process of learning, it is really important to have a good teacher who can lead you forward and expand the boundaries of your knowledge.