From all-round academic master to chief scientist

The training course after the exam lasts for eight days.

At first, Lin Xiao went to class seriously. Of course, whether he took the class seriously or not is another matter. But later he found that many training team members did not go to study. Basically, only the students who signed up with their own money to attend the class attended the class, so he went to class. He stopped going to class after three days.

Of course, the training camp also opened a self-study room. You can go to the self-study room to study every day. There are also math teachers there. If you encounter problems during self-study, you can go to the teacher and ask.

However, Lin Xiao was just reading a book and had nothing to ask, so he just stayed in the study room and enjoyed the quiet study atmosphere.

However, he didn't look for the teacher. Instead, the teacher wandered around the study room and finally found him.

The teacher in charge of the study room is Xu Hongbing, a mathematics professor.

He walked next to Lin Xiao and took a look at this boy who was called the genius among geniuses in mathematics.

This student is quite famous in their training team, so it is normal for him to know Lin Xiao. However, this student... is actually reading abstract algebra?

Abstract algebra is not easy. Although he is not taught this in school, it does not prevent him from knowing that the failure rate of abstract algebra has always been very high, because most students who fail abstract algebra will also fail abstract algebra.

"Do you understand?"

"Ah?" Lin Xiao came back from the immersion, and then saw the teacher standing next to him, so he shouted: "Teacher Xu."

Then he replied: "It's okay, I understand."

"Takadai, did you watch it?"

"finish watching."

"Okay." Xu Hongbing nodded approvingly. Only such a mathematical genius has truly not wasted his talent.

If Lin Xiaohui forgets to make progress because he is now invincible in mathematics competitions, then he will obviously not have high achievements in the future.

Only by continuous learning and continuous improvement can the talents of geniuses be brought into full play. Otherwise, they will obviously end up like Shang Zhongyong.

At this time, Xu Hongbing thought for a while and said, "Then I will give you a question and you can do the math."

Lin Xiao nodded: "Being respectful is worse than obeying orders."

"You're a very polite guy."

Xu Hongbing joked with a smile, then took Lin Xiao's pen and started writing the title on his draft paper.

Although he does not teach abstract algebra, he has taught it to advanced students, and it is quite simple to ask questions.

[Suppose the n-order square matrix F is a friend matrix of a certain polynomial. Verify that the square matrix commutable with F can only be a polynomial of F. 】

"bring it on."

After writing, Xu Hongbing handed the pen to Lin Xiao.

The difficulty of the question he asked was considered to be on the upper side. He also wanted to test Lin Xiao's level of learning from advanced students and whether he could replicate the performance in the Olympiad where the gods killed the gods and the Buddhas.

In addition, there was also a knowledge point, which was the friend matrix. He wanted to know how well Lin Xiao grasped this remote knowledge point, or whether his knowledge was extensive.

But what surprised him was that Lin Xiao only thought for a minute and started writing without asking him what the friend matrix was.

[Proof: Suppose V is an n-dimensional linear space, ε1, ε2,..., εn is a set of basis. Let ψ be a linear transformation of V, so that the matrix of ψ under the basis ε1, ε2,..., εn is F, that is, ψ(ε1, ε2,..., εn)=(ε1, ε2,..., εn)F.

Because F is a friend matrix, ε2=ψ(ε1), ε3=ψ(ε1),…, εn=ψ^(n-1)(ε1). That is…]

Seeing Lin Xiao's previous two operations, Xu Hongbing suddenly took a breath of air. Could he be able to use linear space and linear transformation so skillfully?

Even in advanced algebra, this knowledge was considered difficult. He had always been cautious when asking such questions in the past, for fear of stumping the students.

Moreover, he did not expect that Lin Xiao would be able to think of using this method to solve it so quickly. Most students basically use standard unit column vectors to solve it.

He couldn't help but sigh in his heart, this student is really amazing.

No wonder he was able to show such momentum in the Olympiad. He was born for mathematics.

With waves in his heart, he just looked at Lin Xiaozhu.

It didn't take long for Lin Xiao to write the last step.

[So C=(n∑i=1)ci1*F^(i-1)(e1, Fe1, Fe1,…, F^(n-1)e1)=(n∑i=1)c1F^i- 1

So C is a polynomial of F.

Certification completed. 】

After writing the last two words one stroke at a time, Lin Xiao put down the pen.

Xu Hongbing saw that he had finished writing and said: "Very good, he did a good job."

Lin Xiao smiled and said: "Actually, it's not too difficult, it's nothing."

Xu Hongbing: "..."

"You don't think it's too difficult?"

Lin Xiao nodded and said truthfully: "It's okay, actually. I just finished reading advanced algebra a few days ago. If I can do it, it shouldn't be too difficult, right?"

Xu Hongbing: "..."

He felt the disdain from the student in front of him for the question he had asked.

Moreover, Lin Xiao actually said that he had only finished reading Advanced Algebra a few days ago?

"Have you just finished reading Advanced Mathematics?"

"yes."

"Self-taught?"

"Self-taught."

"You don't have a teacher to help you?"

"No." Lin Xiao said: "There is no such college mathematics tutoring in my hometown. Before I participated in the Olympiad, I did not participate in any training. Oh, that is, before the mathematics league, our school held a month of mathematics league training. class."

Hearing Lin Xiao's words, Xu Hongbing felt even more unbelievable. Lin Xiao was actually all self-taught?

He originally thought that Lin Xiao was able to do it because of the guidance of a teacher and his own talent.

Perhaps the teachers of mathematical geniuses have little contribution to their achievements, but mathematical geniuses must be indispensable for the guidance of a teacher.

Newton was so powerful, and his teacher was 'Professor Lucas' at the University of Cambridge at that time. Professor Lucas does not refer to a certain person, but an honorary position. Only recognized scholars can obtain this position, and only one person can obtain it at the same time. Being served by a teacher is enough to show how powerful Newton's teacher is.

Let’s talk about Einstein’s teacher, Minkowski. The famous Minkowski space-time occupies a very important position in the world of mathematical physics, and is extremely closely related to Einstein’s later theory of relativity.

Therefore, Xu Hongbing felt incredible.

Lin Xiao's educational environment was so poor, but he still showed such strong mathematical talent.

Sure enough, gold always shines. At the same time, he couldn't help but feel sorry for Lin Xiao. If he had a good teacher to guide him, Lin Xiao would have soared into the sky, right?

For example, I joined the IMO team when I was in junior high school.

But soon, he thought that Lin Xiao would enter college soon. As expected, Lin Xiao would choose those two schools.

In this way, he no longer has to worry about Lin Xiao's future. Such a genius will never be ignored in the university.

Of course, the above is the attitude that he, as a teacher, has towards any student, wishing him well. Putting aside these things, the questions he asked were looked down upon. How could he tolerate this?

Can he suffer the injustice of being a professional mathematician?

He has been invited to participate in the proposition group of CMO and college mathematics competitions, which is why he was invited to tutor these students.

So he said: "Then you are self-taught. You are very powerful and very good. I believe that you will be able to grow better after you go to university."

"Let's do this. I'll give you a few more difficult questions later. When you plan to leave, come to the podium to pick them up."

"OK."

Lin Xiao nodded.

Thanks to the book friend Fleeting Time_Passing Water for the 500 starting coin reward, and to the book friends Extrem, Xiaoshuai Counting Stars, Fat Cat Who Loves Snacks, and 20170728194229879 for the 100 starting coin reward.

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