Starting from a top student and marching towards the sea of ​​stars

Chapter 52 Chapter 52 Four ways to prove Banach’s fixed point theorem
Qiu Chengtong still asked Ning Chen questions in the form of chat.

Ning Chen simply organized his words and answered truthfully:

"Mainly because of my love for mathematics. After I completed the self-study of advanced mathematics courses, I asked the teacher for a course list of mathematics majors, and went to the library to borrow a lot of relevant textbooks. There was still a lot of time in my freshman year. , enough for me to complete a lot of self-study courses..."

Listening to Ning Chen's answer, Qiu Chengtong also nodded repeatedly.

This is basically consistent with Qiu Chengtong's previous guess about Ning Chen. Qiu Chengtong thought that Ning Chen should be a very special kind of student. Relying on his strong talent and perseverance, he insisted on being in an environment where the teaching level is not so good. In, let yourself become outstanding.

"Ning Chen, tell me about your favorite mathematical theorem."

This time, Qiu Chengtong finally asked Ning Chen a professional question, but this question was very open-ended.

"What is your favorite mathematical theorem... it should be Banach's fixed point theorem."

Hearing Ning Chen's answer, Qiu Chengtong also felt very interested.

The Banach fixed point theorem is not a particularly advanced theorem. As long as you have completed a one-year course in mathematics, you will basically understand this theorem and complete the proof of this theorem.

"Why do you like Banach's fixed point theorem?" Qiu Chengtong asked.

"Actually, at the beginning, I didn't think this theorem was so special. But as I continued to study mathematics, I found several methods to prove Banach's fixed point theorem from different angles, which made me It was very interesting."

"All ears." Qiu Chengtong said with a smile.

Without any hesitation, Ning Chen directly picked up the chalk and started writing on the blackboard.

It is not an exaggeration to say that with the knowledge Ning Chen has mastered, even if Ning Chen is asked to say a hundred of his favorite mathematical theorems, he will not be stuck at all.

Ning Chen knew that Qiu Chengtong wanted to understand his mathematical ability and attitude towards mathematics in a more comprehensive way through this question, so he chose a theorem that he thought could best demonstrate these things.

"When I first started self-studying mathematics textbooks, I learned about Banach's fixed point theorem and its proof method for the first time..."

While Ning Chen was writing on the blackboard, he was explaining to the teachers below the podium.

Because the teachers below are all top teachers in the field of mathematics, Ning Chen explained very quickly to avoid making the oral examination too long.

This first proof method is derived from the textbook. Apart from showing that Ning Chen's mathematical foundation is very solid, there is nothing special about it.

"The second proof method is what I thought of when I was studying differential manifolds..."

When Ning Chen explained the second proof method, the expressions of several teachers began to change.

Speaking of which, this proof method is not difficult for them to understand, but before Ning Chen explained it, they never thought that this method can also prove Banach's fixed point theorem.

After explaining the two proof methods, Ning Chen suddenly realized that his oral examination seemed to be a bit long.

"Teachers, the next two methods...do you want to continue listening?"

A teacher next to Qiu Chengtong said to Qiu Chengtong:

"Professor Qiu, there are many students behind us, why don't we just forget about it."

Qiu Chengtong ignored the teacher's words at all.

"It doesn't matter, keep talking, I'm very interested."

Naturally, Qiu Chengtong would not care about these rules, anyway, since this is a competition held in his own name, he must have the final say.

At worst, we can just let the students behind us postpone it. Those students who are not so satisfied can also shorten the oral examination time.

After getting Qiu Chengtong's consent, Ning Chen continued:
"The third proof method is what I thought of when I was learning the calculus of variations..."

While Ning Chen was explaining these things to several professors, several students were waiting anxiously outside the examination room. "Isn't my oral exam at 7:15? Why is it almost 7:[-] now and it's not my turn yet?"

Tang Ding kept looking at the time on his watch and pacing outside the examination room.

In anxiety, Tang Ding found the staff and asked.

"Teacher, I was notified yesterday that I will have an oral exam at 7:15, why hasn't it arrived yet?"

"Student, this is just a reference time, and the specific information is subject to the on-site notice."

"Okay, then I'll wait."

A student next to Tang Ding saw this and said to Tang Ding:
"It's like seeing a doctor in a hospital. Don't care what time you are registered. If you haven't finished reading the last patient, you won't be able to go in when it's time."

"Hey, that's true. But who was the last one to go in? Why didn't you come out for so long?"

In the examination room, Ning Chen continued his explanation.

"The last method came to my mind when I came into contact with the knowledge of cohomology groups..."

Finally, after writing several more blackboards, Ning Chen completed his explanation.

After listening to Ning Chen's entire explanation, Qiu Chengtong was completely convinced by Ning Chen.

"I really didn't expect that you could give so many different proof methods for a simple Banach fixed point theorem. And each of these different proof methods has its own significance."

Qiu Chengtong had to admit that when he first learned this knowledge, he didn't think as much as Ning Chen did.

Now it seems that there is indeed a reason why Ning Chen was able to achieve excellent results in the written examination.

"Ning Chen, I see that you just explained things in a thorough and orderly manner, just like a teacher. Do you usually give lectures like this to others?"

Qiu Chengtong was somewhat surprised by Ning Chen's ability to explain. Among the outstanding students Qiu Chengtong had come into contact with, there were few who could express themselves as clearly as Ning Chen.

Even in terms of expressive ability alone, many university teachers may not be able to compare with Ning Chen.

"I take some tutoring classes during my free time. While exercising my abilities, I also earn some living expenses."

Of course, Ning Chen's answer was just an excuse, and it was mainly due to Ning Chen's experience as a teacher in his previous life.

Ning Chen has been in contact with all kinds of students in education and training institutions, and he has trained himself to teach in different situations.

"Well, it would be good to be a tutor."

Qiu Chengtong glanced at the time and found that it was past 7:[-].

If this continues, I won't be able to complete the oral exam on this day, and there will be an awards ceremony in the afternoon.

"Okay, let's go here then."

"Okay, thank you teachers."

After finishing the oral test, Ning Chen could finally relax completely. He had completed all the tasks of this competition.

The next step is to wait for the results to come out.

Tang Ding, who had been waiting outside the examination room for a long time, saw that the door of the examination room was finally opened, so he hurried over.

(End of this chapter)