Chapter 408 seems to be a bit difficult
On Monday at 1: ., Xu Qingzhou took a taxi to MIT. Seeing that there was still half an hour before class, he simply found a bench on the side of the road and sat down.
Take out the notes on complex functions from your bag.
In addition to mathematics, complex functions can be used to describe phenomena such as electromagnetic fields and fluid mechanics. In electromagnetism, complex functions can also be used to describe the distribution of electric and magnetic fields. In fluid mechanics, they can be used to describe the flow characteristics of fluids.
He has been trying to start from these aspects these days to see if he can come up with something new.
Just as Xu Qingzhou was watching intently, a voice suddenly sounded in his ears.
"Excuse me, how do I get to Room B6-112?"
He looked up and saw an Asian-looking girl asking timidly.
Xu Qingzhou glanced at the time and saw that there were still 10 minutes until class. He packed up his things and stood up, smiling and saying, "I'll take you there."
"No need to trouble you, just show me the way."
The girl was very embarrassed and waved her hands repeatedly.
"I was just about to go over there."
Xu Qingzhou shook his head and turned a corner, walked into the teaching building, glanced at the girl, and asked, "Are you from Xia?"
"The same to you?!"
The girl was stunned at first, then looked surprised and asked in Chinese.
"Yeah." Xu Qingzhou nodded slightly.
"It's great to meet a compatriot. I just thought you might be from Xia Country."
The girl said: "This is my first time studying abroad, and I haven't adapted to the living habits and environment here yet."
“It would be nice if you could spend more time abroad.”
Xu Qingzhou chuckled, paused, and asked, "Are you interested in prime numbers?"
"Not really. This class has high credits. Besides, it's Professor Roberts' class. I've read many of his papers before."
As the girl was talking, she looked at the boy next to her. When she saw Xu Qingzhou noticed that he was peeking at her, she said, "You look familiar. By the way, my name is Sun Simin, and I major in pure mathematics."
"Xu Qingzhou."
"Oh, Hello."
Sun Simin nodded first, then her body stiffened, "Wait, you are Xu Qingzhou!"
"Let's go. Class is about to start. Find a seat by yourself." Xu Qingzhou nodded with a smile. This girl looked a little silly, but he saw a little bit of his past self in her.
After staying in the domestic education system for a long time, I felt very uncomfortable when studying abroad.
"Oh, alright."
Sun Simin came back to her senses and saw that everyone in the classroom was staring at her. She felt a little helpless and lowered her head to look for a seat.
There were 22 people in this elective course. Perhaps because the class was about to start, he took a rough look and found that there were enough people.
"Xu Qingzhou!"
A tall and thin young man came up to me, staring.
Xu Qingzhou felt a little helpless. How did these foreigners manage to pronounce the first word incorrectly?
Even though he was complaining, he still nodded and said hello.
"Idol, we finally meet." The young man said excitedly.
Xu Qingzhou said helplessly: "I'm very happy to meet fans. However, I have more important things to do now than to hold a fan meeting."
The lecture hall suddenly became lively.
Xu Qingzhou walked up to the podium and did not waste any time. He waved his hand to signal everyone to be quiet and said with a smile, "Unfortunately, Professor Roberts cannot teach the class due to work reasons. I will take over the class. I hope everyone will not be disappointed." "No, no, no, we are very lucky!"
"False God!" someone else shouted.
"."
许青舟正式开始上课，从素数的定义开始：“素数是指只有1和它本身两个正因数的自然数，且最小的素数是2例如，2、3、5、7等都是素数。”
"The uniqueness, infinity, and distribution patterns of prime numbers are the basis for studying prime numbers and the key to understanding their application in various fields."
10 minutes passed.
"Brother, do you think it's very simple?"
Offstage, the young man chatted with the person next to him.
The person next to him nodded and sighed: "When I met Xu Qingzhou just now, I was a little excited, but now I have no pressure at all, and even feel a little bored."
In the corner, Sun Simin had a serious expression on his face. In just a short while, he had already written down a page of notes.
The young man sighed: "Me too. Wait, this one seems to be a little difficult."
30 minutes later, the classroom was surprisingly quiet.
The young man looked at the whiteboard, with only one question in his mind: "Who am I and where am I?"
At this time, Xu Qingzhou had already moved on from easy-to-understand conceptual things to the distribution law of prime numbers, and began to talk about Mertens' theorem and the prime number theorem.
Everyone's eyes were fixed on the equations on the blackboard with serious expressions, and quite a few people were already showing confusion.
Most of what Xu Qingzhou talked about were basics, but it was like a big boss who had already reached the maximum level instructing a rookie in the foundation-building stage on the most basic moves and techniques. Although most of them were basic content, they were mixed with the big boss's understanding of "Tao".
It is still difficult to gain a comprehensive understanding.
Sun Simin could no longer keep up, and while marveling at the process, she took out her phone to record the steps.
Xu Qingzhou thought it was pretty good. It was indeed a magical feeling. When he took out the familiar knowledge and repeated it again, he would suddenly discover new things.
For example, when estimating the asymptotic formula for the sum of reciprocals of prime numbers, we found that the formula was sufficient to derive the algorithm of the sieve of Ehrlich, and new content could be extracted from the remainder.
Or, when you encounter a problem, you can solve it in four or five ways.
"Mertens' constant is related to the zeta function, and the Euler product of the zeta function is often used to explore number theory objects. In this case, in order to conveniently explore the properties of the equation when s is near 1, we can try to set s=1+δ."
He began to derive relevant questions and concepts.
The young man turned around and saw someone next to him taking pictures of the whiteboard with his phone while taking a bunch of notes. He couldn't help but whispered, "Do you understand?"
"I don't understand." The man shook his head and raised his chin towards the back of the classroom. "Look at Dr. Deris's expression and you should know that what Xu Qingzhou said is very important."
The young man turned around and saw a young man listening attentively.
Xu Qingzhou finished writing the last row of formulas on the whiteboard. His first class at MIT was coming to an end. He put down his marker and said with a smile, "Everyone, today's class ends here. At the end, I will leave a problem. I hope someone can solve it in the next class."
He wrote the question on the whiteboard.
The general Selberg asymptotic formula is derived using this technique. It is necessary to complete the original proof of the Selberg formula and then derive it to an arithmetic progression.
Hua Luogeng left similar exercises 70 years ago, which is considered the most computationally intensive part of number theory in the proof of the prime number theorem. The exercise left by Xu Qingzhou does not require much computation, but it has very high requirements for basic skills.
At the very least, it is extremely difficult for ordinary undergraduates.
But 90% of the people who can get into MIT have something good.
After the lecture, Xu Qingzhou did not stay long. He left his email address, packed up and left.
(End of this chapter)
