Chapter 408

Monday, 1:30 PM, Xu Qingzhou took a taxi to MIT. Seeing it was still half an hour before class, he simply found a bench on the side of the road and sat down.

Took out the notes on complex functions from his bag.

Besides mathematics, complex functions can be used to describe phenomena such as electromagnetic fields, fluid mechanics, etc., and 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 had been trying to start from these aspects these days, wanting to see if he could come up with something new.

Just as Xu Qingzhou was engrossed in reading, a voice suddenly rang in his ear.

"Excuse me, may I ask how to get to room b6-112?"

He looked up and saw an Asian-faced girl asking timidly.

Xu Qingzhou checked the time; there were 10 minutes before class, so he simply packed his things and stood up, saying with a smile: "I'll take you there."

"No need to trouble you, just point the way for me."

The girl was very embarrassed and waved her hands repeatedly.

"I happen to be going there."

Xu Qingzhou shook his head and said. He turned a corner at the street corner, walked into the teaching building, looked at the girl, and asked: "Are you from Xia?"

"You are too?!"

The girl was stunned first, her face surprised, and she asked in Chinese.

"Mm." Xu Qingzhou nodded slightly.

"It's so good to meet a compatriot... I just felt you might be from Xia..."

The girl said: "Studying abroad for the first time, I haven't quite adapted to the living habits and environment here yet."

"You'll get used to it after staying abroad for a while."

Xu Qingzhou said with a light smile, paused, and asked again: "Are you interested in prime numbers?"

"Not really, this course has high credits... and, it's Professor Roberts' class; I've read many of his papers before."

The girl was sizing up the boy beside her while talking. Seeing Xu Qingzhou discovered she was peeking, she said: "You look so familiar, right, my name is Sun Simin, pure mathematics major."

"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 yourself." Xu Qingzhou nodded with a smile. This girl, why does she look a bit silly? However, in her, he saw a bit of his own shadow from before.

Having stayed in the domestic education system for too long, he was very unadapted when studying abroad.

"Oh oh, okay."

Sun Simin came back to her senses. Seeing everyone in the classroom staring at her, she was a bit at a loss, lowering her head to find a seat.

This elective course had 22 people. Perhaps because class was about to start, he looked roughly, and the number was enough.

"Xu Qingzhou!"

A tall and thin young man greeted him, staring.

Xu Qingzhou was a bit helpless; how did these foreigners manage to mispronounce the first character?

Although complaining, he still nodded and greeted.

"Idol, we finally met." The young man was excited.

Xu Qingzhou said helplessly: "Very happy to meet a fan... however, compared to holding a fan meeting, I have more important things now."

The tiered classroom immediately became lively.

Xu Qingzhou walked onto the podium, didn't waste time, waved his hand to signal everyone to be quiet, and said with a smile, "It's a pity that Professor Roberts cannot teach due to work reasons; I will be teaching on his behalf, I hope everyone won't be disappointed." "No, no, no, we are very lucky!"

"Xu God!" someone even shouted.

"..."

Xu Qingzhou officially started the class, starting from the definition of prime numbers: "Prime numbers refer to natural numbers that only have two positive factors, 1 and itself, and the smallest prime number is 2. For example, 2, 3, 5, 7, etc., are all prime numbers."

"The uniqueness, infinity, distribution laws, etc., of prime numbers are the basis for studying prime numbers, and are also the key to understanding the application of prime numbers in various fields."

10 minutes passed.

"Brother, do you feel... it's very simple..."

Offstage, the young man chatted with the person beside him.

The person beside him nodded and sighed: "Seeing Xu Qingzhou just now, I still had some expectations; now I have no pressure, even feel a bit bored."

In the corner, Sun Simin's expression was serious; in just this short while, she had already taken a page of notes.

The young man sighed: "Me too... wait, now this... seems to still have some difficulty."

No errors in the content, keep reading!

30 minutes passed. The classroom was surprisingly quiet.

The young man looked at the whiteboard, his mind only had one sentence: "Who am I, where am I?"

At this time, Xu Qingzhou had already entered the distribution laws of prime numbers from the simple and easy-to-understand conceptual things, and started talking about the Mertens Theorem and the Prime Number Theorem.

Everyone's eyes were fixed on the formulas on the blackboard, their expressions solemn, and a considerable number of people already showed confusion.

Most of the content Xu Qingzhou taught was basic, but it was like a full-level big shot pointing out the most basic moves and techniques to a Foundation Establishment stage rookie; although most were basic content, they were mixed with the big shot's understanding of the "Dao".

Wanting to master it thoroughly was still very difficult.

Sun Simin couldn't keep up at all, and while amazed, she used her phone to take pictures of the steps.

Xu Qingzhou felt it was quite good; it really had a magical feeling, taking familiar knowledge out and teaching it again, suddenly discovering new things.

For example, just now when estimating the asymptotic formula for the sum of reciprocals of prime numbers, he discovered that the formula was sufficient to derive the algorithm of the Sieve of Eratosthenes, and new content could also be extracted from the remainder.

Or, encountering a problem, one could easily solve it in four or five ways.

"The Mertens constant and the zeta function are related, and the Euler product of the zeta function is often used to explore number theory objects. At this position, to conveniently explore the properties of the equation when s is near 1, we can try setting s=1+o."

He started to extend to corresponding problems and concepts.

The young man turned his head, seeing the person beside him using his phone to take pictures of the whiteboard click-click, and also taking a pile of notes, couldn't help but ask in a low voice: "Did you understand?"

"No." The man shook his head, and pointed his chin towards the back of the classroom again, "Look at Dr. Drees' expression, you should know that what Xu Qingzhou is teaching is very important."

The young man turned back, and sure enough, saw a young man listening intently.

Xu Qingzhou finished writing the last row of formulas on the whiteboard, and his first class at MIT was considered to be coming to an end. He put down the marker and said with a smile: "Everyone, today's class ends here. At the end, I will leave a question, I hope someone can solve it by next class."

He wrote the question on the whiteboard.

Using techniques to derive the general Selberg asymptotic formula, it is necessary to complete the most primitive proof of the Selberg formula, and then derive it to an arithmetic progression.

Hua Luogeng left a similar exercise 70 years ago, which can be considered the number theory part with the largest calculation volume in the process of proving the Prime Number Theorem. The question Xu Qingzhou left behind doesn't have a large calculation volume, but the requirements for the foundation are very high.

At the very least, for ordinary undergraduates, it counts as hell difficulty.

However, being able to enter MIT, 90% of people have something, right.

Xu Qingzhou finished teaching, didn't stay long, left his email, packed his things, and left.

(End of chapter)