Which of you understands?

Author: Qian Yueqiu

Which of you understands?

Tang Yanshan looked at the draft paper in his hand, and his facial expression gradually became solemn and serious. After about half a minute of touching it, he raised his eyes and looked at Xu Yun to ask about the relevant situation of this question.

"How did you start studying algebraic geometry?"

"I've been studying abstract algebra recently, and I came across the concept of algebraic geometry and wanted to understand it."

With a simple and honest smile on his face, Xu Yun met Tang Yanshan's gaze and answered in a deep voice.

It is impossible for him to bluntly say that he wants to prove the Hodge conjecture. This is still far away from his current mathematical level.

This explanation is undoubtedly more appropriate.

Tang Yanshan checked Xu Yun's final grades and knew that he had mastered the professional courses in his sophomore year very well. It was quite normal for him to start studying the contents of his junior year now. By then, he would be more confident in participating in the Higher Education Society Cup and win the trophy.

return.

Abstract algebra is a textbook for junior college students, but algebraic geometry is more complicated to understand.

You won’t be exposed to learning until you are admitted to graduate school.

Xu Yun had not yet fully understood abstract algebra, so he thought about studying algebraic geometry and would inevitably make some mistakes.

I didn't think about how I could run fast when I learned to walk.

The more talented a person is, the more they must work steadily and master every basic knowledge thoroughly.

It was precisely because of this concern that he specifically asked Xu Yun to make sure that the other party did not bite off more than he could chew.

After hearing Xu Yun's answer, he hesitated a little but decided to talk about it.

Then he stood up, picked up a piece of chalk between his thumb and index finger, faced the blackboard and started writing the argument for this question.

Xu Yun stared intently, fearing that he would miss any step.

The most important thing in the process of learning algebra is to combine images and equations. Think of the image as the set of all points on the coordinate plane that satisfy a specific equation, that is, the set of all solutions to the equation on the coordinate plane. Think of the equation as an abstract description of the image.

.

But in algebraic geometry, there are countless polynomials and images like this.

at the same time.

The graduate students in the audience were also attracted by the content on the blackboard, and they all confirmed what Tang Yanshan was writing.

"What Professor Tang wrote seems so complicated."

"Appears to be an algebraic geometry proof."

"This guy is too evil. Does he start studying algebraic geometry as a freshman?"

"I must have been a fake graduate student. I couldn't understand the process Professor Tang wrote."

"Where did he find the question?"

Tang Yanshan ignored his graduate student. After writing the entire proof process, he turned around and explained it to Xu Yun. During the process, he occasionally asked a few related extended questions.

After Xu Yun's own abilities were greatly improved, what he was best at was understanding problems.

Therefore, after listening to Tang Yanshan's explanation, he suddenly understood and answered all the questions fluently.

After speaking, Tang Yanshan smiled and asked, "Do you understand?"

"I understand." Xu Yun nodded.

Hearing this, a happy smile appeared on Tang Yanshan's face.

If he had just come into contact with Xu Yun, he might have replied, "You know nothing."

But now he knows Xu Yun's strength and character very well. Since he said he understood, there must be no problem.

It was just those graduate students who were miserable. After listening to Tang Yanshan's explanation, they still had blank expressions on their faces. It was obvious that they didn't understand it at all. Although they wanted to ask Tang Yanshan to explain it to them again, they couldn't say it.

Exit. After all, the people who asked the question have already understood it. How could they, the auditors, have the nerve to speak and embarrass Tang Yanshan.

Tang Yanshan did not erase the formula on the blackboard, but then he thought of something and gave Xu Yun a few special instructions.

"I know you are very talented in mathematics, but for now you still need to learn abstract algebraic real variable functions and functional analysis well. It is not too late to learn about algebraic geometry later."

"Don't worry, Professor Tang, I will make a plan." Xu Yun answered according to Tang Yanshan's words.

The matter was basically over at this point, but Tang Yanshan noticed that Xu Yun had no intention of leaving, so he picked up the cup and took a sip of tea to moisten his throat before speaking.

"What else can you do?"

"Professor Tang, can you recommend some topology-related textbooks to me?"

Xu Yun revealed his purpose with some guilt.

When Tang Yanshan heard this, his expression immediately dropped.

I just said that I can plan well, but as a result, the problems of algebraic geometry have not been completely solved, and now I have to contact topology again.

I really think I have forty-eight hours in a day.

"You kid..."

He was about to teach aloud, but he suddenly stopped just after saying three words.

Then he waved his hand and answered.

"never mind."

"With your personality, even if I don't let you learn it, you will definitely get in touch with it yourself in private."

"I'd better recommend some suitable textbooks to you."

"This will at least save you some detours."

While speaking, he took out a pen from his pocket and still wrote the names of several textbooks on the scratch paper.

"These textbooks can be found in the school library. Anyway, remember to arrange your time reasonably." Tang Yanshan put away his pen and handed the draft paper to Xu Yun in front of him again.

"Thank you, Professor Tang." Xu Yun suddenly felt like he had found a treasure, took it and thanked him quickly.

It just so happened that the bell rang for the end of get out of class at the same time, and Tang Yanshan started to pack his things and prepare to leave. Obviously, he would have other things to be busy with later.

Soon, as Tang Yanshan and Xu Yun left the Q&A room one after another, the graduate students immediately stood up and came to the blackboard.

Discuss with the large number of formulas on the blackboard.

“I don’t know where this junior student found the question, but it’s quite classic and interesting.”

"If any of you understand it, please explain it. I still don't quite understand it."

"I knew I should have asked Professor Tang to speak twice more just now. I really regret it."

"Do you think that junior student really understands it or does he pretend to understand it?"

"I understand a little bit."

As one of the tall boys raised his hand, everyone quickly shifted their attention and took out their notebooks or turned on their cell phone cameras to ask the other person to speak again.

The learning atmosphere was simply more intense than in the class just now.

Tang Yanshan didn't know what was happening in the Q&A room at this time. As soon as he reached the stairs, he saw Xu Yun waiting there.

He stopped temporarily and asked: "If you have anything else to do, please tell me everything."

"I'm waiting to go to the history department."

Knowing that Tang Yanshan was going to the Department of History to pick up his lover, Xu Yun didn't want to waste too much time.

With a smile on his face, he got straight to the point.

"It's just a little something."

"I knew you wouldn't give me something for no reason. If you have anything to do, just tell me." A smile appeared on Tang Yanshan's lips when he heard these words. He seemed to have guessed the situation, but after he finished speaking, he added: "

Let’s first say that if it can be done, I will definitely help. If it can’t be done, it’s useless even if you go to Dean Qin.”

"Professor Tang, I want to join the research group in our department to participate in project research."

Xu Yun did not hesitate this time. After telling his true purpose, he looked at Tang Yanshan's expression.

In order to complete the task, he must join the research group, even if it is just to learn and become familiar with it.

However, after noticing Tang Yanshan's solemn expression, his mood immediately calmed down and he understood that this matter might be ruined.

Just as he was about to respond, Tang Yanshan's voice sounded in his ears first.

"You want to prepare for the Higher Education Club Cup, right?"

Without waiting for Xu Yun to answer this question, he continued: "Mathematical modeling is different from real research. If you have experience in this field, it will be more friendly to you during the competition."

"Let me help you pay attention first."

Xu Yun didn't expect that Tang Yanshan would think of the Higher Education Society Cup, but seeing that things were promising, he naturally wouldn't worry about it.

He quickly expressed his gratitude from the bottom of his heart: "Thank you, Professor Tang."
To be continued...