Zhang Zhou and Gu Zhengliang looked at each other. can see that kind of innocence in their eyes......

What the hell is this? Don't listen to it, really.

If you don't know enough about the prepositions of algebraic geometry, you won't understand it.

It just so happens that the two have a fairly clear understanding of their knowledge reserves.

It is true that some of their classmates have been exposed to the content of GTM211 and even GTM52 early, but they really haven't been exposed to it.

Typical climbers have not yet been learned, and adults want to teach them to run.

After all, in the high-dimensional transformation, Chinese characters seem very simple, they are all commonly used words, but if you use mathematical language to express ......

"What is a high-dimensional transformation? For example, on a smooth manifold m, ξ can be defined as a spinor field, and its representation in a local coordinate system involves elements of the Clifford algebra, which are algebraic structures used to describe rotation and reflection in space.

Then its mathematical representation is this form......"

Xu Changshu turned around again and gave the answer.

"You should understand, so let's go back to the original topic......

……

Zhang Zhou and Gu Zhengliang have completely given up, it's not that they can't understand it if they miss a point, they can't understand it from the beginning.

The two didn't even bother to take up the pen again. And once they decided to give up, the two of them also felt relaxed and could focus on the classmates around them.

Everyone seemed to be listening very seriously......

However, as Professor Xu explained more deeply on the podium, the two soon found that their distractions began to increase......

This is a very mysterious feeling, and it can also be heart-to-heart between scumbags. No matter how serious they listened on the surface, as long as they made eye contact, both of them could tell that the thing was starting to paddle......

It felt very devastating, but when Zhang Zhou and Gu Zhengliang found out that there were other classmates who couldn't keep up, their mood suddenly improved.

Yes, these people may have a better foundation than them, and they must be more talented in mathematics than them, but when it comes time to not understand, is it different and incomprehensible?

This shows that at least in Qiao's algebraic geometry learning, everyone is still on the same starting line, which is good.

In one class, fifty minutes, Zhang Zhou and Gu Zhengliang felt that time could pass so quickly.

Xu Changshu also grasped the time very well, so he just talked about three example questions according to the usual rhythm, and the bell rang after class, and the third question was just finished. There was no drag, and Xu Changshu sat in the first row of the classroom with a teacup as usual.

It's just that the ten minutes of this recess are a little dull, and only Li Weiyang and Zhu Huanian came to Professor Xu in the ten minutes of recess, and they didn't know what they were talking about.

A few minutes later, Xu Changshu walked up to the podium without waiting for class and wrote two questions on the board.

A few minutes passed in a flash, and when the music for class started again, the two questions had already been written on the blackboard.

Question 1: The effect of the imaginary number ξ.

Consider a vector field v(x,y,z) = (x2y2,2xy,z) defined in a three-dimensional Euclidean space. The transformed vector field ξv is calculated by applying the transformation ξ(x,y,z)=(y,x,z) of ξ, and the properties and geometric significance of the transformed vector field are analyzed.

Question 2: Application of manifold factor μ in geometric transformations.

Let m be a three-dimensional manifold with the Riemann metric g, and the manifold factor μ describe the local rate of change of the metric g. If the value of the μ at a point p∈m is greater than a certain threshold, the geometry around that point will be deformed. Now, consider a simplified model where 2μ(x,y,z)=x2+y2+z2. Describe how the μ affects the path when the point (x,y,z) moves along the vector field v(x,y,z)=(y,x,0).

When the bell stopped, Xu Changshu knocked on the blackboard and said, "Okay, according to what I talked about in the last class, let's solve these two questions." A slight change, but not much. How the next course is arranged depends on your ability. I will give you some hints to flexibly understand the transformation of dimensions, that is, the increase or decrease of variables. ”

The students under the podium had mixed reactions.

Some people don't even bother to read the questions, while others continue to think about the example problems they explained before during the recess.

The most representative of the former is naturally Gu Zhengliang and Zhang Zhou.

As for the other students who did not try to solve the problem, they also have a very clear understanding of mathematics like the two of them...... There's no need to force a problem when you haven't fully figured out the basic concepts.

Of course, there are also attempts to solve problems.

For example, the squad leader Li Weiyang, the minor Zhu Hua Nian, and the Olympiad champion Luo Yao have already picked up the notebook and pen, but there is really no one who can start writing hard at this moment......

Most of them are staring at the subject of transcription...... Nibble on the tip of the pen.

It's not that these children are talented, it's just that the content is too abstract, and it is indeed a bit difficult to do example problems after only one lesson.

The classroom was quiet at first, but after ten minutes it began to whisper.

Xu Changshu didn't bother to care, sitting on the podium drinking tea, looking at the prepared papers.

I didn't even have the heart to go around the classroom and see how well the questions were answered. It's not that he looks down on these genius kids, he fully understands these basic concepts and can solve the problem casually, it took two weeks. Next door, the Institute for Advanced Study in Princeton took even longer to study those theorems and foundational problems.

This is when the masters already have a deep understanding of algebraic geometry. Although the children of Qiao Ban are extremely talented, and their basic skills are definitely more solid than those of other students, they must be far worse than those masters.

Even if these two questions are just simple variations compared to the example problems explained before, they are not fully understood at this stage.

Of course, if someone can really solve it, Xu Changshu will be very excited, and even if the mathematical talent is not as good as Qiao Ze, it is not much worse.

In this way, half an hour passed in the sound of "buzzing" discussions.

Xu Changshu suddenly put down the paper, stood up and stretched, and then patted the podium: "Okay, quiet." ”

The classroom quickly fell silent.

"Has anyone answered the two questions? Some raised their hands. ”

No one raised their hand.

Xu Changshu smiled and said, "Oh, it seems that everyone hasn't fully understood, so did anyone draw the corresponding figure, raise your hand." ”

Three hands were raised.

"Okay, show it to me."

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"Well, that's wrong...... You're wrong, hey, I wish you a good year, half right, worthy of praise...... Alright, let's all go back to our seats. ”

Xu Changshu glanced around the classroom, he must be too lazy to talk about the topic, there is no need to waste that time, but these little guys still have to be trained.

"It's something you're going to be exposed to in the second half of your second year, and it won't be okay now. Today's two lessons are just to teach you to be humble. I know there must be some of you who are still unconvinced. But I want you to ask yourself the first question, whether it is easy to solve the problem, or whether it is easy to start a study from scratch. ”

After speaking, Xu Changshu paused, gave these little children time to think, and continued: "Yes, I admit that you are all very talented. But no matter how talented you are, can you compare with Professor Qiao? When Professor Qiao was solving the problem of mass gap early last year, he found that existing mathematical tools could not solve this problem at all.

So some groundbreaking mathematical methods were used, and finally after a year of research and development, it became the current discipline, that is, the Joe algebraic geometry that you will inevitably be exposed to in the future. Professor Qiao was only 19 years old at the time. I know that many of you are only 17/8 years old, younger than Professor Joe, but can any of you pat your chest and promise that you will be able to achieve this in two years?

Do you really think that Professor Qiao started to study these mathematical problems after coming to Xilin Institute of Technology? No, let me tell you this, Professor Qiao has been thinking about the mass gap problem of the roots of the Yang-Mills equation since he was in the sixth grade of primary school. Come on, a few of you who already have a foundation in advanced math or calculus in the sixth grade of elementary school raise their hands to show me. ”

This time, the audience weakly raised five hands.

Scold......

"What about branches like linear algebra, Lie groups, noncommutative geometry, quantum mechanics, and so on? No one, right? If you understand the Yang-Mills equation, you will know that if you want to think about it, these are all things that you have to learn. In the sixth grade of primary school, Professor Qiao has already learned these prerequisites through self-study.

So, tell me, do you still think that the foundation of mathematics that you have laid before is very strong? I teach mathematical analysis in Yanbei, and I often tell new students that the mathematics content you study in high school is not the same thing as the mathematics content in mathematical analysis. When it comes to higher math, too much knowledge is counterintuitive.

In the same way, I'm going to tell you today that you'll have to wait until your sophomore year to really start getting into Joe's algebraic geometry to really understand why mathematics is an abstract art. Joe's algebra is a special algebraic system in which every concept is extremely abstract.

For example, even the simplest supercoiled numbers contain generators, such as spinors and vectors, and follow specific reciprocal and anti-reactive relations. Our aim is to use elements and operations in supercoiled algebra to construct and demonstrate complex theoretical frameworks and even models of the universe.

So since you have chosen mathematics, please give up those feelings of superiority. Because in this era, there is only one mathematical genius, and his name is Qiao Ze. So far, at least, no one of the contemporary mathematicians has the right to be proud of him.

And your greatest luck is that some of them can become students of Professor Qiao at the master's level if they can show their best side in these two years. The premise is that you can meditate on all the lessons for these two years.

As a reminder, the textbooks and course arrangements you use are all personally decided by Professor Qiao, and they are all necessary to learn if you want to fully master Joe's algebraic geometry. He didn't leave his name on the textbook, he just didn't care about these false names, do you understand? ”

"Got it!"

Although the morale of the answer this time was not too high, it was very neat.

"Alright, let's get out of class."

The words fell, and the music after class also happened to sound, and Xu Changshu walked out of the classroom.

The next moment, Zhang Zhou and Gu Zhengliang were "surrounded" by their classmates.

This may not be accurate, because the position of the two is in the middle of Qiao Ban, which means that the two of them have been surrounded all the time, but they usually don't communicate much. But today, the children, who were younger than the two of them, all took the initiative to come over.

"Lao Zhang, Lao Gu, I have a question that I am quite curious about, when you were roommates with Professor Qiao, ......" Li Weiyang was the first to ask.

"Didn't I tell you earlier...... Professor Qiao doesn't attend classes every day, and he doesn't stay in his dormitory except during bedtime, basically watching videos in the library or doing research in their rented house, hey...... Why do you keep asking? Zhang Zhou said impatiently.

"Uh...... Actually, what I want to ask is, how did you adjust your mentality when you were roommates with Professor Qiao? Don't you really think it's going to be a big hit? Li Weiyang had a curious baby's expression, and his face was already young and immature, not like he was scolding.

But obviously this is more uncomfortable than swearing, especially the tone is still so sincere.

Just when the smiles on the faces of the two froze and their hearts were full of MMP, there were people next to them to help.

"Yes, yes, the mentality of the two seniors is really good. Hey, what Professor Xu said just now made me want to change majors. It feels like big things are much easier than math. It's too hard to learn. In the afternoon, I just understood a concept, or the simplest one, I really don't know how Professor Qiao came up with it! It's horrible! ”

The youngest Zhu Huanian added.

"Let's ......" Gu Zhengliang opened his mouth to say, and suddenly didn't know how to continue.

Fortunately, the attention of these geniuses has been taken away from the two of them and put on Zhu Huanian.

Then everyone really gathered together and started a lively and passionate discussion.

"Xiao Zhu, tell us about the part you understand."

"Uh...... Okay......"

Zhang Zhou and Gu Zhengliang naturally couldn't join in this kind of discussion.

The two looked at each other again, and only felt the unevenness of the world. Anyway, these people's mentality repair function is also very good, isn't this a heated discussion?

……

Xilin Institute of Mathematics Building.

Qiao Ze didn't know that Xu Changshu used his deeds to teach Qiao Ban's children a lesson, mainly because he didn't care much about these.

For him, a quiet research environment is the most important thing.

In the office on the other side, Li Chengze was nervously communicating with Doudou.

On the one hand, it is not very adaptable......

But there is no way, Professor Qiao must know many things, but he is too lazy to deal with them, so it is enough to communicate directly with Doudou. Just like Lu Bei, Qiao Ze's schedule is all Doudou reminding Lu Bei, saving the trouble of manual recording.

On the other hand, the content of this exchange is big and terrifying.

It's about rats......

"Are you sure it's true?" Li Chengze nervously typed this question in the dialog box.

Soon Doudou gave the answer in the chat box, which is still its style, free from humans, and still uses rhetorical questions.

"Do you know why you humans always have problems that remain unsolved?"

Although he didn't like Doudou's way of chatting, Li Chengze still quickly responded: "I don't know, you said." ”

"Because the people who are often responsible for solving these problems are the ones who create them. Hilarious"

Li Chengze ignored Doudou's expression at the end of his answer, and an inexplicable frustration suddenly rose in his heart......

Even artificial intelligence believes that Huaxia is destined to rise, why do some people refuse to believe it when they die?!

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