Zhang Zhou and Gu Zhengliang exchanged glances. Both could see a kind of helplessness in each other's eyes...
What the hell is this stuff? Don't even bother, seriously.
When the content gets too abstract, if you don't have enough foundational knowledge in algebraic geotry, you won't understand it.
Luckily, both of them had a pretty clear understanding of their own knowledge reserves.
So of their classmates had certainly encountered GTM211, or even GTM52, much earlier than they had, but they themselves hadn't.
It was a classic case of not knowing how to crawl, yet the adults were already trying to teach them how to run.
After all, high-dinsional transformations—while their written form in Chinese looked deceptively simple, employing familiar characters—beca incomprehensible when described using mathematical language...
"What are high-dinsional transformations? Well, it's really simple. If you don't currently have an intuitive understanding, you can temporarily treat ξ as a differential operator. For instance, on a smooth manifold M, ξ can be defined as a spinor field, whose local representation in coordinate systems involves elents of Clifford algebra—these elents describe algebraic structures for rotations and reflections in space.
So, its mathematical representation appears in this format..."
Xu Changshu turned back to the blackboard once more and wrote down the answer.
"You all should understand this now. Let's return to the original problem statent..."
...
Zhang Zhou and Gu Zhengliang had already completely given up. This wasn't a matter of missing a few details and not understanding—it was not understanding from the very beginning.
The two of them didn't even bother picking up their pens to take notes anymore. And once they had decided to give up, they felt a strange sense of relief as they turned their attention to observing their classmates.
On the surface, everyone seed to be listening attentively...
But as Xu's lecture delved deeper, Zhang Zhou and Gu Zhengliang quickly noticed that the number of people zoning out increased...
It was a subtle phenonon—there was a certain unspoken bond between academic underachievers. No matter how intently soone appeared to be listening, just one glance was enough for them to judge that "this person has started slacking off."
Initially, they felt disheartened. But when Zhang Zhou and Gu Zhengliang noticed that other classmates were also starting to lose track, their mood suddenly improved.
Sure, maybe those people had a stronger foundational grasp, and undoubtedly their mathematical talent surpassed theirs, but when it ca to the point of not understanding, didn't they also fail to understand?
This at least proved that when it ca to learning Qiao's Algebraic Geotry, everyone was starting from the sa baseline. That was nice.
An entire fifty-minute class session passed, and to Zhang Zhou and Gu Zhengliang's amazent, ti had never flown by so quickly.
Xu Changshu managed the timing well too, finishing three examples within his normal pace right as the end-of-class bell rang. No overti was needed, and Xu, as usual, picked up his tea cup and sat in the first row of the classroom.
However, the ten-minute break felt slightly stifling. During the break, only Li Wei Yang and Zhu Huanian approached Professor Xu, chatting about sothing.
A few minutes passed, and before the next class officially began, Xu Changshu walked back to the podium and started writing two problems on the blackboard.
The brief interval vanished quickly, and by the ti the class-resuming chi rang, both problems were already neatly written out on the board.
First problem: The impact of the virtual boundary number ξ.
Consider a vector field \\( v(x, y, z) = (x^2 - y^2, 2xy, z) \\) defined in three-dinsional Euclidean space. Apply the transformation \\( ξ⋅(x, y, z) = (-y, x, z) \\) using ξ and calculate the transford vector field \\( ξ⋅v \\). Analyze the properties and geotric significance of the transford vector field.
Second problem: Application of the manifold factor μ in geotric transformations.
Let M be a three-dinsional manifold equipped with a Riemannian tric \\( g \\), where the manifold factor μ describes the rate of change in the tric \\( g \\). If the value of μ at a point \\( p ∈ M \\) exceeds a certain threshold, the geotric structure surrounding that point will deform. Now, consider a simplified model in which \\( 2μ(x, y, z) = x^2 y^2 z^2 \\). Describe how μ influences the path when the point \\( (x, y, z) \\) moves along the vector field \\( v(x, y, z) = (-y, x, 0) \\).
Once the bell stopped, Xu Changshu knocked on the blackboard and said, "Alright, solve these two problems based on what I taught last session. There are slight variations, but not much. From here onward, how the course proceeds will depend on your skills. Here's a tip: flexibly grasp the idea of dinsional transitions—that is, the addition and subtraction of variables."
The reactions of the students below the podium varied.
So didn't even bother reading the problems, while others were still imrsed in thinking through the previous examples discussed during the break.
The forr group definitely had Zhang Zhou and Gu Zhengliang as its representatives.
As for the other students who opted not to try solving the problems, they, like Zhang Zhou and Gu Zhengliang, had a very clear perception of their mathematical abilities… knowing there was no point in forcing themselves to attempt the problems without fully understanding the foundational concepts.
Of course, there were those who did attempt the problems.
For instance, the class monitor Li Wei Yang, underage Zhu Huanian, and math Olympiad champion Luo Yao had picked up their pens and notebooks, though none of them truly dived in with fervent energy...
Most were simply staring at the copied problems on the board… chewing thoughtfully on their pencil ends.
This wasn't because their innate talent had hit its limit—it was just that when the content was too abstract, and they'd only been introduced to it in a single lecture, asking them to solve examples was genuinely unreasonable.
At first, the classroom was very quiet, but ten minutes in, whispered conversations began erupting.
Xu Changshu couldn't be bothered to intervene, sitting at the podium sipping tea and flipping through his pile of prepared papers.
He didn't even take the ti to walk around the room and see how the students were doing with the problems. It wasn't that he looked down on these gifted children—he fully understood that mastering these foundational concepts to the point of easily solving problems had taken even him two whole weeks. Researchers at the Institute for Advanced Study in Princeton spent even more ti working on basic problems and proofs.
And that was under the condition that those renowned scholars already possessed deep understanding of algebraic geotry. While the students in Qiao Class were undoubtedly exceptionally talented with much stronger fundantal skills than their peers, they were still leagues away from competing with those legendary mathematicians.
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