The simple test made Professor Zhou Hai of the School of Mathematics see Xu Chuan's mathematical skills, and he was also a little envious of Chen Zhengping of the School of Physics.

How could he not have met a student who had the skills of a graduate student at the beginning of his college years?

Although no one stipulates that a student cannot have two teachers, and even though they are two completely different subjects, it is not good for him to be cheeky enough to compete with Chen Zhengping.

"Teacher Zhou, I have a question I want to ask." Zhou Hai was about to leave, but was stopped by Xu Chuan.

"Oh? What is the problem, let's hear it. Zhou Hai asked with some curiosity.

Xu Chuan took out the hanging schoolbag from the chair, took out a gray notebook from it, and opened it to find the handwriting of the past two days.

After confirming that there was no mistake, he handed it to Zhou Hai.

"Mr. Zhou, these are some of the problems I listed when I read "The Factorization of Linear Operators and the Geometric Properties of Banach Spaces" in the past two days, and I can't solve them halfway through the deduction, can you help me take a look?"

"Okay, I'll see."

Zhou Hai reached out and took the notebook and looked at it with interest.

Although the simple inquiry just now allowed him to see Xu Chuan's mathematical skills, he did not see his limits.

And the question that can stump him must represent where the knowledge has arrived.

Just let him see the depth of this student.

........

"This word is so beautiful."

When he started the notebook, the neat handwriting on it made Zhou Hai praise in his heart.

To be honest, those who are engaged in mathematics really don't have a few words that look good.

Of course, you don't need to look good in your own handwriting, as long as you can understand what you write in the research stage.

It's the same as programming, as long as the code you write can be run, you can understand what it means and what it does.

As for whether there is a comment or something, does that matter?

Unimportant.

As for the fact that you really want to confirm or research it, it is a big deal to type the paper into the computer.

So basically, the handwriting of math teachers and mathematicians is dragon and phoenix.

......

"Weyl's Law: Eigenvalue Distribution and Computation of Laplace Operators."

"Theorem 1: Suppose Ω⊂Rⁿ is a bounded open region (without requiring the regularity of the boundary), then there is a monotonically ascending unbounded sequence {λκ} satisfies 0<λ₁≤λ₂≤..., limκ→∞λκ=+∞."

"Theorem 2: If the Ω is a cube region, i.e., it is shaped like [a₁,b₁]*[a₂,b₂]......"

"Theorem 3: ....."

"If N(λκ) is the eigenvalue counting function on the bounded open region Ω, then can a pair of isospectral non-equidistant isomorphic fractal drums be constructed in R3 and on this basis, it is proved that the wave number function has an exact second term."

The handwriting on the notebook caught his eye, and Zhou Hai's eyes were all focused on it.

"Isospectular non-isomorphism and fractal drum math problems?"

"It is interesting to construct an isospectral non-equidistant isomorphic fractal drum on the basis of R3 to prove the second term of the wave number function."

"Can you use the principle of regional monotonicity and minimity to give a description of the eigenvalues?"

"Hmm, it doesn't seem to work?"

.....

As he continued to think, Zhou Hai's brows gradually furrowed.

From the state of thinking that it was no big deal to solve the problem at the beginning, to now falling into deep thought and unable to find a way out.

His attention was already focused on the gray notebook in his hand, and he didn't even care about Xu Chuan, he directly took the notebook in his hand and returned to the podium, picked up a white chalk from the podium, and began to perform the calculations on the blackboard.

N(λ)=Cn|Ω|λˆn/2+o（λˆn/2）.

Definition: H¹₀(Ω)={u∈ζ²(Ω)|uQi∈H¹₀(Qi),∀i∈I},H¹(Ω)+{u∈ζ².......}

Nature has an inclusion relationship::H¹₀(Ω)......

Zhou Hai's actions naturally attracted the attention of the students who were taking the test to answer the questions.

Everyone looked up at the blackboard to see what the professor was doing.

But when the mathematical symbols on the blackboard came into view, except for Xu Chuan, the other students were stunned.

Professor Zhou, what are you writing about? Why can't you read a word?

"Chuanshen, Professor Zhou is writing something about Shenma Dongdong? What question did you just send him? ”

A classmate sitting next to Xu Chuan leaned over and asked curiously in a whisper.

He had just seen Kawajin hand Professor Zhou Hai a notebook, as if he had asked a question? Then Professor Zhou went up to demonstrate it?

It should be a question, but what exactly is this demo pushing to? And what exactly is it that can stump a math professor?

"Problems in the Distribution and Computation of Eigenvalues of the Laplace Operator."

Xu Chuan stared at the equation on the black and white, and replied intently.

These calculations are obviously Professor Zhou Hai's derivation of the problem, and they have some inspiration for him, but they are not much, at most, they can eliminate a route through this way of thinking, and they will not be able to solve the problem.

"What's the Laplace operator?"

The classmate next to him asked with a desperate face, even if he couldn't understand the mathematical symbols on the blackboard, why couldn't he even understand his classmate's answer now?

Students in the same school and in the same class, is the gap really so big?

"Oh, the Laplace operator is a second-order differential operator in n-dimensional Euclidean space, and it's a real-valued function that you learn in your junior year."

Xu Chuan came back to his senses now, and explained with a smile.

At this time, the classmate next to him nodded as if he didn't understand, although he still didn't understand what the Laplace operator was.

But he understood the term 'real function'.

As for why he only learns things in his junior year, others have started studying them in their freshman year, and he doesn't want to talk anymore.

With full marks in the college entrance examination, can the IMO+IPHO double gold medalists be ordinary people like them?

Apparently not.

So is it surprising that people start studying and researching the curriculum of their junior year in their freshman year?

It's not worth it in the slightest.

He even had the illusion that he should have been.

.......