Great Country Academician

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

Why hasn't he met a student who has a master's degree when he first entered university?

Although there is no rule that a student cannot have two teachers, and even though the two subjects are completely different, he can't have the cheek 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's the problem? Let's hear it." Zhou Hai asked curiously.

Xu Chuan took off 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 questions I listed when I was reading "Factorization of Linear Operators and the Geometric Properties of Banach Space" in the past two days. I can't solve them halfway through the deduction. Can you help me? "

"Okay, let me see."

Zhou Hai reached out and took the notebook, looking at it with great interest.

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

And the question that can stump him will definitely represent where the knowledge has reached.

Just let him see the depth of this student.

"This word is really beautiful."

After picking up the notebook, Zhou Hai praised the neat handwriting on it.

To be honest, there are really few good-looking characters who are engaged in mathematics.

Of course, those who are engaged in mathematics don't need their own handwriting to be beautiful, as long as they can understand what they write in the research stage.

This is the same as programming. As long as the code you write can run, you can understand what it means and what it does.

As for whether there are comments or not, is that important?

unimportant.

As for really wanting to prove or research it out, it’s a big deal to spend some time typing the paper into the computer.

So basically the handwriting of math teachers and mathematicians is flying around.

"Weyl's Law: Eigenvalue distribution and calculation of Laplace operator."

"Theorem 1: Assuming ΩR is a bounded open region (no requirement for the regularity of the boundary), then there exists a monotonically rising unbounded sequence {λκ} that satisfies: 0\u0026lt;λ≤λ≤, limκ→∞λκ=+∞."

"Theorem 2: If Ω is a cubic area, that is, it is shaped like [a, b]*[a, b]"

"Theorem three:."

"If N(λκ) is an eigenvalue counting function on a bounded open region Ω, then, whether it is possible to construct a pair of equidistant isomorphic fractal drums in R3, and on this basis, prove that its wave number function has an exact second term."

Once the handwriting on the notebook came into view, Zhou Hai's eyes focused on it.

"Isometric Isomorphism and Fractal Drum Mathematics?"

"Constructing an isospectral and non-isometric isomorphic fractal drum on the basis of R3 to prove the second term of the wave number function is interesting."

"Can you use the principle of regional monotonicity and minimalism to give a characterization of the eigenvalues?"

"Well, it doesn't seem like this method will work?"

As the thinking continued, Zhou Hai's brows gradually wrinkled.

From the beginning when I thought it was no big deal and could solve the problem at my fingertips, now I am lost in thought and can't find a way out.

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

N(λ)=Cn|Ω|λn/2+o（λn/2）.

Definition: H(Ω)={u∈ζ(Ω)|uQi∈H(Qi), i∈I}, H(Ω)+{u∈ζ.}

Naturally there is an inclusion relationship:: H (Ω)

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

Everyone raised their heads to look at the blackboard, wanting to see what the professor was doing.

But when the mathematical symbols on the blackboard came into view, all the students except Xu Chuan were dumbfounded.

Professor Zhou, what are you writing about? Why can't I understand a single word?

"God Chuan, Professor Zhou is writing something crazy? What question did you just send him?"

A classmate sitting next to Xu Chuan came over and asked curiously in a low voice.

He just saw with his own eyes that Chuan Shen handed Professor Zhou Hai a notebook, as if asking a question? Then Professor Zhou went up to give a demonstration in a daze?

That should be a question, but what exactly is this demo pushing for? And what kind of problem can stump a math professor?

"Problems in Laplacian Eigenvalue Distribution and Computation."

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

These calculation formulas are obviously Professor Zhou Hai's derivation of the problem, and he has some inspiration, but not much. At most, one route can be ruled out through this way of thinking, and this problem cannot be solved.

"What is a Laplace operator?"

The classmate next to him asked with a look of despair, it's fine if he doesn't understand the mathematical symbols on the blackboard, why can't he even understand the classmate's answer now?

Students in the same class in the same school, listening in the same class, is the gap really that big?

"Oh, the Laplacian operator is a second-order differential operator in the n-dimensional Euclidean space. It is a real-valued function, and it will only be learned in the third year."

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

This time, the classmates around him nodded half-understanding, although he still didn't understand what the Laplace operator was.

But at least he understood the term 'real-valued function'.

As for why he learned something in his junior year, others started to study it in his freshman year, and he no longer wanted to talk about it.

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

Obviously not.

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

Not worth it.

He even had an 'illusion' that it should be like this.