Chapter 70 Questions that Stump the Mathematics Professor
The simple test allowed Professor Zhou Hai from the School of Mathematics to see Xu Chuan's mathematical skills, and he also became a little envious of Chen Zhengping from the School of Physics.
How come he hasn't met a student who has the skills comparable to a graduate student when he first enters college?
Although no one stipulates that a student cannot have two teachers, and even though they are two completely different subjects, he cannot shamelessly compete with Chen Zhengping.
"Teacher Zhou, I have a question." Zhou Hai was about to leave, but was stopped by Xu Chuan.
"Oh? What's the problem? Let me tell you." Zhou Hai asked curiously.
Xu Chuan took off the hanging schoolbag from the chair, took out a gray notebook, opened it and found the handwriting of the past two days.
After confirming that there was no mistake, he handed it to Zhou Hai.
"Teacher Zhou, these are some questions I listed when I was reading "Factorization of Linear Operators and Geometric Properties of Banach Spaces" in the past two days. I couldn't solve it halfway through the deduction. Can you help me? ”
"Okay, let me take a look."
Zhou Hai reached out and took the notebook, looking at it with interest.
Although the simple inquiry just now allowed him to see Xu Chuan's mathematical skills, it did not see his limits.
And the questions that can stump him must represent where the knowledge has reached.
Let him see how good this student is.
"This word is so beautiful."
After taking the notebook, Zhou Hai praised it in his heart for the neat handwriting on it.
To be honest, those who engage in mathematics really don’t have many good-looking words.
Of course, those who engage in mathematics do not need to have good handwriting. During the research stage, as long as what they write can be understood.
This is just like programming. As long as the code you write can run and you can understand its meaning and functions, it will be fine.
As for whether there are comments or something, does that matter?
unimportant.
As for really confirming or researching it, the worst case is that it takes a little more effort to type the paper into the computer.
So basically the handwriting of math teachers and mathematicians is very fast.
"Weyl'sLaw: Eigenvalue distribution and calculation of Laplace operator."
"Theorem 1: Assuming that ΩR is a bounded open region (no requirement for regularity of the boundary), then there is a monotonically rising unbounded sequence {λκ} that satisfies: 0<λ≤λ≤, limκ→∞λκ=+∞."< br>
"Theorem 2: If Ω is a cubic area, it is also shaped like [a, b]*[a, b]"
"Theorem Three:."
“If N(λκ) is the eigenvalue counting function on the bounded open region Ω, then can we construct a pair of isospectral isomorphic fractal drums in R3, and on this basis, prove its wave number? The function has an exact second term ”
The handwriting on the notebook came into view, and Zhou Hai's eyes were all focused on it.
"Is there any problem in the mathematics of equispectral non-isometric isomorphism and fractal drum?" "It is interesting to construct an equispectral non-isometry isomorphic fractal drum based on R3 to prove the second term of the wave number function."
"Can we use the principles of regional monotonicity and minimization to give a characterization of eigenvalues?"
"Hmm, this method doesn't seem to work?"
As his thoughts continued, Zhou Hai's brows gradually wrinkled.
From the beginning, I thought it was no big deal and could easily solve the problem, but now I am lost in thought and can't find a way out.
All his attention was focused on the gray notebook in his hand. He didn't even care about Xu Chuan. He directly took the notebook in his hand and returned to the podium. He picked up a piece of 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 inclusive relationship:: H (Ω)
Zhou Hai's actions naturally attracted the attention of the students who were taking the test to answer questions.
Everyone looked up at the blackboard to see what the professor was writing.
But when the mathematical symbols on the blackboard came into view, all the students except Xu Chuan were stunned.
Professor Zhou, what is he writing? Why can't I understand a word?
"Sichuan God, Professor Zhou is writing about some magic stuff? What question did you just give 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 Sichuan God handed Professor Zhou Hai a notebook and seemed to ask a question? Then Professor Zhou absentmindedly went up to demonstrate?
It should be a question, but what exactly is this demonstration pushing? And what kind of problem can stump a mathematics professor?
"Problems in the distribution and calculation of eigenvalues of the Laplacian operator."
Xu Chuan stared at the calculations in black and white and replied intently.
These calculation formulas are obviously Professor Zhou Hai's derivation of the problem. They have inspired him a little, but not much. At most, they can eliminate one route through this kind of thinking and cannot solve the problem.
"What is the Laplacian operator?"
The classmate next to me asked with a look of despair. It’s okay if you can’t understand the mathematical symbols on the blackboard. Why can’t you understand the students’ answers now?
Students from the same school and class attend the same class. Is the gap really that big?
"Oh, the Laplacian operator is a second-order differential operator in n-dimensional Euclidean space. It is a real-valued function and can only be learned in the junior year."
Xu Chuan finally came to his senses and explained with a smile.
The classmates around him nodded in understanding, although he still didn't understand what the Laplacian operator was.
But at least he understood the term 'real-valued function'.
As for why he only learned things in his junior year, while others started studying them in their freshman year, he no longer wanted to talk about it.
Can the IMO+IPHO double gold medal winner with perfect scores in the college entrance examination be an ordinary person like them?
Obviously not.
So is it surprising that people start studying and researching junior year courses in their freshman year?
Not worth it at all.
He even has the 'illusion' that this is how it should be.