parentshiftbook Chapter 27 Knowledge Reserves
Chapter 27 Knowledge Reserves
The first question on the test was this difficult; Professor Nolan is really ruthless.
If Li Ang hadn't been burying himself in university textbooks and grinding experience points these past two days, he might have actually been intimidated by the first question posed by Kayla Nolan.
This question tests the property of the average value of a harmonic function... The value of a harmonic function at the center of a circle is equal to the average value of its integral over the circumference...
"Furthermore, note the discontinuity of the boundary function; this can be directly calculated using Poisson's integral formula..."
"The boundary function is discontinuous; there are still pitfalls here..."
『u(0)=1/2π∫0↓2π↑u(re^iθ)dθ……』
"Use the integral from the control convergence theorem..."
Finally, we can determine that the value of u(x, y) at z=0 is 1/2.
In less than three minutes, Li Ang came up with the answer to the first big question.
This caught the eye of Kayla, who was still nearby.
Li Ang was too focused when he was doing the problems.
Kayla has met many gifted students and many fellow scholars who study mathematics, but very few can match Li Ang's abilities.
It's no wonder that Li Ang, who never went to school, could achieve such high proficiency in mathematics.
Based on this alone, Li Ang will be a master at solving math problems and researching mathematical conjectures with a pen in the future.
In addition, Li Ang answered the first question extremely quickly.
This demonstrates that Li Ang has a very good grasp of the theorems and formulas involved in advanced mathematics and can easily cope with various challenges.
While Kayla was pondering, Li Ang was scribbling on the test paper, and the answer to the second major question was beginning to take shape.
Seeing this, even Kayla, a mathematics professor at the University of Chicago, couldn't help but think to herself, "That's right."
After a moment of reflection, Kayla carefully led Nicole out of the office, closing the door behind them.
At this moment, Li Ang was engrossed in the exam paper in front of him, and whether the two people beside him were there or not had no effect on him.
As expected, the difficulty of the exam increased with each question.
Of course, this isn't a big problem for Li Ang's current level of mathematics.
What delighted Li Ang was that his experience in mathematics was increasing at a faster pace than when he was trying to figure it out himself by reading books.
This also reflects that the difficulty of the test set created by Kayla Nolan may have reached the ceiling of college students' mathematical level.
……
Two hours later.
The office door was pushed open from the outside.
Kayla and Nicole walked in together.
The situation on the ground was quite different from what Kayla had expected.
Li Ang did not lie on the table deep in thought.
He was intently flipping through a classic anatomy textbook called "Gray's Anatomy".
Kayla glanced at him with a hint of surprise, then quickly walked over to Li Ang. "Li Ang, time's up. Let me take a look at the test paper..."
As Kayla glanced at Li Ang's exam paper out of the corner of her eye, even though she was somewhat prepared, her pupils couldn't help but widen slightly.
The test paper was completely filled with answers.
It's incredible that a student with no high school education, who is entirely self-taught, was able to complete the questions she created herself.
Kayla set the time limit at two hours because she didn't want to waste each other's time. Deep down, she didn't think Li Ang could finish the questions within the allotted time.
After all, even the top juniors at the University of Chicago wouldn't be able to finish it within the allotted time.
As it turned out, Li Ang actually finished it.
"Professor Nolan, you've arrived...and Nicole too."
Li Ang looked up and saw Kayla and Nicole, and greeted them.
"Yes, Li Ang, even though the teacher was waiting outside, she was thinking about you the whole time..."
"Alright, Nicole, let's get down to business." Kayla waved her hand sternly. "Leon, sit here and rest for a bit. I want to see your test paper."
"Okay, Professor Nolan."
After saying that, Kayla pulled out a chair, spread Li Ang's exam paper on the table, and began to look at it carefully.
Nicole, curious, wanted to come over and see what was going on.
But after only a couple of glances, Nicole pouted and stopped looking.
What kind of amazing questions are on the exam paper?
"right."
"That's right."
"All correct!"
Kayla flipped through the papers from beginning to end and was surprised to find that Li Ang had actually gotten a perfect score on the test.
Of course, it's not without flaws.
For example, the last big problem that Li Ang solved was extremely complicated. Such an extremely complex solution could not possibly be the standard answer.
Li Ang got it right; it can only be said that he has a very solid foundation in theoretical mathematics, but he still needs to improve in some applications of advanced mathematical methodologies.
The answer area contains hundreds of lines of problem-solving processes, each step interconnected. A problem in any line will lead to a deviation in the final answer.
But Li Ang's paper was so neat, without any trace of correction.
What does this level of control mean?
In Kayla's view, even the doctoral students he personally supervised could not achieve the same level of performance if they used Li Ang's method to solve problems.
Deep down, Kayla had completely accepted the math genius in front of her who was only a high school student.
After a pause, she said, "You answered the test very well, Li Ang. You are indeed more than qualified to study at the University of Chicago..."
Before Li Ang could react, Nicole had already raised her small, white fist to her chest and cheered in celebration.
Kayla adjusted her glasses, glanced at Nicole to signal her to be quiet, and continued, "But I have a question for you."
"Professor Nolan, please go ahead."
"First, there's the block matrix problem you helped Nicole with. I noticed you made quite a few extensions to the Gaussian elimination method based on the block matrix structure, especially in the areas of Weinstein factorization and Schur complement theory. Could you elaborate on your thoughts?"
Kayla didn't start by talking about today's test paper; instead, she brought up the question Nicole had asked a few days ago.
"Okay, Professor Nolan. I have indeed been thinking about that question, here..."
Li Ang took out a piece of draft paper and started writing and drawing on the spot. The content was exactly the direction he had been thinking about and researching yesterday.
After listening to Li Ang's words, Kayla took a very subtle deep breath to calm herself down.
Any lingering doubts have now completely vanished.
"Did you already think of all this before you helped Nicole answer this question?"
"No, I only built a framework at the time. Later, when I was reading books, I figured out that this could be optimized into an M-matrix or an H-matrix... However, due to my limited knowledge, I don't seem to have the necessary mathematical tools to continue researching this problem."
It's hard for non-professionals to imagine how Keira Nolan felt after Li Ang said those humble, even self-deprecating, words.
Is this something a high school student would say?
If this level of research is considered insufficient in terms of knowledge, then 99% of the students in the University of Chicago's mathematics department would be considered insufficient.