I was a top student in America.
Chapter 103 You've even figured this out?
Chapter 103 You've even figured this out (Please subscribe)
Since learning ordinary differential equations, Li Ao has shifted his daily study focus to complex analysis and numerical computation.
He has gradually become familiar with topics such as analytic functions, residue theorem, and harmonic functions.
Further on, we move on to more advanced topics such as conformal mapping and analytic continuation.
The level of abstraction is significantly higher, and the difficulty is also considerable, leaving many undergraduate mathematics students questioning their existence.
But instead of being intimidated by these tedious formulas, Li Ao found them quite enjoyable.
In addition, after completing the discrete average of convex functions, he developed a strong interest in numerical computation and analysis. Now when he goes to the public library to study online, he usually carries "Numerical Analysis" and "Numerical Linear Algebra" with him, along with C++.
As one becomes more proficient in the finite difference algorithm, their intelligence attribute steadily increases.
That noon, Li Ao carried his secondhand laptop and water bottle and rode his bicycle early to the small discussion room on the third floor of the Eckhart Building at the University of Chicago, ready to sit in on Professor Jensen's routine group meeting.
When he pushed open the door, he was carrying two thick professional books, "Complex Analysis" and "Numerical Analysis," under his arm.
Since David Walsh spent a few days as Li Ao's teaching assistant at the summer camp and witnessed firsthand the kid's terrifying learning speed, he's now completely unfazed.
They even felt that it was quite reasonable for all of this to happen to Li Ao.
After all, he's just a high school student who hasn't even gone to university, yet he already has two respectable SCI papers accepted.
Isn't it normal that you can read a complex analysis faster than flipping through a novel?
David has even changed his previous habit of acting like a teaching assistant and has started to urge Li Ao on from time to time, hoping that he can learn more so that he can give him some good advice on his current project.
"Leo, come sit down. You're here so early today, the group meeting hasn't even started yet."
"Have you finished learning complex analysis?"
David saw Li Ao push the door open and waved first.
Benjamin, who was sitting next to him, also looked up and greeted him: "Good afternoon, Leo."
.
Benjamin originally lived in Wisconsin, but inspired by Li Ao, he didn't go home after returning from the IMO. Instead, he rented a short-term apartment in Hyde Park and planned to spend the rest of the summer vacation in his research group.
Li Ao nodded politely in response, walked over to the two of them, pulled out a chair, and sat down.
He first placed the kettle on the table, then unzipped his backpack and took out the heavy, secondhand notebook.
While waiting for the machine to boot up, he slowly picked up where David left off: "No, but I want to study the finite difference discretization algorithm today, and also practice some coding. Complex analysis can wait."
This is indeed a rather strange thing.
In the past, wherever Li Ao went, his standard equipment was always a thick book and a stack of draft paper. He would sit down and start working on problems.
This is the first time I've ever seen someone bring their computer directly to study algorithms and programming like this.
The main reason Li Ao did this was because there was a workshop on numerical simulation scheduled for tomorrow, and the speaker was a professor from the Department of Physics at the University of Chicago.
He figured he could find an opportunity to ask a few key questions during the Q&A session, which would not only improve his skills but also perhaps boost his intelligence. That's why he decided to start by coding some code today to familiarize himself with the seminar content in advance.
After listening, David and Benjamin stopped writing and looked at each other, both seeing a hint of surprise on each other's faces.
They originally thought that Li Ao was able to publish SCI papers one after another because he must have devoted all his energy to pure mathematics.
Who would have thought that he would now be researching numerical computation and program simulation?
Moreover, judging from his nonchalant tone, it's clear that this isn't the first time he's encountered these things.
A bizarre thought couldn't help but pop into David's mind:
Does Leo's day have forty-eight hours?
He couldn't hold back any longer and blurted out, "You've even mastered numerical calculations?"
"I wouldn't say I fully understand it, I'm just interested. Physical models and numerical calculations are the very scenarios that test the practicality of mathematical tools, so how can I not learn them well?"
Li Ao looked at him and answered with a serious expression.
As soon as he finished speaking, his gaze returned to the screen.
With hands on the keyboard, accompanied by the crisp "click-clack" of the keys, lines of C++ code quickly appeared behind the cursor.
This time, he practiced finite difference discretization, and wrote common numerical algorithms, including solving tridiagonal linear equations, Rayleigh quotient, and spectral radius estimation of discrete operators, etc.
Time passed slowly, and a notification appeared on the panel.
[Under intense study conditions — Intelligence +0.1]
David and Benjamin, who were standing nearby, leaned over to watch for a while, their expressions slowly shifting from initial surprise to blank stare.
I used to think that it was one thing for this guy to be good at math, but the fact that he was willing to spend time studying numerical methods and programming was enough to make me feel ashamed of myself.
But now that I'm staring at the screen in person, I realize that their coding skills are just as good as their math problem-solving skills.
David had always thought his touch typing speed was among the best of his peers, but compared to Li Ao's dazzling output, he felt like a two-finger typing grandpa who had just started using a computer.
What's most infuriating is that Li Ao hardly needed to check for errors or debug the entire process. The program, which was running line by line, didn't even pause or report an error, as if this kid had a built-in compiler in his brain.
Seeing this, the two of them lost even the mood to discuss their research topics as usual.
He simply sat there silently, sighing to himself. He couldn't understand why the differences between species could be so great, and yet he had to run into them at such close range.
Amidst setbacks and self-doubt, they persevered until nearly 2 PM. As soon as the group meeting ended, everyone packed up their things and returned to their offices.
The next morning.
Li Ao sat at the dining table in the apartment, quickly finished the breakfast his grandmother had prepared, and casually folded up the few pages of notes he had stayed up all night to organize and stuffed them into his backpack.
After his grandmother went downstairs to chat with the neighbors, he hopped on his bicycle and headed straight for the Gordon Center for Integrative Science at the University of Chicago, braving the summer breeze.
After parking his car and finding the large conference room, he belatedly realized that he had managed to snag a seat today, except for the fact that he arrived early—
Good morning, it was partly due to luck.
He had no idea that the physics department seminar would be this popular.
Looking around, the tiered conference room, which can accommodate more than 150 people, was already packed with people. Even the back aisles were full of people, and there were many students peeking out from the doors and windows.
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