This was Qiao Yu's first time standing on the podium during class.
The perspective was different, and indeed the feeling was not quite the same. It turned out everything could be seen clearly, and any little movement was inescapable. It seemed that many times he had been overconfident, always thinking the teacher couldn't catch his small actions from below.
Actually, it was simply a matter of whether they wanted to address it or not.
Especially these little...no, high school older brothers and sisters, who didn't know how to hide their emotions at all. Whatever they were thinking inside was written plainly on their faces; they seemed very easy to deal with...
Then Qiao Yu glanced at Lan Jie standing by the side of the podium.
Sure enough, teachers were different. At least just by looking at that emotionless face, you couldn't explore what they were thinking at the moment.
After a sweep of the gaze, he finally focused his attention on the problem.
"Let's have everyone take a look at this problem. Hmm, even though it's slightly simple, it belongs to a very typical function equation analysis problem. You should be able to tell at a glance that this problem requires you to first consider the value of the function at a specific point to solve the equation...
At the same time, you can verify and eliminate various possibilities by constructing specific functions. With these two pieces of knowledge, I believe everyone already knows how to solve this problem."
"Ahem... Qiao Yu, directly explain your thought process." Lan Jie couldn't listen anymore and coughed twice beside him.
"Oh."
Qiao Yu nodded and resignedly picked up the chalk: "The first step is to prove that f(x) is strictly monotonically increasing. Let's start from the given f(f(x))=f(x^2)+x, and consider differentiating both sides with respect to x. We can assume f'(x) represents the derivative of f(x). Obviously, when f′(x)=0, then 0=1, which is a contradiction, therefore, f′(x)≠0..."
...
Five minutes later, Qiao Yu put down the chalk.
Beside him, Lan Jie sighed. Sure enough, this kid couldn't be stumped.
Qiao Yu's attention was on the new students below the podium. The situation didn't seem too good, only five students seemed to be thoughtfully following his problem-solving process, which included Ma Yufei and Lu Jia, whom he had interacted with.
The expressions on the majority of the students clearly didn't look like they understood, especially many were sneaking glances at Lan Jie standing on the other side of the podium...
Those pure and innocent eyes didn't seem to be pretending.
It wasn't just that they didn't understand; they couldn't even judge if what they were solving was correct or not!
Sure enough, Ma Yufei and Lu Jia approaching him wasn't an isolated case. These guys didn't seem particularly capable.
For a moment, Qiao Yu felt a bit sympathetic towards Lan Jie.
Hoping these people would win medals after training just to help the good guy earn some bonus money, the difficulty was truly too high.
It also made Qiao Yu immediately realize why Lan Jie was so good to him.
A competitor like him, who didn't need much training to compete, seemed to indeed be a scarce resource—highly sought-after. If the school had a choice, they wouldn't gather high school students with such clearly inadequate math skills to attend Olympic Competition training.
"Qiao Yu, you can step down now." Lan Jie nodded at Qiao Yu and then walked onto the podium.
As Qiao Yu stepped down, his back towards the blackboard returning to his position, Teacher Lan's voice followed.
"Qiao Yu's thought process was very clear, but he glossed over some crucial steps which you may not have completely understood. Let's take a look at the second question that Qiao Yu analyzed. While considering possible function forms using the construction method, Qiao Yu directly used f(x)=x+1 to substitute into the original equation, which actually requires some calculation...
Similarly, when proving uniqueness, Qiao Yu used the contradiction method to guide the analysis of possible differences in functions. The steps he omitted are actually derived from the derivative's monotonicity in the first question, and after supplementing, it looks like this...
To sum up, solving this problem requires a comprehensive use of differential basics, function property analysis, construction methods, and the contradiction method, etc. Today, I've also prepared a thought-provoking problem for you all, ... By the way, Qiao Yu, see me in the office."
...
Completely not giving Qiao Yu the time to negotiate business with classmates in the classroom, after class, Teacher Lan took Qiao Yu back to his office.
However, Qiao Yu didn't regret it much, as he already realized explaining the problems clearly to these classmates wasn't an easy task.
For example, he just watched helplessly as Lan Jie went through an example problem from earlier that evidently had a very obvious conclusion, one that anyone with a brain could figure out, and re-proved it again. The half-empty blackboard he left was filled completely...
Had it been him, just writing the board alone in this class would leave his hand crippled, making Qiao Yu deeply appreciate that teaching was indeed not easy.
"Come over, pull up a chair next to me." As they entered the room, Lan Jie directly gestured to Qiao Yu.
Qiao Yu obediently pulled over a chair and sat down.
Lan Jie had already opened the laptop, navigating to the Overleaf interface.
"This is an online LaTeX editor, there's no Chinese version, but given your level of English, you should have no problem using it. Let me introduce some main commands to you, starting with creating a paragraph..."
Without any unnecessary words, as soon as Qiao Yu sat next to him, Lan Jie began teaching him how to use the LaTeX editor, just as he promised over the phone yesterday.
This math teacher once again witnessed Qiao Yu's talent.
Qiao Yu didn't seem to take any notes—every operation only needed to be demonstrated once, and he understood it completely.
Command, formula editing, various lists, common package operations and debugging—all perfectly reproduced.
Initially, Lan Jie thought Qiao Yu was a bit reluctant when he said he understood, but when he let Qiao Yu try it himself, his skilled operation made Lan Jie doubt whether this kid had encountered it before and was just here to play with him today.
Originally, Lan Jie planned to let Qiao Yu return to school tomorrow during his rest time to reinforce what he had learned, but it seemed unnecessary now.
"Alright, that's about all you need to master. The reference definition is for writing papers, which you don't need for now. Go back and try doing some problems using the Little Alibaba Mathematics Competition Official Website's test system, and then upload your answers. You should have it fully mastered by then."
Seeing Qiao Yu finish the demonstration, Lan Jie spoke with a sigh of admiration.
After all, it took him at least a week to learn how to use this thing back in the day, and he wasn't nearly as proficient as Qiao Yu is now.
In the past, Lan Jie felt that the gap between him and those top students at Huaqing and Yanbei wasn't that significant—maybe it was just a bit of bad luck, or their mentor was exceptional, offering more resources. But now he no longer had this idea.
This world was indeed very unfair. Many students appeared to excel in academics, but the majority had already given their all, while the top ones might have just casually learned—the hell how do you compete with that?
And this guy skipped class for two days to earn money in an internet cafe just a few days ago...
"It really is quite simple. If I had known, I would have just found a tutorial to learn it randomly yesterday." Qiao Yu nodded, stating a fact.
Lan Jie looked at this little guy in silence and reminded him: "By the way, your class will start the first round of mock exams on Monday. Class thirteen doesn't need extra classes on the weekend, so start preparing. This time, apart from math, the other subjects might be quite difficult."
Qiao Yu glanced at Lan Jie, suddenly realizing that this math teacher seemed to have quite an influence, even able to organize exams for the ninth grade. He wasn't as pathetic as Qiao Yu had imagined...