I was a top student in America.

In the small lecture hall of the Mathematics Building, Professor Philip of the Department of Mathematics at UIUC is standing on the podium.

"Our workshop is not only a review of the courses in real analysis and complex analysis, but more importantly, it aims to train your innovative application of knowledge and your ability to solve difficult problems."

"Today's lesson mainly covers convergence theorems and several common applications of Lebesgue integrals in function spaces. We'll go over the exercises next time."

Sitting in the audience were dozens of senior undergraduate students preparing for the Putnam Competition, as well as some lecturers and professors who were observing the proceedings.

Li Ao and Benjamin, as auditors, also sat among the crowd.

Li Ao sat in the middle, his attention completely focused on the lecture notes in front of him.

He started by looking at the definitions of external measure and measurable set, and then proceeded line by line to understand the concepts.

After an unknown amount of time, several lines of notifications suddenly popped up in my field of vision—the system upgrade is finally complete.

System upgrade complete.

[Hidden Attribute Unlocked: Reputation]

Current Reputation: 100.0

[Unlock the term: Clear Expression]

[Entry Effect: When expressing opinions, you can quickly clarify the logic, find the most suitable way to express them, and clearly and accurately convey information, enhancing understanding. The effect strengthens as reputation increases.]

"It actually unlocked a hidden attribute."

Li Ao stopped flipping through the lecture notes.

He speculated that the reputation score of 100 might be related to the previous report in the Chicago Tribune or the early securing of a spot on the IMO national team.

In any case, getting a bonus attribute right after unlocking the new attribute is a pleasant surprise.

According to the entry, this ability will be of great help to him in writing papers and giving reports later.

Mathematical proofs emphasize clear logic; if you can clearly explain your ideas, you've already achieved half the success in scientific research.

It will be very useful whether it's for publishing research findings or applying for research funding in the future.

Pulling his thoughts back, Li Ao saw that there was still some time before get out of class ended, so he lowered his head and continued to look at the lecture notes.

……

At noon, the group from room 314 had lunch at the restaurant.

With the second phase of testing fast approaching, everyone's goal for the afternoon was surprisingly the same—to find a place to practice coding problems.

"I'm going to go to the lecture hall to reserve a seat for the afternoon's practice materials class and review the questions I got wrong in the first stage. I'm off now."

As soon as he stepped out of the restaurant, Kevin turned back and greeted him.

Taylor sighed, "We're all in the same boat. I'm also afraid of being called to the evening tutoring session. Let's go together."

After finishing the number theory and plane geometry topics in the last two days, the scope of the second-order test has been basically determined.

Each topic contains many extremely difficult proofs and construction problems, and with the addition of algebra topics later on, the number of problems is quite large.

To finish the entire test before the exam, you have to squeeze in study time during class breaks whenever you can.

Li Ao knew that Kevin's current grades were on the edge of selection, and he could easily fall out of the top six if he wasn't careful, so it was no wonder that he was working so hard.

This kind of high-pressure environment before exams is very common in summer camps.

"After all, this is the last big test, and nobody wants to mess up at this crucial moment," Kevin said, shrugging helplessly.

Ethan then turned to Li Ao: "Leo, what are your plans for this afternoon?"

"I'll go to the library to revise my paper first, and then I'll come find you guys for a group discussion later," Li Ao replied casually.

For others, securing a spot on the national team would require fierce competition, but he had already secured one, so there was no need for him to focus all his energy on the exam.

During the group discussion in the evening, it's enough to go over today's exercises.

The important thing now is to finish writing the thesis and continue learning ordinary differential equations and real analysis.

Moreover, having just received the new term "clear expression" today, he also wants to test its effectiveness on his own short essays.

Kevin and the others weren't worried about Li Ao's progress. After agreeing to meet in the public discussion room that evening, they hurriedly left with their documents.

……

Li Ao arrived at the Granger Engineering Library, walked around, and found an empty seat.

"Luckily, it's not peak time right now," he muttered to himself as he took out his laptop and plugged it in.

The regular study areas in the Granger Library are always first-come, first-served.

Many doctoral students returned to campus this week after their vacation, and the library is noticeably more crowded, often packed in the evenings.

However, since I had just finished lunch, it wasn't difficult to find a spot.

He turned on his computer and opened the newly installed LaTeX editor.

"Let's reorganize the statement of the lemma first."

He typed on the keyboard, rewriting the proof process according to his previously planned approach.

Unlike before, this revision was exceptionally smooth. When dealing with the difficult points of weight normalization, endpoint estimation, and integral averaging, the thought process was as clear as stating a simple high school problem, without the slightest hesitation.

In just over ten minutes, he broke down the originally lengthy weighted average lemma into three logically distinct segments.

He then conveniently changed the proof of the discretization special case to the form of first explaining the construction and then substituting it into the inequality chain.

During the polishing and rewriting process, a notification popped up on the panel:

Writing an academic paper... Intelligence +0.1

【Intelligence: 116.0】

"Just revising the paper over and over again is too slow to improve intelligence," Li Ao glanced at the panel. "I still need to finish it quickly and continue studying real analysis and ordinary differential equations."

He put aside his thoughts and continued polishing the paper, trying to finish it as soon as possible so he could show it to Professor Jensen.

On Wednesday afternoon, the Black Belt group held its final special lecture.

This lecture will focus on algebra, covering the classic construction of inequalities and sequence problems, as well as the analysis of past IMO problems.

Normally, the lectures are conducted by the summer camp coaches, but Li Ao was slightly surprised when the lecturer walked into the classroom.

The person who arrived was Professor Philip from the Mathematical Analysis Seminar.

However, on second thought, since the other party could be in charge of the Putnam Competition seminar for undergraduates, it would certainly be more than enough for them to teach algebra topics.

"Algebra is a required subject in the IMO, and there are many difficult problems in previous years. It will be the focus of your next stage of testing."

Professor Philip stood on the podium, skillfully delivering his opening remarks, "And the mathematical beauty within it is also unique, which you will gradually come to appreciate in the future."

What Li Ao didn't notice was that Benjamin in the front row was secretly delighted.

As soon as Professor Philip entered the classroom, he took advantage of his front-row seat and stood up to greet him.

In the recent seminars, Benjamin has made a lot of attempts to get close to Professor Philip, contacting him more frequently than he has with Professor Jensen, and has finally become a familiar face to him.

In his view, being able to become familiar with the lecturers on algebra topics would not only highlight his special status, but might also allow him to glean some insights into the direction of the phase test.

If he gets a good score in the exam, it will prove the value of his IMO gold medal, which is far beyond what ordinary newcomers can achieve.

……