Top Student: Wasteland Technology Invasion

"Studying math is nowhere near as fun as playing LOL. Forget it, I'll just stick to reading my novel." Yuan Qi shook his head and sighed, looking utterly disappointed.

Lin Chuan glanced at him.

Yuan Qi scored 149 points in the college entrance examination mathematics, making him the second-best student in dormitory 303, after Zhu Lin.

Don't be fooled by their casual talk; they're probably studying hard behind the scenes.

Of course, what others do is none of his business; he needs to focus on his studies.

Time passed, and Lin Chuan became immersed in the world of mathematics.

Without comparison, you wouldn't know that the efficiency of learning basics in the real world is not much different from that in the wasteland world.

However, the wasteland world has a skill: a scientific intuition bonus, making the final difference between the two too great.

Lin Chuan felt that his thinking was being restricted by something when he studied in the real world.

Given that the time flow rate between the wasteland and the real world is 4:1, he can learn far more in the wasteland.

"It seems learning in the wasteland is much more rewarding."

Of course, we can't slack off on our studies in the real world either.

"After all, this is currently the only way to earn learning coins."

Lin Chuan buried himself in studying the materials, with prompts occasionally popping into his mind.

[Learning Coin +1]

[Learning Coin +1]

[Your hard work has earned you +1 math experience point.]

……

Over the next few days, Lin Chuan borrowed textbooks from the library, including "Analytic Geometry," "Ordinary Differential Equations," "Complex Functions," and "Functional Analysis," to gain mathematical experience in the wasteland world.

Of course, he didn't forget to transport a small amount of supplies to the wasteland every day to renovate the safe house.

After using the skill multiple times and traversing between the two worlds, Lin Chuan discovered that the skill was more powerful than he had originally imagined.

Before each crossing, he could see endless chaotic air currents churning, and at the same time, he could vaguely sense the things around the landing anchor point.

This put Lin Chuan, who had been worried about landing and being seen by monsters or people in the real world, at ease.

Finally, Tuesday arrived.

Nearly two hundred students from the School of Mathematics gathered in the lecture hall of the East Teaching Building, exchanging ideas in a buzzing voice.

Then a man who was not yet thirty years old and had thinning hair walked up to the podium carrying a stack of test papers.

The man picked up the chalk and wrote several large characters on the blackboard with a "swish, swish, swish" sound, then turned around and looked at everyone.

"Hello everyone, I am Professor Tang Beichen's doctoral student, my name is Li Zheng. You can call me Senior Brother Li or Teaching Assistant Li."

"Today, I am here to preside over this selection test for the Qiushi liner."

"First of all, I want to clarify that you don't need to worry about the difficulty of this exam, although I personally think it's quite difficult."

"The exam will not affect your GPA for Higher Algebra and Mathematical Analysis."

"You have two hours. Now, please put any items that are not related to the exam in front of you. The exam will officially begin in ten minutes."

Soon, Lin Chuan received the test paper.

A faint sense of excitement instantly enveloped my entire body.

In those four days, he used up all his learning coins and finished all the math courses for his first and second years of university in the wasteland world.

He wanted to test how effective his learning was.

After quickly glancing at the test paper, Lin Chuan turned his attention to the first question.

This is a computational problem involving linear spaces and linear transformations.

Let V be a linear space consisting of all polynomials of degree no more than n over the number field R. A linear transformation T: V → V is defined as T(f(x)) = f′(x) + xf(x). Find the dimensions of the kernel space ker(T) and the image space im(T) of T, and discuss the invertibility of T.

This question is essentially beyond the knowledge base of a first-year university student.

But the question posed no difficulty to Lin Chuan.

He spent sixteen hours in the wasteland over the past four days. It may not sound like much, but he used up all his learning coins and had more than twelve hours of scientific intuition active, making his learning efficiency dozens of times higher than in the real world.

For Lin Chuan, the operator symbols related to "Higher Algebra" were already as familiar as his own body.

As he picked up his pen to answer the question, mathematical symbols flowed from his pen like sprites, dancing gracefully on the exam paper.

The first problem was quickly proven.

Next is the second question, an extremely ingenious problem involving matrix properties and determinant calculations.

The third question concerns series and uniform convergence.

Question 4, a question about quadratic forms and positive definite matrices...

While Lin Chuan was completely focused on answering the questions, many students in the School of Mathematics had already contorted their faces and wished they could twist their bodies into a knot.

No.

Is this the difficult test paper that the teaching assistant mentioned?

Be yourself!

For example, Lin Chuan's roommate, Sun Ang, was still reviewing the first major question.

In his eyes, the test paper for the Qiushi liner selection test was not filled with symbols of higher algebra operators, but with little people dancing!

Who exactly set this question?

Sun Ang was somewhat relieved. Fortunately, the advanced algebra problems he usually encountered in the Department of Applied Mathematics were not like this, otherwise he would have even considered transferring to another department.

At this moment, Sun Ang really wanted to imitate a line he had seen in "Science Fiction World: The Three-Body Problem".

"Mathematics no longer exists, or perhaps it never existed at all."

"What a mess."

Time passed in a stifling atmosphere.

Lin Chuan has finished the last question.

It lay quietly at the end of the exam paper, the question stem very clear.

Let V be a finite-dimensional linear space over the complex field, and T:V→V be a linear transformation. If the minimal polynomial of T has no repeated roots in C, prove that T is diagonalizable.

Upon seeing this question, even though Lin Chuan had studied "Advanced Algebra" and "Functional Analysis" intensively in the wasteland world, he couldn't help but frown slightly.

Because this question involves the extension of the diagonalization condition of linear transformations in advanced algebra to functional analysis, Lin Chuan even doubted that it would be possible for senior students, let alone first-year students, to solve it.

Lin Chuan had reason to believe that this question was one that Professor Tang, whom Assistant Li had just mentioned, had specifically left for a certain prodigy.

His gaze lingered on the question for a full three minutes before his brain began to rapidly process, breaking down and reorganizing the problem.

『 mT(λ) has no multiple roots, we can set mT(λ)=(λ−λ1)(λ−λ2)⋯(λ−λk), where λi are different from each other. 』

Since the minimal polynomial has no repeated roots, a projection operator for the eigenspace can be constructed.

『im(Pi)=ker(T−λiI)……』

Having figured out the key point, Lin Chuan immediately began to write down his arguments.

Time ticked by, and when the last stroke was made, Lin Chuan wrote the words "proof complete".

"Elegance, at least it's proven to be quite elegant."

Lin Chuan glanced at the exam paper with satisfaction, stretched his limbs, and prepared to check how much time was left in the exam when a strange feeling suddenly welled up in his heart.

My thoughts on the final, most challenging question instantly formed a clear framework before my eyes.

"This is……"

"Inspiration gathered from reading in the wasteland?"

"If we generalize the conclusions of finite-dimensional algebra to infinite dimensions, it seems we can obtain some very interesting results."

Having studied in the wasteland world for the past few days, Lin Chuan has benefited greatly from the skill: Scientific Intuition, and has also accumulated a lot of inspiration in his mind.

Unexpectedly, while working on the last big question today, I connected these inspirations together.

His entire brain seemed to awaken, with various pathways swirling together like tree branches, and inspiration came in droves.

Lin Chuan quickly unfolded a draft paper and wrote down all the information he had thought of.

"Non-self-adjoint operators," "continuous spectrum," "eigenvector completeness," and "invariant subspaces"—each of these almost corresponds to an extension of the eighth problem. Lin Chuan was also consuming draft paper at an almost frantic pace.

Various simulation results were presented one by one on the draft paper.

He only needs to summarize afterwards, and he might be able to put together a paper that can be published in a core journal.