Linear Operator and Linear Functional Optimal Inversion Theory

Ever since getting the system, Lu Zhou felt that his life had become incredibly orderly. Early every morning, he carried his secondhand laptop to the library. For him, this experience was simply unprecedented.

It was still the same old spot. Lu Zhou opened his laptop, found an outlet by the wall, and plugged it in. After thinking for a while, he typed several large words into a Word document.

[Linear Operator and Linear Functional Optimal Inversion Theory]

[Abstract: This paper studied the inversion problems of several types of linear functionals and linear operators when complete or partial information was given. It introduced the basic results of optimal inversion theory, particularly the construction of optimal inversion methods...]

Lu Zhou had thought of this topic last night while lying in bed and flipping through his notes. When Professor Tang had discussed the Fourier Inversion Formula, he had casually mentioned several fields in modern mathematics that were not exactly popular, but were relatively cutting-edge.

After combining that with information he had found online, Lu Zhou came up with this topic.

As for how to solve it?

Well...

With his current level of knowledge, there was definitely no way he could solve it himself, so he had to use some conventional methods.

If he remembered correctly, the Black Technology System's points could be used to solve real-world technical problems. He had tried asking it for a proof method for the Riemann Hypothesis, but there had been no response at all. Either the answer exceeded his Mathematics level, or the point cost was an astronomical figure he could not afford.

Surely the system would react to a problem at this level, right?

With that thought, Lu Zhou focused on the computer screen and began silently chanting in his heart, System, system, system...

Hmm...

There did not seem to be any reaction.

Hmm?

Suddenly, a warm current shot up from his back to the crown of his head. Lu Zhou felt his mind heat up, and then, with a boom, an enormous stream of information exploded in his consciousness. Lines of text floated past his eyes one after another.

[Points consumed: 65]

[Based on Mathematics LV0, providing the optimal solution method...]

The feeling did not hurt. On the contrary, it was strangely enjoyable. Just as Lu Zhou began wondering whether he had turned into an M, he suddenly woke up.

Staring at the snow-white computer screen, Lu Zhou looked at his hands, then at the keyboard. His muttering carried a trace of barely concealed excitement.

"S-Solved it?"

He had really solved it!!!

If he had not been in the library, he probably would have shouted in excitement.

Just like when he had mastered Zhou's Conjecture Proof Method, the core reasoning behind the entire problem had been branded directly into his brain like a hot iron.

From the process to the answer, every number, every symbol, even every punctuation mark was concise and filled with the beauty of mathematics.

The only flaw was that this beauty was too bare-boned. He needed to use language to enrich its substance and turn it from pure theory into a paper.

A paper that other people could understand.

Somewhere deep down, Lu Zhou seemed to understand something about the significance of the Black Technology System.

But what he could not understand was why any of this existed.

At that moment, a ballpoint pen reached over and gently poked his arm.

"Um, classmate..." Chen Yushan asked with a blush, embarrassed. "Could I ask you about another math problem?"

She had not wanted to ask him in the first place, but she had asked everyone around her about this problem, and not a single person could solve it.

She had no choice. A person had to bow their head under someone else's roof.

Chen Yushan chose to endure the humiliation and decided to forget the "humiliation" he had inflicted on her the day before yesterday.

Coming back to his senses, Lu Zhou said, "Sure. Hand me the problem."

Chen Yushan sighed in relief, quietly moved her chair over, and sat beside Lu Zhou.

Lu Zhou glanced over the problem twice and found that it was much harder than the one from the day before yesterday. It was probably on the same level as the problem Liu Rui had asked him.

But no matter how difficult it was, it could not escape the broad framework of advanced algebra. Especially for him, as long as it was a problem from an exercise book, there was no such thing as being unable to solve it.

Picking up his pen, Lu Zhou began writing and calculating on scratch paper.

While Lu Zhou worked on the problem, Chen Yushan secretly glanced at his profile.

Although his personality was not particularly likable, he unexpectedly looked quite good when he was serious.

As Chen Yushan waited boredly for Lu Zhou to solve the problem, she suddenly noticed the Word document on his computer screen and quietly asked, "Classmate, are you working on your graduation project?"

To still not have finished a graduation project by June, he really was something else!

While solving the problem, Lu Zhou casually replied, "No, that's a paper. I'm submitting it to SCI."

Upon hearing that, Chen Yushan's face filled with admiration.

Oh my god, she had run into a genius!

She really could not tell. He looked so young, yet he was actually a graduate student!

And he had already started submitting papers to SCI during graduate school. Incredible!

Chen Yushan asked with a face full of admiration, "Senior, what major are you in?"

Lu Zhou had been solving the problem expressionlessly, but when he heard the word "senior," he suddenly smiled shyly. "Uh... Mathematics."

"Mathematics? Oh my god, anyone who can learn mathematics well is practically a god..." Chen Yushan sighed sincerely, and the admiration in her heart grew even stronger.

She was in the business school. Although she was doing quite well in her major, mathematics was the one subject that gave her headaches. She was about to enter her senior year, and the mountain that was the graduate school entrance exam stood right before her, leaving her, someone who still wanted to continue her studies, terribly worried.

"Solved. I wrote the process and reasoning on the paper. Think it over yourself, and you should be able to understand it." Lu Zhou pushed the scratch paper toward Chen Yushan and softly added, "Mathematics depends on two things: talent and practice. Unlike other sciences, just listening to someone explain it is useless."

This was the library, after all, not a suitable place to discuss problems. Quietly exchanging a few words was fine, but if they kept talking, they would probably get plenty of dirty looks. So Lu Zhou stopped there and left the things she needed to understand for the girl to think over herself.

Chen Yushan quickly thanked him. After taking the scratch paper, she pulled out her phone and shyly asked in a low voice, "Um... Senior, can I add you on WeChat? If I run into problems I can't solve, I'd still like to ask you."

"No problem." Lu Zhou did not think much of it. He took out his low-end Xiaomi phone and let the girl scan his QR code.

"Thank you. I'll treat you to a meal next time." Chen Yushan thanked him again with a blush, moved her chair back, and continued writing diligently.

At that moment, Lu Zhou suddenly came back to his senses. He seemed to have forgotten to clear up a misunderstanding.

How was he a graduate student? He was just a freshman newbie.

Though he would be a sophomore in a few months.

But after thinking about it, going over specifically to clarify it would seem a little crazy, and it would make the other person awkward too. He would wait until another opportunity came up to explain the misunderstanding.

With that thought, he shook his head and put the matter out of his mind. His eyes returned to the screen, his fingers lightly tapping the keyboard as he focused on writing his paper.

Although the system had provided the solution based on Mathematics LV0, there was one thing Lu Zhou could be certain of: the knowledge used in this solution definitely did not come from his own tiny store of knowledge. It had been drawn from the system's own database.

As he wrote the paper, Lu Zhou also took notes in the handwritten notebook beside him, listing the knowledge points he could not understand and marking question marks beside steps he had doubts about.

When other people wrote papers, it was like squeezing water from a sponge. For him, however, it was like using a dropper to drip water into a sponge. Compared to outputting, it was more of an input process.

Lu Zhou spent the entire day in the library. Even for lunch, he made do with the buns he had bought in the morning.

Looking at the paper of several thousand words on the screen and the two full pages of notes he had written, he leaned back in his chair and stretched hard.

"All that's left is to thoroughly understand the knowledge points in my notes. I'll look up whatever information I can... and ask the teacher about anything I can't find in books."

"Also, the overly complicated parts of the paper's proof can be simplified a little. When the time comes, I'll search CNKI. Anything already proven in other papers can have its proof removed and simply be cited."

"Finally, there's the plagiarism check... That shouldn't be much of a problem for me. After all, every word was written by yours truly."

Or by the system, but there was not much difference anyway.

It was getting late, and his stomach had begun growling. Lu Zhou heaved himself out of his seat and headed out of the library.

Should he have grilled meat rice or curry rice for dinner?

After dinner, he would stop by Old Tang's office. If Lu Zhou remembered correctly, Tang should be on duty in the classroom for senior-year graduate exam questions at this hour.

Mm, it was happily decided!