Learning Brings Happiness

A basketball game brought Shen Qi and Xu Rui back to good terms. The two drank ice-cold cola outside the school's convenience store, feeling refreshed.

Back in the classroom, Xu Rui was no longer spirited, his mysterious dominance gone, replaced by listlessness.

Shen Qi hadn't forgotten the math problems Zhang Wanbang had left him. Three problems remained unsolved, their difficulty further increased. They required the comprehensive application of concepts like the Frobenius matrix rank, Laplace's theorem, Cramer's rule, and subsequent deductions proposed by Fourier and Poincare, delving into the theoretical system of infinite-order matrices.

Although Advanced Algebra was abstract, it was still an introductory course in the math department. Even without fully understanding the abstract concepts, one could barely follow the procedures through rote memorization.

Shen Qi struggled to follow the procedures, working until 10 PM before finally completing the solutions to the last three problems.

The next morning, Shen Qi arrived at Zhang Wanbang's office and handed over his answer sheet.

"It seems you've encountered some obstacles," Zhang Wanbang said, taking the answer sheet and quickly scanning it. Shen Qi facing difficulties was within his expectations.

"Yes, Teacher Zhang. Since matrices are derived from determinants, what on earth are quaternions useful for? I thought about it all night and couldn't figure it out. Actually, I just guessed the last three problems."

"I studied applied mathematics before switching to teacher education. I didn't understand this problem until my sophomore year. Shen Qi, go back to the classroom for now and come back to see me at noon. Also, I must remind you, don't focus all your energy on mathematics. What about Chinese? What about English? I am your math teacher and your homeroom teacher. I can tell you responsibly that the college entrance examination won't only test mathematics."

"Oh, okay, I understand."

Shen Qi returned to the classroom and took out his Advanced Algebra textbook to continue studying. He didn't pay attention in Chinese class again.

"I'm completely immersed in math, unable to extricate myself. What should I do?"

After school at noon, Shen Qi went to Zhang Wanbang's office again.

Zhang Wanbang gave him two sheets of paper. One was the grading of the five problems from yesterday, and the other was a blank sheet with five new problems written on it.

After eating lunch, Shen Qi began to study these two sets of problems.

Zhang Wanbang had graded yesterday's five problems and left comments in the blank spaces of the answer sheet:

"Although it may seem on the surface that mathematics is just a language or a tool, most of its vivid concepts can provide keys to new fields of thought."

"Determinants and matrices are complete reforms in the language of mathematics. Shen Qi, you must deeply understand this point to achieve something in algebra."

"For the third problem, you misunderstood the Frobenius characteristic equation. Remember, the minimal polynomial is the polynomial of the lowest degree that a matrix satisfies, and it is unique."

"For the fourth problem, f(λ)=(λ-λ1)^k1(λ-λ2)^k2...(λ-λi)^ki. I haven't seen your solution process firsthand, but I can say with certainty that you are mechanically applying the Jordan normal form."

"However, the fact that you could mechanically arrive at the correct answer proves you have some skill. At least you know how to grope for a method, but this method is not the simplest one."

"The meaning of mathematics is to solve the most complex problems in the simplest and most efficient way."

"Now I will tell you the most concise method for the Jordan normal form. Let J=XXXX..."

Zhang Wanbang's annotations on the answer sheet were the distillation of his lifelong learning. He used limited space to interpret the most core mathematical ideas and techniques, guiding Shen Qi.

These things couldn't be learned from textbooks, at least not as specifically, focused, and targeted as Zhang Wanbang's annotations.

Shen Qi understood instantly, and the bottleneck that had troubled him for over a week was broken: "So that's how it is, so that's how it is! Everything Teacher Zhang wrote is pure gold, I've benefited greatly!"

The system flashed a line of text: "Host received guidance from a master in the field of mathematics, comprehended new professional skills, scholar points +100."

"100 points! That's so much!" Shen Qi jumped up excitedly. Teacher Zhang, you are a master! You teach me knowledge and help me earn scholar points. A thousand words can be summarized into four: your kindness as a teacher is as great as a mountain."

Shen Qi absorbed and digested yesterday's five problems, labeling this "secret document" as "Internal Reference 1" and storing it in his backpack.

Next, Shen Qi began to study "Internal Reference 2," which were the 5 problems Zhang Wanbang had assigned today.

Mathematics is different from other natural sciences; this discipline cannot verify theoretical hypotheses through experimental equipment.

Mathematical experiments mainly rely on imagination. After fully grasping and understanding various theories and concepts, proficiency is improved through deduction, proof, and hypothesis.

For the next two weeks, Shen Qi's routine was to visit Zhang Wanbang's office once in the morning and once at noon to exchange "Internal References."

To Shen Qi, Zhang Wanbang had two identities. In the classroom, Zhang Wanbang was an ordinary math teacher, explaining high school math concepts.

Outside the classroom, Zhang Wanbang was the "master" who guided Shen Qi, imparting deeper mathematical knowledge.

"Host listened attentively to one physics class, scholar points +1."

"Host did not listen attentively to Chinese class, scholar points +0. But the host solved a math problem during Chinese class, scholar points +5."

"Host engaged in 1 hour of physical exercise such as running and playing basketball, scholar points +1."

"Host received guidance from a master in the field of mathematics, comprehended new professional skills, scholar points +100."

"Host self-studied Mathematical Analysis for 3 hours, scholar points +10."

Shen Qi's schedule was packed. He consistently earned 120-130 scholar points daily.

The channel that contributed the most was "received guidance from a master in the field of mathematics," which referred to the extracurricular interactions between Shen Qi and Zhang Wanbang.

Zhang Wanbang's explanations of high school math in class could no longer provide Shen Qi with even 1 scholar point.

However, in more specialized mathematical fields, Zhang Wanbang consistently provided Shen Qi with 100 scholar points daily.

Driven by the "master-disciple mode," Shen Qi's practical math skills further improved. His "Internal Reference" series had reached "Internal Reference 15," and his research scope had expanded to areas like indefinite integrals, Fourier series, bifoliate rotational hyperboloids, and ellipsoids, covering branches such as Advanced Algebra, Mathematical Analysis, and Analytic Geometry. Shen Qi could now likely pass the professional exams for first and second-year math majors without failing.

April was a month of rapid progress for Shen Qi.

By April 20th, Shen Qi had accumulated 4205 scholar points. "Finally, I can level up again."

Upgrading from Math Level 2 to Math Level 3 required 3000 scholar points.

"System, I want to upgrade. Raise my Math level to 3."

"Deducted 3000 scholar points. Host's Math level has been raised to Level 3."

Both Level 2 and Level 3 are defined by the system as advanced levels, understandable as early advanced and intermediate advanced.

Host: Shen Qi

Age: 17

1. Math Level 3 (0/5000)

2. Sports Level 1 (0/1000)

3. Chinese Level 0 (0/100)

4. English Level 0 (0/100)

5. Physics Level 0 (0/100)

6. Chemistry Level 0 (0/100)

7. Biology Level 0 (0/100)

8. History Level 0 (0/100)

9. Geography Level 0 (0/100)

10. Politics Level 0 (0/100)

Remaining scholar points: 1205

The system performed a subject ranking. Shen Qi's Math level of 3 was far ahead, his Sports level of 1 was second, and the remaining eight subjects were all Level 0, tying for third.

To upgrade Math from Level 3 to Level 5 requires a total of 15,000 scholar points.

Shen Qi earns a stable 100+ scholar points daily. 15,000 scholar points can be obtained within a foreseeable timeframe.

Doing a quick calculation, Shen Qi will be able to save up 15,000 scholar points in 4 months at the latest. He will definitely be able to prioritize upgrading Math to Level 5 before graduating high school.