A basketball game reconciled Shen Qi and Xu Rui, and the two drank cold Coke outside the school store, feeling comfortable.

After returning to the classroom, Xu Rui was no longer in high spirits, and the domineering honey disappeared, replaced by listlessness.

Shen Qi has not forgotten the mathematical problems left to him by Zhang Wanbang, and there are still three problems that have not yet been solved, and the difficulty of these three problems has been further deepened, requiring the comprehensive application of the concept of Frobius matrix rank, Laplace's theorem, Clem's law, and the subsequent inferences proposed by Fourier and Poincaré, which involve the theoretical system of infinite order matrices.

Although Gao Dai is abstract, it is an introductory course in the Department of Mathematics after all, and even if he can't fully understand those abstract concepts, he can barely follow the routine by rote memorization.

Shen Qi followed the routine with great difficulty, worked until 10 o'clock in the evening, and finally completed the solution to the last three questions.

The next morning, Shen Qi came to Zhang Wanbang's office and handed Zhang Wanbang the answer sheet.

"Looks like you've hit some obstacles. Zhang Wanbang took the answer sheet and quickly browsed, and Shen Qi encountered obstacles that he expected.

"Yes, Mr. Zhang, since matrices are derived from determinants, what the hell is the use of quaternions? I didn't figure it out all night, but in fact, I was blind to the last three questions. ”

"I learned applied mathematics first and then transferred to the teacher, I didn't figure out this problem until my sophomore year, Shen Qi, you go back to the classroom first, and come back to me at noon." In addition, I must remind you, don't put all your energy into mathematics, you won't learn Chinese, you don't want English? I am your mathematics teacher and your class teacher, and I can tell you very responsibly that the college entrance examination will not only test mathematics. ”

"Oh, got it. ”

Shen Qi returned to the classroom, took out "Advanced Algebra" and continued to study, but he didn't listen to the Chinese class.

"I'm addicted to mathematics and can't extricate myself, how can I break it?"

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

Zhang Wanbang gave him two pieces of paper, one was the review of the five questions yesterday, and the other was written on the new five questions on the white paper.

Shen Qi finished lunch and began to study these two topics.

Yesterday's five questions, Zhang Wanbang reviewed them and left notes in the blank space of the answer sheet:

"Although on the surface mathematics is nothing more than a language or a tool, most of its vivid concepts provide the key to new fields of thought. ”

"Determinants and matrices, on the other hand, are completely reforms in the language of mathematics, and Shen Qi must be deeply aware of this in order to make a difference in algebra. ”

"In the third question, you misunderstand the Frobenius eigenequation, and remember that the smallest polynomial is the polynomial with the lowest degree of satisfaction of the matrix, which is unique. ”

"Question 4, f(λ)=(λ-λ1)^k1(λ-λ2)^k2...... (λ-λi)^ki, I haven't seen your problem-solving process with my own eyes, but I can say with certainty that you are copying the standard type. ”

"But you can come up with the right answer, which proves that you have two tricks, at least you know how to fumble the routine, but this routine is not the easiest routine. ”

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

"Now I'll tell you the most concise routine of the standard type, so that J=XXXX......"

......

Zhang Wanbang's annotations on the answer sheet are the essence of his life's learning, and he uses a limited space to explain the core mathematical ideas and skills, and he is pointing out Shen Qi.

You can't learn these things in textbooks, at least not as specific, focused, and targeted as Zhang Wanbang's annotations.

Shen Qi understood in seconds, and the bottleneck that had plagued him for more than a week broke through instantly: "I see, so it is! Teacher Zhang's writing is all the essence, and I have benefited a lot!"

A line of text flashed out of the system: "The host has been instructed by a master in the field of mathematics and has comprehended new professional skills, and the score of the top student is +100." ”

"100 points! It's so spicy!" Shen Qi jumped up excitedly, Mr. Zhang, you are a master, you teach me knowledge, help me brush up on the points of the top student, and a thousand words can be summed up in four words: Teacher is like a mountain.

Shen Qi absorbed and digested yesterday's five questions, numbered this "secret volume" as "Internal Reference 1", and collected it in his schoolbag.

Next, Shen Qi began to study "Internal Reference 2", that is, the 5 questions that Zhang Wanbang came out today.

Mathematics, unlike other natural sciences, is a discipline that cannot be tested with experimental equipment to test theoretical hypotheses.

Mathematics experiments are mainly supplemented by the brain, and after fully understanding various theories and concepts, they can improve their proficiency through derivation, proof, hypothesis, etc.

For the next two weeks, Shen Qi's daily routine was to go to Zhang Wanbang's office once a day in the morning and once at noon to deliver the "internal reference".

For Shen Qi, Zhang Wanbang has two identities, in the classroom Zhang Wanbang is an ordinary mathematics teacher, he explains high school mathematics knowledge points.

Outside the classroom, Zhang Wanbang is a "master" who points out Shen Qi, and he spreads deeper mathematical knowledge.

"The host listens carefully to a physics lesson, and the Xueba points +1. ”

"The host didn't listen carefully to the language class, and the Xueba score +0. But the host solves a math problem in Chinese class, and the Xueba score +5. ”

"The host has 1 hour of running, playing ball and other physical exercises, and the top student points are +1. ”

"The host has been instructed by experts in the field of mathematics and has comprehended new professional skills, and the score of the top student is +100. ”

"The host learns "Mathematical Analysis" by himself for 3 hours, and the Xueba points are +10. ”

......

Shen Qi's time schedule is very full, and he earns a stable income of 120~130 points every day.

Among them, the channel with the greatest contribution is "getting guidance from experts in the field of mathematics", that is, the extracurricular interaction between Shen Qi and Zhang Wanbang.

Zhang Wanbang explained high school mathematics in class, and he could no longer provide Shen Qi with even 1 point of academic excellence.

But in the more professional field of mathematics, Zhang Wanbang steadily provides 100 points of Xueba points to Shen Qi every day.

Driven by the "master-apprentice mode", Shen Qi's practical mathematical ability has been further improved, and his "internal reference" series has been collected to "internal reference 15", and the research scope has been extended to indefinite integrals, Fourier series, double-leaf rotating hyperboloids, ellipsoids and other fields, covering several branches such as high algebra, number fractions, and solutions.

April was a month of rapid progress for Shen Qi.

On April 20, Shen Qi saved 4,205 Xueba points: "Finally, you can upgrade again." ”

Mathematics level 2 to mathematics level 3 requires 3,000 Xueba points.

"System, I'm going to upgrade, math indicators up to level 3. ”

"After deducting 3,000 Xueba points, the host's math index is upgraded to level 3. ”

Levels 2 and 3 are both systematically defined as advanced levels, which can be understood as elementary and intermediate levels.

Host, Shen Qi

Age, 17

1. Mathematics Level 3 (0/5000)

2. Physical Education Level 1 (0/1000)

3. Chinese level 0 (0/100)

3. English level 0 (0/100)

3. Physics Level 0 (0/100)

3. Chemistry grade 0 (0/100)

3. Biology Level 0 (0/100)

3. History Level 0 (0/100)

3. Geography Level 0 (0/100)

3. Politics Level 0 (0/100)

Balance of top student points: 1205

Shen Qi's mathematics index is far ahead with a grade of 3, the physical education index is ranked second with a grade of 1, and the other eight subjects are all tied for third with a grade of 0.

Mathematics level 3 to level 5 requires a total of 15,000 student points.

Shen Qi has a stable income of 100+ Xueba points every day, and 15,000 Xueba points can be obtained in the foreseeable time.

Pinch his fingers and calculate, after 4 months at the latest, Shen Qi will be able to save 15,000 points for top students, and he will definitely be able to take the lead in mathematics to level 5 before graduating from high school.