As a class teacher, Zhang Wanbang is puzzled, is this still the scumbag Shen Qi who is addicted to games and does not learn skills?

As a math teacher, Zhang Wanbang is delighted because his students are talking to him about Gloria and Weierstras.

The discussion lasted about ten minutes, and basically Zhang Wanbang asked a question and Shen Qi answered.

"We generally believe that Gloria is the founder of matrix theory, and Gloria has a corollary that the product of two matrices can be zero, and there is no need for one of them to be zero, as long as one of them is indefinite. Shen Qi, do you think this inference is correct?"

"Actually, Gloria is wrong, this inference is wrong, both matrices must be indefinite. I only know the conclusion, if Mr. Zhang asks me to give proof, my level is limited and I can't do it. ”

"Weierstrass was the first to get the standard type of beam A+λB, Shen Qi, how do you understand the standard type of this beam?"

"A and B here are not necessarily symmetrical, but obey the condition that the absolute value of A + λB is not constant equal to zero. ”

"That's right, then its inverse theorem comes from Sylvestre, and it was proved by Weierstrass, if I'm not mistaken, the senior generation textbooks of our time wrote a sentence about this inverse theorem, do you know this sentence?"

"I ...... I don't know!"

"This inverse theorem says, if the determinant of A+λB is consistent with the elementary factor of the determinant of A'+λB', then a pair of linear transformations can be found to change A to A' and B to B' at the same time, Shen Qi, how do you understand this inverse theorem?"

"I ...... I can't understand ......."

"Gao Dai is indeed too abstract for high school students, but Shen Qi, I am glad that you can learn this level by yourself. ”

"Gloria or Weierstras, matrix algebra or all kinds of determinants, it's hard to explain to you in a few words. Zhang Wanbang casually took out a piece of A4 white paper, wrote down a few lines of mathematical symbols, and then handed the white paper to Shen Qi: "Do as much as you can, come to the office to find me at this time tomorrow." ”

Shen Qi took the blank paper and found that there were five math problems written on it, and it seemed that Mr. Zhang was going to test himself further.

"Okay, I'll see you tomorrow, Mr. Zhang. Shen Qi said goodbye to Zhang Wanbang and left the teacher's office.

Back in the classroom of the second (2) class of high school, Shen Qi began to overcome the exam questions from Zhang Wanbang.

In the first question, prove the Cauchy-Schwarz inequality: XXXXXX (a mathematical formula that cannot be displayed on a mobile phone) and give the conditions for the equality sign to be true.

This question is not too difficult, and the entry-level proof question of "Advanced Algebra" tests the concept of inner product space.

Shen Qi quickly completed the proof and wrote out the proof process on a blank piece of paper.

System: "If the host solves the problem successfully, 2 points will be rewarded." ”

"Yo, 2 points. "Shen Qi can't get Xueba points for doing high school math problems now, but he can get Xueba points for doing college math problems.

At the same time, the Chinese teacher walked into the classroom, and this was a Chinese class.

Shen Qi had no distractions to solve Zhang Wanbang's math problems, he didn't listen carefully to the Chinese class, people's energy is limited after all, and it is difficult to use two minds.

The second problem of Zhang Wanbang is to solve a system of linear equations, which requires a combination of Gaussian elimination and the properties of augmented matrices, which increases the difficulty.

Shen Qi encountered some obstacles in the process of solving the problem, and the elementary transformation of the linear equation system is equivalent to the row transformation of the augmented matrix.

Augmentation matrices → systems of equations

Augmented matrices → systems of equations

Eliminate the x1 term in the first equation

Then the third row of the augmentation matrix transforms

Add 4 times of the second equation to the third equation and subtract the x2 term in the third equation to get a system of stepped equations

Then the augmentation matrix should also be transformed to ......

"Eyes are so flowery...... Shen Qi switches back and forth between the linear equation system and its corresponding augmentation matrix, cutting to his doubts about life.

Shen Qi forcibly solved the problem, the process was very painful, but gritted his teeth and passed this hurdle, and what he gained was double the pleasure.

After spending an entire Chinese class and burning countless brain cells, Shen Qi finally solved the second question from Zhang Wanbang.

"If the host solves the problem successfully, 5 points will be rewarded. ”

Originally, you could get 1 point of Xueba points in the Chinese class, but Shen Qi didn't listen carefully, so the contribution of this Chinese class to the Xueba points was 0.

In fact, it doesn't matter, because Shen Qi solved two math problems in Chinese class and gained 7 points for being a top student.

"Doing two math problems is equivalent to taking seven Chinese classes and doing 200 math problems for college students...... Forget it, let's rest for a while. During the recess, Shen Qi took out "Advanced Algebra" from his schoolbag and reviewed the professional courses of the college students in the Department of Mathematics.

First-year students in the Department of Mathematics have three compulsory basic courses, namely Advanced Algebra, Mathematical Analysis, and Analytic Geometry.

Among them, the simplest is the solution, which can be understood as a three-dimensional version of high plane analytic geometry.

In terms of abstraction, the most difficult is the high generation. In terms of the amount of calculations, the most difficult thing is to count the points.

As for the subsequent branches such as real variable functions, functional analysis, topology, partial differential equations, differential geometry, and algebraic geometry, whoever has the ability will study it, and whoever has no ability will fail the course.

"Hey, Shen Qi, what kind of book are you reading?" Chen Xiaoting, who was at the same table, noticed that Shen Qi was reading a strange book.

"Gao Dai. Shen Qi closed "Advanced Algebra" and pushed it to Chen Xiaoting's desktop.

Chen Xiaoting was dumbfounded when she saw the cover: "Advanced algebra, full-time college mathematics textbook, this ...... This is a textbook for college students?"

"That's right. Shen Qi nodded.

"I'll just look at it, and don't speak. Chen Xiaoting symbolically turned a few pages, and then returned "Advanced Algebra" to Shen Qi: "Could it be that your perfect score cheats are this "Advanced Algebra"?"

No, this book doesn't directly help improve high school math scores. ”

"Then why are you studying it?"

"What Gao Dai provides is an abstract thinking logic, saying that it is useful, it is useful, saying that it is useless, that it is worthless. In the face of the incomparably huge mathematics, Shen Qi is still an apprentice, what is the ultimate meaning of mathematics, Shen Qi can't say clearly, he explores it in his own way of understanding.

"It's so profound, but it has nothing to do with me, I only scored 85 points in this math test, and I really regret being assigned to the science class. Chen Xiaoting's grades in mathematics, physics and chemistry are very average, and she relied on Chinese and English to pull points, barely maintaining the overall score ranking in the middle grade.

At this time, the school radio began to play the athletes' march, and it was time for recess exercises.

"Let's go, it. Shen Qi got up and beckoned Chen Xiaoting to go downstairs together.

Chen Xiaoting covered her lower abdomen and smiled awkwardly: "I am unwell, I won't do exercises today." ”

Oh, the big aunt is here, that really can't do, it's easy to get out of the way. Shen Qi has heard all kinds of rumors about his aunt, and the current high school students know everything: "Then you have a good rest, and tell me what you need." ”

"Actually, it's not a big deal, you just go and it. Chen Xiaoting's face flushed, how can you be embarrassed to tell you boys about the needs of girls?

Within minutes, thousands of students were assembled in the school's large playground, lined up by class.

Nangang No. 2 Middle School has a long history, founded by patriotic revolutionaries in the Republic of China period, the principal strictly implements the basic policy of "strong physique, balanced development, education without class, and equal treatment".

After the ninth set of broadcast gymnastics, Shen Qi stayed on the playground, and the next step was physical education class.

For most boys, physical education is the happiest time, and it is a rare adjustment after heavy schoolwork.

The principal of Nangang No. 2 High School fulfilled his promise of "strong physique and balanced development", and physical education classes will be retained until the third year of high school, while in some high schools, physical education classes will be abolished in the second year of high school.