I Just Want to Be a Quiet Top Student

As a homeroom teacher, Zhang Wanbang was puzzled. Is this still the scumbag Shen Qi who is obsessed with games and ignorant?

As a mathematics teacher, Zhang Wanbang is delighted because his students are discussing Cayley and Weierstrass with him.

This discussion lasted about ten minutes, basically Zhang Wanbang asked questions and Shen Qi answered.

"We generally believe that Cayley is the founder of matrix theory. Cayley has a deduction that the product of two matrices can be zero, and one of them need not be zero, as long as one of them is indeterminate. Shen Qi, you Do you think this inference is correct?"

"Actually, Cayley is wrong. This deduction is wrong. Both matrices must be indefinite. I only know the conclusion. Teacher Zhang, if you want me to give a proof, my level is limited and I can't do it."

"Weilstrasse was the first to obtain the canonical form of the bundle A+λB. Shen Qi, how do you understand the canonical form of this bundle?"

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

"That's right, then its inverse theorem comes from Sylvester, and it was proved by Weierstrass. If I remember correctly, the advanced textbooks of our era wrote a sentence about this inverse theorem, Do you know this sentence?"

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

"This inverse theorem says that if the determinant of A+λB is consistent with the elementary factors of the determinant of A'+λB', then a pair of linear transformations can be found to simultaneously change A to A' and B to B', Shen Qi How do you understand this converse theorem?"

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

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

"Cayley or Weierstrass, matrix algebra or various determinants, it is difficult to explain clearly to you in a few words." Zhang Wanbang took out a piece of A4 blank paper, wrote down a few lines of mathematical symbols, and then handed the blank 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. It seemed that Teacher Zhang wanted to test himself further.

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

Back in the classroom of Class Two (2), Shen Qi began to overcome the exam questions given by Zhang Wanbang.

The first question is to prove the Cauchy-Schwartz inequality: XXXXXX (a mathematical formula that cannot be displayed on a mobile phone), and give the conditions for the establishment of the equal sign.

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

Shen Qi quickly completed the proof and wrote the proof process on the white paper.

System: "The host solves the problem successfully, and rewards 2 Xueba points."

"Hey, 2 points for mastery points." Shen Qi can no longer get mastery points for doing high school math problems, but he can get mastery points for college math problems.

At the same time, the Chinese teacher walked into the classroom. This section is a Chinese class.

Shen Qi was completely focused on solving Zhang Wanbang's math problems. He didn't listen carefully to the Chinese class. After all, one's energy is limited and it is difficult to focus on two things.

The second question Zhang Wanbang posed was to solve a linear equation system, which required the comprehensive use of Gaussian elimination method and the properties of augmented matrices, which made it more difficult.

Shen Qi encountered some obstacles in the process of solving the problem. Performing elementary transformations on linear equations is equivalent to performing row transformations on their augmented matrices.

system of equations → augmented matrix

augmented matrix → system of equations

Eliminate the term x1 from the first equation

Then the third row of the augmented matrix is ​​transformed

Add 4 times the second equation to the third equation, cancel the x2 term in the third equation, and get a ladder-shaped equation system

Then the augmented matrix has to be transformed into...

"My eyes are blurry..." Shen Qi switched back and forth between the linear equation system and its corresponding augmented matrix, cutting to the point where he doubted life.

Shen Qi bit the bullet and forcibly solved the problem. The process was very painful, but he gritted his teeth and passed the hurdle, and the reward was double the pleasure.

After spending a whole Chinese class and burning countless brain cells to death, Shen Qi finally solved the second question posed by Zhang Wanbang.

"The host solves the problem successfully, and rewards you with 5 Xueba points."

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

In fact, it doesn't matter, because Shen Qi solved two math problems in the Chinese class and gained 7 points of mastery.

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

Freshman students in the Department of Mathematics have three compulsory basic courses, which are "Advanced Algebra", "Mathematical Analysis", and "Analytic Geometry".

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

From the level of abstraction, the most difficult is Gaodai. In terms of the amount of calculation, the most difficult thing is counting points.

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

"Hey, Shen Qi, what book are you reading?" The deskmate Chen Xiaoting 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, a full-time college mathematics textbook, this... is this a textbook for college students?"

"Right." Shen Qi nodded.

"I'll just read it, and don't say anything." Chen Xiaoting symbolically flipped through a few pages, and then returned "Advanced Algebra" to Shen Qi: "Could it be that this "Advanced Algebra" is your perfect book?"

"No, this book does not directly help improve high school math scores."

"Then why are you studying it?"

"What Gao Dai provides is a kind of abstract thinking logic. If you say it is useful, it is very useful. If you say it is useless, it is worthless." Shen Qi is still an apprentice in front of the extremely huge mathematics. The ultimate meaning of mathematics What it was, Shen Qi couldn't tell clearly, he explored it with his own way of understanding.

"It looks so profound, but it has nothing to do with me. I only scored 85 points in the math test this time, and I really regret being assigned to the science class." Chen Xiaoting's grades in mathematics, science and chemistry were very average. Maintain the overall score ranking in the middle and not slipping.

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

"Let's go, let's do some exercises." Shen Qi got up and called Chen Xiaoting to go downstairs together.

Chen Xiaoting covered her belly and smiled awkwardly: "I don't feel well, so I won't do exercises today."

Oh, the big aunt is here, so you really can't do exercises, bouncing around is prone to accidents. Shen Qi has heard all kinds of rumors about the aunt, and now high school students understand everything: "Then you have a good rest, and tell me what you need."

"Actually, it's not a serious problem. You can go do some exercises." Chen Xiaoting blushed, how dare she tell you boys what girls need?

Within a few minutes, thousands of students gathered on the school playground, and they lined up by class.

Nangang No. 2 Middle School has a long history. It was established by patriotic revolutionaries in the period of the Republic of China. The principal strictly implements the basic policy of "building a strong body, balanced development, teaching without discrimination, and treating people equally". social commitment.

After the ninth set of radio gymnastics was over, Shen Qi stayed on the playground, and then came the physical education class.

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

The principal of Nangang No. 2 Middle School has fulfilled the promise of "building a strong body and balanced development". Physical education will be kept until the third year of senior high school. In some high schools, physical education is abolished in the second year of senior high school.