In 1978, I was admitted to Harbin Institute of Technology

Chapter 14: I accidentally used too much force and made Mr. Qian’s student autistic!

The first question is this:

Given the function y=x+(2m+1)x+m-1 (m is a real number)
(1) For what value of m does the extreme value of y reach 0?

(2) Prove that no matter what the value of m is, the vertex of the function graph (i.e., the parabola) is on the same straight line L1. Draw a sketch of the parabola for m = -1, 0, and 1 to verify this conclusion.
(3) Among the lines parallel to L1, which ones intersect the parabola and which ones do not?
Prove that: For any straight line parallel to L1 and intersecting the parabola, the line segments intercepted by each parabola are equal.

Suspect you cheated in the college entrance exam?

The first quadratic function question is exactly the same as the last question in the college entrance examination mathematics paper, even the numbers have not changed!

Xie Wei frowned and looked at Liang Hongbin, who continued to stare at him calmly.

"Don't think too much, just look back..."

When Xie Wei quickly flipped through the questions at the back, he felt even worse.

"Teacher Liang, is this really the advanced mathematics for the entrance exam? Using Maxwell's equations through calculus to describe the changing laws of electric and magnetic fields; using calculus to derive and calculate the Lorentz transformation and energy-momentum relationship in relativity, these belong to high-energy physics, right? They have nothing to do with mechanical automation..."

Before he finished reading, Xie Wei stopped, stared at the other party with dissatisfaction, and questioned him rudely.

The other party was also a professor at Harbin Institute of Technology and might be Liang Hongling's brother, but Xie Wei lost his initial politeness.

The whole set of questions, except for the relatively basic questions related to functions, trigonometric functions and derivatives in the front, directly enters the difficult questions related to indefinite integrals, partial differentials, group theory and group representation theory, Riemannian geometry, etc.

This set of handwritten questions is definitely not something that can be solved by students who have not studied seriously for 10 years and have just taken the college entrance examination!
Liang Hongbin was not angry with Xie Wei and remained calm.

"Not doing it will not affect admission. The school will make adjustments to the subsequent learning based on the level of the students who did this set of questions."

At this point, he paused, looked at the change in Xie Wei's expression, and continued, "The 77th class that enrolled in the first half of the year were all admitted based on merit, but the differences in their basic skills were huge."

This made Xie Wei think.

Does adjusting study according to grades mean that I don’t have to attend basic classes every day?
Seeing Xie Wei looking at him, Liang Hongbin seemed to know what he was thinking and added, "Students with excellent grades only need to take the final exam and do not need to take basic courses on weekdays."

Do!
Must do!
Freshman year consists of public courses and professional basic courses.

Many of the high-precision and cutting-edge technologies of the 1970s and 1980s were not even within Xie Wei's professional knowledge when he was in college.

Xie Wei needs to be familiar with the current properties of various materials and the technical level of electronic components in order to bring out the truly advanced technologies in the future.

Naturally, I don't want to spend too much time learning backward technical knowledge.

"Teacher Liang, please sit down for a while."

Before they could settle down, Liang Hongling went to school with Du Guowang. They were unfamiliar with the environment and couldn't even pour water for Liang Hongbin.

Seeing Xie Wei's sudden enthusiasm, Liang Hongbin smiled even more.

He signaled Xie Wei not to worry about him and stood by, as if he was going to watch Xie Wei do the questions. Xie Wei didn't pay any attention to him either.

Sitting at the desk, he took out the Hero brand iridium pen that he had used for half a year and began to write furiously.

The last question in the college entrance examination was just a quadratic function, which was quite difficult for the students from the third grade who had not studied seriously for ten years and had little time to review before the exam.

The college entrance examination had just been resumed, and many people couldn’t even find the high school textbooks, let alone the “Five Years of College Entrance Examination and Three Years of Simulation”, let alone various review materials.

For someone like Xie Wei, who was a pseudo-nerd in school and tutored a pair of children into C9 universities in middle age, he doesn't even need to think.

"For the first question, just use the matching method to find the perfect square formula, and then substitute y=0;"

"For the second question, just expand the equation and compare the coefficients;"

"The third question..."

In less than three minutes, the solution process and function curve of the final question in the college entrance examination that stumped most candidates were fully presented, exactly the same as the standard answer.

For the questions that most freshmen had never encountered before and that in-school students had difficulty solving, Xie Wei just read the questions once and started solving them without any thought.

Liang Hongbin from the same group didn't feel anything when Xie Wei was doing the first question. It was not long after the college entrance examination, and Xie Wei had done it once. It can be seen that Xie Wei was in the same state from the beginning to the end. His answer was exactly the same as the standard answer. From the twitching of his mouth to the final dumbfoundedness, he even regretted coming here.

Especially for questions that used calculus to derive and calculate the Lorentz transformation and the relationship between energy and momentum, Xie Wei wrote the formula and directly wrote the answer without any process...

Liang Hongbin understood the answer, but found that the derivation process used by Xie Wei was missing steps, and he couldn't understand it!

"Huh, finally done..."

Two and a half hours later, Xie Wei put down his pen and rubbed his sore wrist.

Seeing the last question with several pages of calculation process written on it, he rolled his eyes and looked at Liang Hongbin, whose expression kept changing and eyes were dull, and said dissatisfiedly: "Teacher Liang, Mr. Qian asked the seniors of the 58th class of USTC to delay for half a year to cram for advanced mathematics. Is it appropriate for you to give it to a freshman who just took the college entrance examination?"

Yes.

Liang Hongbin went too far.

The last question: Launch a rocket from the earth, go around the sun, and then return to the earth. Please list the equation and find the solution.

No parameters, no formulas.

The key point is that this question is not just about math!

At each stage of a rocket launch, the interference of the gravity of the earth and the sun on the rocket must be taken into account, as well as the relationship between the rocket's own weight and speed after the fuel is consumed; it is even necessary to consider the elliptical orbit of the earth around the sun and calculate the second-order derivative of the polar coordinates of the earth's orbit...

In particular, the verification requires the use of the Tsiolkovsky formula, which is the formula of the relationship between the rocket flight speed and the rocket engine jet speed, rocket mass, and fuel mass, which was created by Tsiolkovsky, the founder of modern astronautics and the father of world aerospace.

Even students who are not majoring in aerospace can't solve this problem.

Fortunately, Xie Wei had made this thing when he saw it on the Internet.

"Have you come across these before?"

Liang Hongbin took a deep breath, and came back to his senses from the extremely high speed at which Xie Wei answered the questions correctly without thinking. He took a question that Xie Wei had done and looked at him with burning eyes.

Originally, he planned to follow Mr. Qian's scoring method when he graduated from college. He simply squared the score and multiplied it by 10. A score of 60 would be considered a pass!
As long as Xie Wei can get 36 points, he will pass.

Xie Wei believes that the questions about his college entrance examination results that were in doubt were actually easy-score questions given by the question setters because they were worried that he would not get enough points of 36!
"Teacher Liang, do you know any seniors from the 58 class of USTC?"

Xie Wei asked tentatively.

The latter nodded awkwardly, "The 58th Mechanics Class of USTC..."

Back then, Mr. Qian asked Liang Hongbin and others to solve this problem. Everyone spent a whole day solving it, two of them fainted, and no one was able to solve it completely. How long did it take Xie Weicai?

40 minutes!

How can it not be embarrassing?

Hearing this, Xie Wei's mouth twitched and his expression kept changing.

What the hell!
Mr. Qian was so embarrassed when he tested the graduates with questions that they gave them to him to do. How shameless of him!
Just when I thought that the other party was the first batch of students after the father of China's aerospace industry returned to China, I immediately realized that something was wrong!
For the last question, Xie Wei calculated based on the Tsiolkovsky formula, the liquid rocket nozzle velocity of 4.5km/s, and the load ratio of 0.000027, that one ton of payload would require more than 180 tons of fuel, which directly negated the feasibility of the project. At the same time, he used the Hall thrusters used in China in the st century to propel the -ton Tiangong space station to change its orbit to verify the problem.

Hall thrusters are something that the Soviet Union, which currently has the most advanced aerospace technology, has not yet fully mastered, and NASA has not even started yet. It will take more than ten years for China to get started!
You know, this kind of Hall thruster is not only used for changing the orbit of spacecraft and satellites.

If this thing is installed on an intercontinental missile...

Finished!

If you are not careful, you may use too much force.

"what happened to you?"

Seeing Xie Wei's expression change drastically, Liang Hongbin became worried.

(End of this chapter)