Chapter 9 He is not a mathematics major
Looking at this question, many students have no idea at all and don’t know where to start.
This is also a very normal thing for them. After all, they have just started learning mathematical analysis. When encountering such a comprehensive problem, it is indeed difficult to find the solution to the problem at once.
A few students seemed to have some ideas and began to write on the straw paper to try to answer the question.
After reading the question, Ning Chen first determined that it was a question that he had never seen before, but he quickly found a way to solve the problem.
After all, Ning Chen is a contestant who has studied the entire "Mathematical Analysis" by himself, plus "Advanced Algebra", "Analytical Geometry", "Elementary Number Theory", "Abstract Algebra (Elementary)", "Mathematical Modeling" and other With the blessing of several mathematical knowledge, Ning Chen had problem-solving abilities that were superior to those of mathematics majors.
“First make a difference between f(x+t) and f(x), determine the range of this difference, and then according to the first form of Kronecker’s theorem, let α1, α2,..., αn be any Real numbers, θ1, θ2,..., θn are real numbers that are linearly independent on the integer ring..."
Ning Chen quickly wrote his problem-solving process on the paper, with several pauses in the middle. It took me a short period of thinking, but in the end I completed the entire proof process relatively smoothly.
"So the sequence {tn} is what we want. In summary, the original proposition is proved."
After writing the entire proof process in a relatively simple way, Ning Chen breathed a sigh of relief. .
Speaking of which, Ning Chen was not satisfied with his proving speed.
“It seems that I usually do too few questions, so I get stuck in the middle. If I were a mathematics major, I should have completed the entire proof process long ago.”
But when Ning Chen looked up, he found that none of his classmates had raised their hands.
Everyone was either staring blankly at the questions on the big screen, or frowning and biting their pens, writing and revising on the straw paper, but no complete ideas emerged.
Looking at everyone's painful state, He Sheng on the podium looked relaxed.
Since everyone had answered the questions so smoothly before, in order to prevent the students from being too proud, He Sheng specially asked a question that was a little over the top to kill everyone's enthusiasm.
Seeing that no one raised their hands, He Sheng walked off the podium and patrolled back and forth in the aisle.
When he walked to the last row, He Sheng saw that Ning Chen hadn’t started writing and thought that Ning Chen didn’t have any ideas.
But when He Sheng carefully looked at the process on Ning Chen's scratch paper, he was surprised to find that Ning Chen had already completed the proof of the problem.
Although Ning Chen's proof process was a bit simple, He Sheng knew that Ning Chen's idea was completely correct.
"This... was all written by yourself?"
"Yes, teacher, but I don't know if I wrote it correctly."
In fact, Ning Chen was very concerned about his own problem-solving The idea was still very confident, but Ning Chen was not quite sure about the problem-solving format, so he tentatively asked He Sheng.
"There is nothing wrong with your proof, go and write it on the blackboard!"
He Sheng's words were filled with uncontrollable excitement. After all, He Sheng could not have imagined that the first place in the entire classroom would be The first person to ask this question was Ning Chen.
There are more than a hundred students majoring in mathematics, but none of the auditors majoring in materials can do it quickly or well. This will inevitably make He Sheng feel incredible.
Ning Chen hesitated for a moment, then walked towards the podium.
Other students in the classroom also raised their heads and focused their attention on Ning Chen. Seeing that the unknown student came to the podium, the mathematics students were all surprised and started talking among themselves.
“Who is this student? Why did Teacher He let him go to the front?”
"I don't know, but since Teacher He asked him to come up, it seems that he really solved this problem."
"It can't be a student who transferred from other majors. I haven't seen him before. Pass this person.”
“If you transferred from another major, you wouldn’t be able to learn so quickly. Maybe you are a student who has taken a leave of absence before and has already learned these courses.”< br>
Ning Chen didn't pay attention to other people's comments. He didn't even bring a draft paper, so he picked up the chalk and started writing the process.
Because Ning Chen has completely memorized the entire proof idea in his mind, if he writes it according to the scratch paper, the speed will be slower.
In addition, because the whole process has to be faced by all students, Ning Chen deliberately wrote the process in more detail, without omitting many intermediate processes as he just did on the draft paper.
Ning Chen’s chalk writing is pretty good. Because he was a math teacher in an education and training institution in his previous life, Ning Chen is very accustomed to using chalk.
Looking at Ning Chen writing the proof process of this question on the blackboard without any pause, the students in the classroom started talking one after another.
“This person looks very simple. I feel that his process of writing proofs is very smooth. He is not a new teacher in our major, right?”
“Although I can’t understand what he writes. process, but I still feel it’s awesome.”
"Looking at this posture, I really don't know if the four blackboards are enough for him."
A few students suddenly understood something after seeing the proof ideas written by Ning Chen.
"So that's it. The entire problem-solving idea first uses the first form of Kronecker's theorem, and then discusses a1, a2, and a3 to see whether they are linearly independent on the integer ring, and further proves the above conclusion { tn} is the highest bound..."
"I understand it somewhat, but if I hadn't seen his ideas, I wouldn't have thought of this method at all. This requires too high a mathematical foundation. , you must list all the situations, and you can’t omit anything.”
“Give me two hours, I may be able to solve this problem, but if I only have twenty minutes. , I’m afraid I can’t even think of the basic idea.”
When Ning Chen almost finished using two blackboards, he finally finished writing the process of this question.
"The writing is very good, go back."
He Sheng did not ask Ning Chen to explain his proof process to everyone, so Ning Chen did not stay on the podium and went straight to him on the seat.
Almost all the students in the classroom looked at Ning Chen along the way, their eyes filled with various emotions.
Next, He Sheng explained to everyone the process of Ning Chen’s writing.
After He Sheng's explanation, some students understood Ning Chen's problem-solving ideas, but this was only to an understandable level. It was still impossible for them to do it alone.
"The classmate just now is a freshman majoring in materials. We, the students majoring in mathematics, still need to continue working hard."
(End of this chapter)