Volume 1: Student Life Chapter 121 After Submitting the Paper
"If α is an irrational number, then any μ∈[0,1] is a cluster point of the sequence {nα-[nα]}, where [x] represents the integer function."
This is an inference that is easy to prove.
Although simple, it is practical.
From then on, Chen Zhou's mind was opened up and he began to write down the answer to the last question.
"…consider using the proof by contradiction and assume that limn→＋∞f(n)=L, since μ is an irrational number…"
"…we will have f([nkμ])=f([nkμ]-nkμ), and consider taking the limit of this equation from k to +∞…"
"… This means that L = limn→ +∞f([nkμ]) = limn→ +∞f([nkμ] - nkμ) = f(0)…"
“… Taking any real number x0, there exists a sequence of positive integers {mk} that tends to positive infinity, satisfying x0＋mkμ－［x0＋mkμ］→0（k→＋∞）.”
“So we can get L = limn → + ∞ f ([x0 + mkμ]) = limn → + ∞ f ([x0 + mkμ] - x0 - mkμ + x0) = f (x0)…”
"Combining the above content, we can infer that (Ax)f(x)≡f(0), but the continuous identity function defined on the real axis does not have a minimum positive period, so the counter-assumption is overturned and the proposition is proved."
After finishing writing, Chen Zhou went back and reviewed it again.
No errors were detected.
Chen Zhou prepared to hand in his paper.
However, he glanced at the draft paper and it was still blank.
After thinking about it, Chen Zhou wrote his name on it.
Then, stand up, hand in the paper, and leave.
The first exam of the midterm exam season ended with a score of 1.
The classmate sitting behind Chen Zhou was still concentrating on solving a problem. Suddenly, he looked up and found that Chen Zhou was gone.
The classmate looked around again and found that Chen Zhou was the only one missing.
He muttered to himself, "Isn't he so nervous that he's breathing fast? Can he hand in the paper early?"
After leaving the classroom, Chen Zhou went straight back to the dormitory.
I turned on the computer, took out the draft paper and pen, continued with my thoughts before the exam, and continued working on the project.
Like Shen Jing's work, the part that Chen Zhou is responsible for also requires continuity analysis.
Start with the direction the helicopter is facing or away from the satellite, and consider the elevation angle of the satellite.
This topic is actually a simulation experiment, using mathematical analysis as a tool.
Combined with mathematical methods such as geometry, various parameters of rotor communication are comprehensively analyzed.
Thinking of this, Chen Zhou's thoughts became completely free.
He no longer sticks to the surface of the subject.
Instead, it is more about combining the characteristics of different mathematics courses and making comprehensive use of mathematical methods to solve this problem.
About half an hour later, Zhao Qiqi and two other people returned to the dormitory together.
As soon as he entered the dormitory, Zhao Qiqi asked, "Brother Chen, how did you solve the last question? Was it beyond the syllabus?"
Chen Zhou thought for a moment and said, "It's not beyond the scope..."
Zhao Qiqi and the other two looked at each other, and Li Li asked, "Chen Zhou, the last question is about fraction 2?"
Chen Zhou turned his head and glanced at Li Li, then nodded slightly. "I guess so. I used a corollary of Dirichlet's approximation theorem in number theory to solve it. This theorem is also in Calculus 2, and it is a result about the pointwise convergence of the Fourier series."
After hearing what Chen Zhou said, Li Li said, "I was thinking of this theorem as well, but this part is at the end of Calculus 2, and I haven't fully grasped it yet. I also don't know the inference you mentioned..."
Zhao Qiqi and Zhu Mingli seemed to be thinking about something...
Chen Zhou then said, "Professor Wu always starts a debate about the topic, and the questions are always beyond the syllabus. You should be used to it. And this is only the last chapter of Mathematics 2, so it can't be considered an out-of-syllabus question."
Zhao Qiqi: "Then why are you talking about a corollary of the number theory theorem?"
Chen Zhou: “They are all connected, just the same.”
Zhao Qiqi: “…”
Zhu Mingli: “…”
Li Li walked silently to the desk, sat down, and took out the textbook on Mathematics and Fraction 2.
After the exam, Huang Yemei took the collected test papers and came to Wu Xiping's office.
As soon as Huang Yemei opened the door, she said, "Professor Wu, I didn't expect that some students would hand in their papers ahead of schedule for the test you gave. I don't know how they did."
Wu Xiping was bending over his desk writing some materials. He said without even looking up, "Is it just Chen Zhou?"
Huang Yemei asked in surprise: "How did you know?"
Wu Xiping replied: "At present, no one except him can complete this test paper completely."
After a pause, Wu Xiping put down the pen in his hand, raised his head and said with a smile: "It seems that you, as a counselor, still don't care enough about our mathematics students."
Huang Yemei was slightly stunned, not understanding what Wu Xiping meant. She said, "Nothing has happened to the freshmen in the Department of Mathematics recently. I have been to all the students' dormitories in the past two months since school started, and they are all pretty good."
Wu Xiping asked, "When you went to Chen Zhou's dormitory, did you notice anything different?"
Huang Yemei thought for a moment and replied, "Well... Chen Zhou wasn't there when I went there. According to other students, he seemed to have gone to the library to read."
Suddenly, Huang Yemei thought of the pile of textbooks that Chen Zhou took away from her when school started.
It was not long after school started, and she went to Chen Zhou's dormitory.
Seeing the pile of textbooks, she flipped through them casually. Only one or two had words on them, so she didn't care.
Now that she thought about it carefully, she realized something was wrong. Two of the books she had just taken away had writing on them? Was he reading them, or was he just drawing them casually?
Wu Xiping took the test papers for this exam, found Chen Zhou's, and looked through them.
There are 7 big questions, the answers are neatly written, the thinking is clear, and the answers are all correct.
Wu Xiping took out a red pen, made a few strokes, and wrote a big red number "101".
Then, he handed the test paper to Huang Yemei.
Huang Yemei took the test paper, took a look at it, and immediately looked up at Wu Xiping.
Wu Xiping smiled and said, "This kid is as expected."
Huang Yemei actually heard a hint of admiration in Wu Xiping's tone.
Although she had not been a counselor in the Department of Mathematics for long, she had heard of Wu Xiping's name.
Students complained bitterly about the test papers Wu Xiping gave, saying that some of the questions were beyond the syllabus.
Some students even choose to fail several points and retake the course.
This was the first time she heard Wu Xiping praise a student openly.
"By the way, if undergraduate students in our school apply for research projects individually, are there any requirements?" Wu Xiping usually does research projects in addition to substitute teaching. He understands the school regulations in this regard, but is not familiar with them.
Huang Yemei asked in confusion: "Undergraduate student? Is it Shen Jing, the one you have been accompanying?"
Huang Yemei knew the student Shen Jing. He had been working on a project with Wu Xiping since his sophomore year.
Shen Jing is now a junior. If he is good enough, he can indeed apply for a project independently, but according to the school regulations, it is still difficult, very difficult.
Wu Xiping nodded first, then shook his head: "It's Shen Jing and Chen Zhou."
Huang Yemei was slightly stunned. Why is it Chen Zhou again? Even if he scored full marks in the math test, he shouldn't be applying for a research project, right? Isn't this a freshman who has just been enrolled for two months?
