Volume 1: Student Life Chapter 102: First Topic Discussion
Chen Zhou first replied to Wu Xiping: "OK, Professor, I'll be there right away."
Within two seconds, Wu Xiping gave him an "OK" gesture in return.
Putting away his phone, Chen Zhou sorted out the information, said something to Yang Yiyi, then stood up and walked towards the seminar room.
Chen Zhou couldn't quite remember the location of the seminar room. He followed the signposts in the library and searched for a while before he arrived at the seminar room.
In the seminar room, there were not only Professors Wu Xiping and Zhang Zhongyuan, but also a young face.
"Let's get to know each other." Wu Xiping pointed at the young face and introduced him to Chen Zhou, "This is your senior from the mathematics department, Shen Jing."
This Shen Jing was none other than the senior who helped Chen Zhou with the registration procedures on the first day of school.
Chen Zhou greeted him, "Hello, senior."
Before Wu Xiping could introduce him again, Shen Jing also recognized Chen Zhou. He looked at Chen Zhou in surprise: "Why is it you? Chen Zhou, aren't you a freshman?"
"Uh... coincidence." Chen Zhou explained.
Shen Jing was about to ask more, but was interrupted by Wu Xiping: "Do you know each other?"
Shen Jing nodded and briefly talked about the registration.
Wu Xiping smiled and said, "It seems that you two brothers are quite destined to be together."
"Yes." Shen Jing said again, "I thought the newcomer Professor Wu mentioned should be a sophomore student at least. I didn't expect it to be Chen Zhou."
Zhang Zhongyuan interrupted, "There are probably many things you haven't thought of. Okay, let's stop talking about the pleasantries and chat privately later. Now that everyone is here, let's start the first topic discussion."
Wu Xiping smiled and said, "Look, we can't ignore Professor Zhang. It would be embarrassing for him to watch us chatting, haha."
Zhang Zhongyuan glanced at the old fellow and didn't retort him. He just opened his notebook.
Seeing this, Wu Xiping immediately stopped laughing.
He was too familiar with Zhang Zhongyuan's action. What he meant was, you probably don't want to have a discussion on the topic in a friendly manner? Then, you can't blame me for preparing too many questions...
Zhang Zhongyuan's questions are his own thoughts and doubts from the perspective of this research topic.
This is normal, but the key is that Zhang Zhongyuan's thoughts and questions are one question mark after another.
There was a time when Wu Xiping did not take Zhang Zhongyuan's action into consideration. As a result, during a topic discussion, he was so frustrated by Zhang Zhongyuan's questions.
After a discussion on a topic , my voice became hoarse.
"Ahem..." Wu Xiping coughed twice and asked Chen Zhou and Shen Jing to sit around. "Our topic this time is mainly the application research of the mutual penetration and integration of advanced algebra and mathematical analysis."
"I have also sent the information about this research topic to your emails. I believe you have all read it and have your own understanding of it."
"Then..." After a brief pause, Wu Xiping called on Shen Jing, "Shen Jing, you are the senior, so please tell us your opinion on this topic first."
Shen Jing thought for a moment and began to say, "As students in the Department of Mathematics, mathematical analysis and advanced algebra are the two most important courses we start studying as soon as we enter university."
"At the same time, they are also the two most basic courses in mathematics. Almost all subsequent courses will use them. Advanced algebra will be completed in the freshman year, and mathematical analysis will be studied until the fall semester of the sophomore year."
At this point, Shen Jing paused, glanced at Chen Zhou, and continued, "Advanced algebra mainly includes two parts, polynomial algebra and linear algebra. Mathematical analysis can generally be divided into five major parts: limits, continuity, differential calculus, integral calculus, and series."
"Our task is to find the connection between the two."
"For example, the research objects of mathematical analysis all belong to the real number domain, but some problems cannot be solved within the real number domain, or at least are very complicated to solve. For example, the proof of the fundamental theorem of algebra in advanced algebra requires the use of complex number theory..."
"…the basic theory of complex numbers involves the content of complex variable functions, and the origin of complex variable functions is that the research object of mathematical analysis is extended from the real number field to the complex number field…"
"…by exploring the contents of both, we can find many more examples of this. So, although the problems in mathematical analysis and advanced algebra are different, there is a close connection between the two."
“Therefore, I think we should start with the specific problems involved in mathematical analysis and advanced algebra to study this topic.”
"Professor, these are some of my views."
After Shen Jing finished speaking, Wu Xiping and Zhang Zhongyuan looked at each other and saw admiration in each other's eyes.
Wu Xiping nodded, and then said to Chen Zhou: "Chen Zhou, you can also tell me what you think."
"Okay, professor." Chen Zhou organized his words and said, "Regarding the differences and connections between mathematical analysis and advanced algebra, my views are basically the same as those of Senior Shen Jing..."
"…But I need to add that, in my personal opinion, advanced algebra is studied from the perspective of macroscopic foundations, while mathematical analysis is studied from the perspective of internal mathematical relationships."
"In other words, advanced algebra is like the skeleton, while mathematical analysis is the interior. They both represent different perspectives on the mathematical world..."
"...Well, advanced algebra can guide the study of mathematical analysis from a macro perspective. Advanced algebra's in-depth study of space constructs space through bases and operation rules. At the same time, space can be described from different perspectives through base transformations, which corresponds exactly to the various transformation techniques in mathematical analysis..."
"... Regarding the research ideas for this topic, I agree with Senior Shen Jing's opinion. We can start with the specific issues involved in the two and study the internal connection."
“But I would like to add that in the study of the problem, the contents of the two can be specifically linked.”
"Let me give you an example here. In mathematical analysis, the problem of zero points of functions is generally solved by using methods such as the intermediate value property of continuous functions, Rolle's theorem, and Darboux's theorem. Some problems can be solved by Weierstrass's approximation theorem."
"But if we connect mathematical analysis with advanced algebra knowledge, we will get a simpler algebraic solution."
"Professor, this is my personal idea. Please add to it."
After Chen Zhou finished speaking , he glanced at Shen Jing, who was looking at him in surprise.
Wu Xiping and Zhang Zhongyuan looked at each other again. Wu Xiping's eyes showed surprise and admiration, while Zhang Zhongyuan's eyes were full of admiration.
Zhang Zhongyuan also raised his eyebrows at Wu Xiping, as if to say, look, is this kid the same as I said, is he as handsome as I was when I was young?
