Chen Zhou first sent a message back to Wu Xiping: "Okay, professor, I'll be there soon." ”

Within two seconds, Wu Xiping gave him an "OK" gesture back.

Putting away his mobile phone, Chen Zhou sorted out the information, then said hello to Yang Yiyi, and then got up and walked towards the seminar room.

Chen Zhou didn't remember the location of the seminar room very much, so he followed the road sign in the library and looked for a while before coming to the seminar room.

In the seminar room, there were not only two professors, Wu Xiping and Zhang Zhongyuan, but also a young face.

"Let's get to know each other. Wu Xiping pointed to the young face and introduced to Chen Zhou, "This is the senior of your mathematics department, named Shen Jing." ”

This Shen Jing is none other than the senior who went through the registration procedures for Chen Zhou on the day of school.

Chen Zhou greeted, "Hello, senior." ”

Without waiting for Wu Xiping to introduce again, Shen Jing also recognized Chen Zhou, and he looked at Chen Zhou in surprise: "How could it be you? Chen Zhou, didn't you just enter your freshman year?"

"Uh... Coincidental coincidence. Chen Zhou explained.

Shen Jing was about to ask again, but was interrupted by Wu Xiping: "You know each other?"

Shen Jing nodded and briefly said about the report.

Wu Xiping said with a smile: "It seems that you two brothers are quite fateful. ”

"yes. Shen Jing said again, "I think the newcomer you mentioned Professor Wu should be a sophomore, but I didn't expect it to be Chen Zhou." ”

Zhang Zhongyuan interjected: "There are still many estimates that you didn't expect. Okay, the two of you will go back and have a private chat. Now that everyone is here, let's start the first topic discussion. ”

Wu Xiping smiled and said, "Look, we can't leave Professor Zhang out in the cold, and let him look at us and say hello, it's embarrassing, haha." ”

Zhang Zhongyuan glanced at the old man, didn't bother him, and opened the notebook by himself.

Seeing this, Wu Xiping immediately stopped laughing.

He is too familiar with Zhang Zhongyuan's action, which means that you probably don't want to have a discussion with the amiable people, right? Then, you can't blame me for preparing too many questions...

Zhang Zhongyuan's question is that he put forward his own thoughts and questions from the perspective of this research topic.

Originally, this was normal, but the key point was that Zhang Zhongyuan's thinking and questions were one question mark after another.

Once, Wu Xiping didn't care about Zhang Zhongyuan's action, but during a topic discussion, he was anxious to be asked by Zhang Zhongyuan.

After a topic discussion, my voice was completely hoarse.

"Ahem..."Wu Xiping coughed lightly twice, beckoning Chen Zhou and Shen Jing to sit around, "Our topic this time is mainly the application research of the interpenetration and fusion of advanced algebra and mathematical analysis. ”

"I have also sent the information about this research to your mailbox, and I believe that you have all read it and have your own understanding. ”

"So..."After a slight hesitation, Wu Xiping called and said: "Shen Jing, you are a senior, let's talk about your views on this topic first." ”

Shen Jing thought for a moment and began to say: "As a student of the Department of Mathematics, mathematical analysis and advanced algebra are the two most important courses we begin to study as soon as we enter the university. ”

"At the same time, they are also the two most basic courses in mathematics, and they are used in almost all post-secondary courses. Advanced algebra is completed in the first year, while mathematical analysis is studied in the fall semester of the second year. ”

Speaking of this, Shen Jing paused, glanced at Chen Zhou, and then continued: "Advanced algebra mainly includes two parts, polynomial algebra and linear algebra. Whereas, mathematical analysis in general can be divided into five major blocks, limit, continuity, differential calculus, integral, and series. ”

"Our task is to find the connection between the two from these contents. ”

"For example, the objects of mathematical analysis belong to the field of real numbers, and some problems cannot be solved within the scope of the real number domain, or at least they are complex to solve. For example, the proof of the fundamental theorems of algebra in advanced algebra requires the help 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 derived from the generalization of the research object of mathematical analysis from the field of real numbers to the field of complex numbers..."

“... More examples of this can be found by exploring the content of both. So, although mathematical analysis is different from problems in advanced algebra, there is a close connection between the two. ”

Therefore, I think it is important to start with the specific problems involved in mathematical analysis and advanced algebra. ”

"Professor, these are some of my opinions. ”

After Shen Jing finished speaking, Wu Xiping and Zhang Zhongyuan glanced at each other, and they both saw a look of appreciation in each other's eyes.

Wu Xiping nodded, and said to Chen Zhou: "Chen Zhou, you can also tell me your opinion." ”

"Yes, Professor. Chen Zhou organized the language for a while, and then said, "Regarding the difference and connection between mathematical analysis and advanced algebra, my views are basically the same as those of Senior Shen Jing..."

“... But I need to add that, as far as I feel, higher algebra is studied from the perspective of macroscopic foundations, while mathematical analysis is studied from the internal mathematical relations. ”

That is, higher algebra is like a skeleton, and mathematical analysis is the interior. Both of them represent different perspectives on the world of mathematics..."

“... Well, higher algebra can guide the study of mathematical analysis on a macroscopic level. The profound study of space in advanced algebra, the construction of space through bases and algorithms, and the description of space from different angles through the transformation of the basis, corresponds to the various transformation techniques in mathematical analysis..."

“... Regarding the research ideas of this topic, I agree with Senior Shen Jing's opinion, and we can start from the specific problems involved in the two to study the internal connection. ”

"But I would like to add that in the study of the problem, the content of the two can be specifically linked. ”

"Here I will also give an example, the zero problem of functions in mathematical analysis generally adopts methods such as the intervalability of continuous functions, Rolle's theorem, Darboux's theorem, etc., and individual problems can be solved by Weierstrass approximation theorem. ”

"But if you connect mathematical analysis with advanced algebraic knowledge horizontally, you will get a relatively simple algebraic solution. ”

"Professor, this is my personal train of thought, please add. ”

After Chen Zhou finished speaking, he glanced at Shen Jing, and the other party was looking at him with a surprised expression.

Wu Xiping and Zhang Zhongyuan glanced at each other again, Wu Xiping's eyes were full of surprise and appreciation, and Zhang Zhongyuan's eyes were full of appreciation.

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 when I was young?