Volume 1: Student Life Chapter 91: First Lesson
The first lesson is mathematical analysis.
In this class, not only students from Chen Zhou's Department of Mathematics, but also students from two other departments attended the class together.
This class was taught by Professor Wu from the School of Mathematics, who has rich teaching experience.
Professor Wu adjusted his black-framed glasses, introduced himself, and then said, "You don't need to be restrained in my class. You can relax completely. You can listen to the class, study on your own, or read other books. I don't make any disciplinary requirements."
Hearing this, the students were overjoyed.
Professor Wu glanced at the happy students and continued reluctantly, "Of course, I have a prerequisite. No matter what you do, you must ensure that you keep up with the course progress. Then, before the end of each class, I will give you a question worth several points based on the course progress to test your learning situation in class."
Okay, it turns out that what I said before was all lies, and this is the point.
Sadness always comes so quickly, especially when you are happy.
Some students began to complain about Professor Wu in a low voice, but Professor Wu didn't care.
Next, Professor Wu picked up the textbook in his hand and said, "This math textbook was written by Professor Wu of Yanda University. It has been used for several classes in Yanda University and the teaching effect is quite good."
“Mathematical analysis is one of the most important basic mathematics courses. It is an important foundation for your subsequent courses and your future work in the field of mathematics. So, I hope you will learn it thoroughly.”
Chen Zhou took a look at the yellow-covered book "Mathematical Analysis" (Volume 1), which he needed to learn this semester.
There are also the second and third volumes, which will be completed in the next two semesters.
"Mathematical Analysis" (Volume 1) has a total of six chapters, covering functions, limits of sequences, limits and continuity of functions, derivatives and differentials, applications of derivatives, and indefinite integrals.
Chen Zhou glanced at the catalog and a smile appeared on his lips.
Chen Zhou was a little worried at first because when the system was activated and he chose the advanced mathematics self-study task for the first time, he had not yet filled in his application form.
After filling out the application form and receiving the admission letter , he logged into the student system and looked up the courses in the Department of Mathematics, but found that there was no such course as advanced mathematics.
Chen Zhou was stunned for a moment and even suspected that this stupid system was cheating him again.
However, the system gave him a word of comfort: "Knowledge is interoperable."
Although he doubted this sentence, he still completed the task. He couldn't be stuck with the task.
But now, after reading the contents of this book, he feels that there is nothing wrong with the statement that knowledge is interconnected.
Yes, that’s right, these contents are already very familiar in advanced mathematics.
For those who are not familiar with the knowledge yet, Chen Zhou believes that they will soon be able to become more familiar with it than before.
Chen Zhou collected his thoughts and heard Professor Wu's voice: "What is mathematical analysis? Mathematical analysis, also known as advanced calculus, is the oldest and most basic branch of analysis."
“The main content of mathematical analysis is calculus, the theoretical basis of calculus is the theory of limits, and the theoretical basis of the theory of limits is the theory of real numbers.”
"Then students, do you know what the most important feature of the real number system is?" Professor Wu asked himself and answered, "The most important feature of the real number system is continuity. With the continuity of real numbers, we can discuss limits, continuity, differentiation and integration. It is in the process of discussing the legitimacy of various limit operations of functions that people gradually established a rigorous mathematical analysis theory system."
"Now that everyone understands the origin of fractions, let's officially start the class." Professor Wu said, and slowly opened the textbook.
Chen Zhou thought it was OK. Who said university teachers lecture very fast? Isn't this pre-class popular science lesson considerate?
However, Professor Wu's next words seemed to be intended to answer Chen Zhou's doubts.
Professor Wu said, "First turn to page 4 and start from the last paragraph. I will tell you about the Dedekind segmentation. This point is very important and must be understood thoroughly."
"Professor Wu, where is the previous content?" someone raised his hand to interrupt.
Professor Wu glanced at the man and replied lightly, "Do I need to explain the assembly to you? Just review it if you want to."
Then he continued his lecture: "Before talking about the Dedekind partition theorem, I need to talk about the Dedekind partition first..."
"…then Dedekind's theorem states that for any partition of R (A|B), there must be a minimum number in B."
"...Bounded sets and absolute boundaries are both conceptual. You can figure it out for yourself. I won't explain it."
"…There are also proofs for several common inequalities. They are relatively simple. See for yourself."
"Then let's talk about functions..."
Chen Zhou looked at Professor Wu who was talking nonstop on the podium in silence. Was this a lecture? This was faster than him flipping through a book...
Soon, the first chapter ended and Professor Wu began to talk about the second chapter, the limit of sequences.
Chen Zhou couldn't help but sigh, fortunately he had finished teaching himself advanced mathematics, otherwise he really doubted whether he could keep up with the progress.
The Dedekind partition and the Dedekind segmentation theorem are not easy to understand.
However, Chen Zhou discovered that Zhao Qiqi and Zhu Mingli had sparkling eyes and were listening with great interest.
The fourth roommate, Li Li, was also buried in a book.
"Sure enough, playing games is just an illusion..." Chen Zhou said silently in his heart, and then looked around at the other classmates in the class.
Except for a very few people who obviously cannot keep up with the progress, most of the students are either concentrating on listening to the class or studying on their own.
There were still twenty minutes left before the end of the get out of class. Professor Wu stopped to take a sip of water and then said, "That's all we'll cover today. The progress is a little slow. Now, it's time to answer questions in this class."
After saying that, Professor Wu turned around and began to write the questions on the blackboard.
Chen Zhou flipped through the book. The yellow-skinned math textbook had already covered two chapters. Was this progress considered slow?
After Professor Wu wrote the questions on the blackboard, he turned back and said to everyone, "Everyone, find a piece of scratch paper and write your name and answer. If you don't know the answer, just write your name."
Chen Zhou first took out a piece of draft paper and wrote his name on it, then looked up at the blackboard and copied the question on the draft paper.
"Let Xn = (1 + ((-1)^n)/n)^n, n = 1, 2, 3..., and prove that {Xn} is a divergent sequence."
The question was very short. Chen Zhou only took a glance at it and finished it.
Professor Wu didn't make it too difficult for everyone in the first class. This question was indeed not difficult.
Chen Zhou wrote:
"Proof: Since k→＋∞lim(1＋(（－1）^2k）/2k)^2k=e"
"And k→+∞lim (1+((-1)^(2k+1))/(2k+1))^(2k+1)=k→+∞lim[1/((1+1/2k)^2k+1)]·[1 /（1＋1/2k）]=1/e”
"Thus n→∞limXn does not exist."
"It is proved that {Xn} is a divergent sequence."
The proof process is also very simple, mainly using the basic theorem of continuity of the real number system.
Chen Zhou checked it and found no problem, so he stood up and prepared to hand the draft paper to Professor Wu.
Chen Zhou noticed that there were still a dozen people left in the classroom.
The three younger brothers in his dormitory had already left.
Chen Zhou politely handed the draft paper to Professor Wu and left the classroom.
