Just turned over a new leaf and became a wise and intelligent student

Chapter 111 The Deterministic Characteristics of Classical Probability Theory and D’Alembert’s Hybrid Mathematical View (23)

"What I told you is just the beginning."

Xu Qingshan didn't intend to waste Ye Xincheng's time for too long.

"After the formation of probability theory, Jacob Bernoulli's discovery of the law of large numbers and normal distribution laid the core foundation for the thorough formation of probability theory and the rapid development of statistics."

"I see, normal distribution, that's what we learned?"

Ye Xincheng felt great when he was listening to Xu Qingshan’s popular science lectures.

It was like I was listening to a divine book.

But what was surprising was that he could actually listen to this kind of heavenly book?
"Yes, in fact, that is also called Gaussian distribution."

"Gauss, the king of mathematics?"

Although Ye Xincheng was not very fond of mathematics, he had heard of Gauss's name.

"Well, although this is only one of Gauss's many achievements, it plays a very important role in probability theory. Gaussian distribution is widely present in nature and social phenomena. For example, indicators such as height and weight can be approximately normal distributed."

Xu Qingshan gave a brief account of the situation.

"Even if that's all, we've already started learning about it in high school. I don't think probability theory is that difficult."

Ye Xincheng suddenly felt confident.

It seems that the gap between what Xu Qingshan is learning and what he is learning is not too big.

"Incorrect."

Xu Qingshan shook his head again and said with a smile.

“This is just the beginning.”

"Later, Laplace's contribution truly laid the foundation for probability theory. He proposed the classical definition of probability and defined the concept of probability from the perspective of realization possibility."

"He also founded analytical methods, introduced the Laplace variable and the Laplace integral, and studied the roots of polynomials and the properties of symmetric functions"

"Stop, stop, stop."

Ye Xincheng quickly called a stop.

If things like normal distribution and Gaussian distribution were still within his scope of knowledge, then he had never even heard of Laplace mentioned by Xu Qingshan.

"That was only two hundred years ago."

Xu Qingshan saw that Ye Xincheng's eyes were rolling around and said with a smile.

"Then there was the Chebyshev inequality, which I used when I first did a math competition. Then Markov created the Markov process, which is also one of the foundations of modern engineering applications."

"Okay, I admit that probability theory is actually quite complicated."

Ye Xincheng admitted defeat, he was truly listening to the divine book.

"complex?"

Xu Qingshan shook his head again.

“It’s still wrong.”

"This is just the foundation of probability theory. What follows is the rigorous expression and beginning of modern probability theory."

"In the 20th century, Kolmogorov used the method of measure theory to make probability theory a rigorous science. The Kolmogorov inequality has become the core tool for analyzing random process phenomena."

“If we were to count the birth, establishment, foundation, improvement, rigor, and evolution of a discipline, and finally its becoming a rigorous and widely recognized discipline, it actually gathered the efforts and inspiration of countless geniuses.”

Xu Qingshan told Ye Xincheng about his insights on probability theory and even mathematics.

He has been inputting intensively recently, but he feels a little bored if there is only input but no output.

While saying these words, Xu Qingshan was also constantly organizing his thoughts.

"The origin and development of probability theory is a long and rich process. From ancient times to modern times, mathematicians have revealed the regularity of random phenomena through continuous research and exploration, and established a complete probability theory system."

"In this process, probability theory has been constantly receiving criticism and comments from all walks of life, and has been continuously integrated and optimized with various disciplines, until it finally became what we have today."

"To the great mathematicians."

Xu Qingshan picked up the "Probability Theory" on his desk.

Ye Xincheng didn't know why, but when Xu Qingshan did this action so casually, he felt that he was very handsome.

He is like the kind of scholar who is full of warmth, but also a cold and aloof academic.

Very visual.

only.

Ye Xincheng found that Xu Qingshan maintained this posture and did not move. His expression became dull and his eyes became empty, as if he had lost his mind for a moment.

"Shan'er?"

Ye Xincheng asked tentatively.

He thought Xu Qingshan was in a strange state, so he looked back and saw no one coming over.

Now it looks like Xu Qingshan’s soul was suddenly sucked away by someone.

It is difficult for Xu Qingshan to describe his feelings at this moment with words and actions.

Just now.

When he was briefly explaining the mathematical history of probability theory to Ye Xincheng, it seemed as if a complete route had been sorted out in his mind.

What he saw and learned, the things written section by section in the books, were spinning, dispersing, and reassembling in his mind in a dancing posture.

He found that he seemed to have discovered something.

It seems to be something that is not so related to mathematics itself, but it complements mathematics.

Xu Qingshan's eyes were out of focus.

He was completely immersed in his own thoughts, and even if Ye Xincheng touched him, he couldn't be awakened.

A hot, clear, surging wave flowed from Xu Qingshan's chest along his throat and cervical vertebrae, all the way into his brain and rushed straight to the top of his head.

In just a moment, he felt that his spiritual platform was bright. Others' foreheads were dark, but Xu Qingshan's were glowing.

“I think I can write something.”

There was joy in Xu Qingshan's words, and he formed a complete idea.

"What are you writing? You couldn't wake me up just now. You scared me."

"No more talking. You go back to study. I'll take some time off and go home first."

Xu Qingshan quickly stood up and went to the office to ask for leave.

However, he seemed to be afraid that he would forget this idea. Even though his memory was now far superior to that of ordinary people, he still took a few homework papers, put a folder under them, and wrote as he walked.

[The deterministic characteristics of classical probability theory and d'Alembert's mixed mathematical view]

That's right.

What Xu Qingshan was writing was the topic of the thesis that he suddenly thought of.

However, what he chose to start with was not the arithmetic or theoretical models of mathematics itself, or the most cutting-edge algorithmic content, nor was it some conjectural solution. It was not that advanced.

He just wanted to express what he felt and gained during his time studying probability theory from the source, and he wanted to describe it.

Xu Qingshan felt that he seemed to have found the original intention of learners to write papers.

Duan Yongming was in the senior year office at that time.

He has returned from Principal Lin's office.

He had just come back and sat on the chair, leaning lazily against the backrest, taking off his reading glasses, preparing to relax for a while before looking at the questions.

But as soon as he looked up, he saw Xu Qingshan walking in from outside the office with a folder.

Duan Yongming's heart skipped a beat.

isn't it?
I just handed in the document, and you're here again?

Our senior high school office is not close to the principal’s office!
It's okay for me, my old bones, to run once, but if you ask me to run several times, I can't bear it.

Duan Yongming sat up straight, stared at the screen, pretending he saw nothing.

He almost buried his head so that Xu Qingshan couldn't see him.

but.

Steal a glance out of the corner of my eye.

Duan Yongming found that Xu Qingshan was not walking fast and was writing while walking, which made Duan Yongming even more speechless.

This young master is still thinking and writing here?
Although Lao Duan himself had told the story over and over again about how Class 1 took Xu Qingshan to the cafeteria to eat while walking, and how he saved time for studying.

But he never expected that one day this boomerang would hit him in the face.

Look at the folder in Xu Qingshan's hand. Doesn't it look like a death warrant for Lao Duan to run errands?

"Miss Zhang?"

Xu Qingshan didn't write very fast. He just simply recorded the ideas and perspectives that came into his mind.

This way, it will be easier to be organized when you write your paper.

But when he entered the office, Xu Qingshan did not see his class teacher Zhang Jingxian.

He had no choice but to go to Duan Yongming.

"Old Duan?"

"Ah Qingshan, I have already given the one just now to Principal Lin. He thinks it is very good, but if you have other ideas, you should be able to wait until the adjustment is completed."

"I want to ask for leave from you. I have something to do."

Xu Qingshan now seems to be a little disrespectful to the teacher, and the person in front of him is the section chief.

Because when Xu Qingshan was talking to Duan Yongming, his eyes were always fixed on the papers in his folder and his pen was always moving.

"Ah? Asking for leave? What for?"

Duan Yongming was stunned for a moment, then heaved a sigh of relief.

"Why didn't you say so earlier? If you want to go back, go back and rest. Why do you need to ask for leave? As long as it doesn't affect other students' studies, it's fine. Remember to send me a message when you leave, and send me a message when you get home. Don't run around, and be safe."

When Duan Yongming heard that he didn't have to run anymore, he breathed a sigh of relief and spoke more heroically.

"Oh, good."

"I suddenly had an idea and wanted to write a paper. It would be more convenient to write it on a computer, so I went home."

Xu Qingshan responded.

Duan Yongming is very easy to talk to.

It’s mainly because of the school’s style. Scores are everything.

Although scores are not the only consideration here, Xu Qingshan's scores are enough to give him privileges.

If he were at Longjiang No. 1 Middle School, most people there might be more relaxed about management, but they would not be able to break the rules for Xu Qingshan.

Xu Qingshan nodded.

He just came over to let you know.

"Okay, be careful."

"Wait, what are you talking about?"

Duan Yongming reacted and couldn't control his voice, so he asked loudly.

"hold head high?"

"I said I had some ideas and wanted to go back and try to write a paper on the computer."

For the first time since entering the office, Xu Qingshan took his eyes off the folder and looked at Duan Yongming with an innocent face.

The new book of Blood Red Boss! Go, go, go!


(End of this chapter)