From small town academic to chief scientist

In fact, just before Zhouyi released this news, the School of Mathematics of Beijing University even advertised on its official blog that its school of mathematics has good feng shui.

It is a courtyard house with unique and unimaginable advantages.

As a result, as soon as the news of Zhou Yi came out, countless netizens started to rush to Beijing University.

Asked what he thought of Beijing University.

In the past, the domestic mathematics community was divided into six major schools: Shangjing, Chinese Academy of Sciences, Shangjing Normal University, Aurora, Nankai and Shanda.

But after Yau Shing Tong returned to China, the Yau Shing Tong Mathematical Science Center was basically the only one.

Only Beijing University and the Chinese Academy of Sciences can have a little discussion with them.

Later, SUSTech introduced Fields Medal winner Effie Germanov, who also had a certain influence.

Up to now, Zhou Yi himself is the founder of Yuzhou Institute of Advanced Studies.

Then the entire Daxia Kingdom mathematics school can only have the birth of the top five new ones.

The strongest one is definitely the Yau Shing-tung Mathematical Science Center of Shuimu University, followed by the Yuzhou Institute for Advanced Study.

Next are the Chinese Academy of Sciences, Beijing University and Southern University of Science and Technology.

However, in the long run, the potential of Yuzhou Institute of Advanced Studies is definitely greater than that of Qiu Chengtong of Shuimu University.

However, from the perspective of outsiders, especially those outside academia,

The Mathematics Department of Shangjing University is still unique.

Therefore, many netizens asked the Mathematics Department of Beijing University what they thought of Zhou Yi’s speech.

How else can they watch, just wait and see the joke.

I originally didn't want to have a head-on confrontation with Zhou Yi, but by chance, I bumped into each other.

[Why does going to Beijing University give me a feeling of schadenfreude? 】

[Nonsense, can you take pleasure in others’ misfortune if you go to Beijing University? Can you not be angry that the golden generation you worked so hard to cultivate was poached by Zhou Yi? 】

[The person above is right, Zhou Yi is Qiu Chengtong’s apprentice, and the relationship between Zhou Yi and Qiu Chengtong is very good.

Can the Department of Mathematics at Beijing University not be happy to see that the Yuzhou Institute for Advanced Study is now in such a turmoil? 】

[Yes, the Mathematics Department of Shangjing University is probably jumping for joy now. 】

[Professor Zhou now says he will give an explanation, but I don’t know what it is. I look forward to a reversal. 】

[I really want to see Shangjing University being slapped in the face by Professor Zhou Yi. It is ridiculous that academics can be related to Feng Shui. 】

[Indeed, when doing academic work, we still talk about metaphysics. Why do we believe in science? 】

[One thing to say is that the poor geographical location of Chongqing High School is probably the biggest impact on enrollment. 】

[Is Princeton University still in a small town? Go there to study for a few years, and then you can live in a big city for the rest of your life.

I think this choice should be a good choice. After all, people who can get high scores are geniuses and mature much earlier than ordinary people. 】

[Yes, after studying for 8 years, I will definitely become a leader in the industry in the future. There is no doubt about this. 】

Internet fans are looking forward to Zhou Yi's follow-up and the confrontation with Beijing University.

But Zhou Yi was too lazy to reply to some of Aite's own comments.

After sending the message, Zhou Yi said to everyone in the Chongqing High Court:

"Everyone, please disperse. I am confident enough to defeat the entire metaphysics community and make them recognize me as the new generation's patriarch."

Seeing that Zhou Yi was so sure, everyone couldn't say anything else, so they all said:

"Okay, let's go now, Professor Zhou, and wait for your good news."

Zhouyi said:

"good."

After they left, Zhou Yi began to take drugs and read "The Book of Changes".

"The enhanced version of the focus capsule that I drew in the lottery was used in the right way to learn "The Book of Changes".

Anyway, this thing must be the best when used on the blade. "

In two days, Zhouyi was able to read Zhouyi to a high level.

I have to say that "The Book of Changes" is indeed a subject of great wisdom.

The mathematical knowledge used is comprehensive, and it is all mathematical knowledge developed after the 16th century.

It even involves a lot of modern mathematical knowledge.

Zhou Yi murmured alone in the room:

"No wonder those who have studied the "Book of Changes" in the past generations have all been masters of mathematics. It basically contains mathematical knowledge.

If the knowledge of mathematical branches such as group theory can be used to further derive it, the so-called rumors that Chongqing High Court has bad feng shui will be self-defeating. "

Zhou Yi closed his eyes and rested his mind for half an hour, and then dictated in the room:

"Write the introduction first. Section 1.1 of the first chapter is called "A Review of Mathematics Research by Yi Scholars in the Past Dynasties."

Combining the conclusions of famous historical figures to demonstrate the contribution of mathematics to the development of "The Book of Changes\

,"It is obviously more convincing, so Zhou Yi put this chapter in the first chapter.

The Yi scholars of all dynasties have worked tirelessly to study mathematics in order to study the "Book of Changes".

You disciples and disciples dare to say that "The Book of Changes" does not require strong mathematical knowledge?

Are you going to bully your master and destroy your ancestors?

Zhou Yi's move directly put himself in the strongest position.

Once these people realize the innovation of "Zhouyi" by mathematics, it is difficult to say whether "Zhouyi" is metaphysics or mathematics.

Then Zhouyi began to describe the development of mathematics in Zhouyi.

Let’s start with the relationship between set theory and Zhouyi.

Zhouyi began to say:

“Set theory is the foundation of modern mathematics. It not only penetrates into various fields of mathematics, but also penetrates into many fields of natural science and social science.

The German mathematician G. Cantor (1845-1918) first proposed the concept of sets. He published a series of papers on set theory from 1872 to 1897, laying the foundation for set theory. "

Zhou Yi first explained the origin of set theory and prepared for what came next. Zhou Yi continued:

""Xi Ci" says: 'Things are grouped together, and things are divided into groups.'

The ‘class’ and ‘group’ mentioned here are very close to the concept of ‘set’ in mathematics.

Many propositions in the study of Yi studies will be more convenient, clear and precise if described in the language of set theory, which will help reveal the essence of the problem.

This chapter first introduces some basic concepts of set theory, and then explains the connection between Yi Xue issues and some basic concepts in set theory. "

Zhouyi then divided this large chapter into four subsections.

"Definition 2.2.3:

Let A_1, A_2,…,A_n. is n sets, take the element α_1 in A_1, take the element α_2 in A_2,... take the element α_n in A_n,

Create an ordered n-element group (a_1, a_2,..., a_n,), which is called an n-ary ordered group of the set A_1, A_2,..., A_n. The set of all n-ary groups of A_1, A_2,…,A_n:

D={(a_1, a_2,…,a_n)丨a_1∈A_1, a_2∈ A_2,…, a_n∈A_n}

It is called the Cartesian product of the set A_1, A_2,..., A_n, and is written as:

D=A_1*A_2**A_n.

Special case: If A_1=A_2=…=A_n=A, then D is called the n-fold Cartesian product of A.

A subset R of A_1*A_2**A_n is called a relation of the set A_1, A_2,..., A_n.

Many concepts in Yi studies are closely related to the concept of set relationship.

Let us give you a random example, which I believe all Feng Shui masters must understand very well.

This should be Example 2.2.1.

The ancient book "Xici" says: "Yi has Tai Chi, which generates two rituals. Two rituals generate four images, and four images generate Bagua." ’

He also said: "When the Eight Diagrams are arranged in a row, the Xiang is among them. Therefore, when they are emphasized, the Yao is among them." ’

What philosophical meaning these words have, we will leave it alone for now.

But from the perspective of set theory, the Yi Gua set can be regarded as the Cartesian product of other sets. For example:

Assume A={1, 0} is the set of "two instruments", and do the double Cartesian product of A:

B=A*A={(1,1),(1,0),(0,1),(0,0)}

In this way, we can get a set of ‘four images’.

Construct the triple Cartesian product of A:

C=A*A*A={(1,1,1)(1,1,0)(1,0,1)(0,1,1)(1,0,0)(0,1,0 )(0,0,1)(0,0,0)}

You will get a collection of ‘gossip’.

Then if we do the 6-fold Cartesian product of A, we can get the Yi Gua set.

The process here is relatively simple and simple, and readers are advised to prove it with confidence. "

Zhou Yi left a homework. After all, he wanted to be the originator of this direction. How could he not leave any homework?

Let these metaphysics teachers experience the pain of mathematics students.

The pain of proof questions.

Zhou Yi took a sip of water, moistened his throat, and continued:

"If we start from the set B of the "four images" and do the triple Cartesian product of B, we can also get a set of Yi Gua.

D=B*B*B.

Similarly, we can also start from the set C of 'Bagua' and do the Cartesian product of C and C, and we can also get a set of Yi Gua,

Due to limited time and relatively simple steps, this is left as an exercise.

Next, we conduct further analysis and find that Yi Gua Ji D can also be regarded as some other forms of Cartesian products.

However, time is limited and the process is relatively simple, so it is left as an exercise for the majority of Yi-learning enthusiasts. "

In each chapter, Zhouyi uses examples from "The Book of Changes" or other ancient books as examples or exercises.

Give it to this group of Yi Xue enthusiasts. When the time comes that these people can’t do it, they will have to beg themselves.

How many people are there who understand both easy learning and mathematics?

Even after these people are done, can they still have their own authority?

Everyone has to ask for help.

Zhou Yi has already calculated it, and by then most of the entire metaphysical world will have to come to beg him.

After finishing the second chapter on the relationship between Zhouyi and set theory, Zhouyi began to write the third chapter.

The relationship between Zhouyi and Boolean algebra.

Before each major chapter, Zhouyi must first write about the relationship between the mathematical knowledge involved and the study of "Yi" in "Zhouyi".

Otherwise, it would be impossible to attract this group of people who tirelessly study metaphysics.

“Boolean algebra first emerged from the study of the laws of logical thinking.

The British philosopher G. Boole (1815-1864) used mathematical methods to study the laws of the relationship between sets. His research work later developed into an independent branch of mathematics.

With the development of electronic technology, Boolean algebra has been widely used in automation technology and electronic computer technology.

A Boolean vector is an array consisting of two numbers, 0 and 1, arranged in a certain order. It is widely used as a mathematical model to describe things with several factors, each of which has two opposite states.

We will see that each hexagram in the Yi Gua set is a Boolean vector, and the Yi Gua set itself is a Boolean algebra.

Therefore, in this chapter I am going to introduce some preliminary knowledge about Boolean vectors and Boolean algebra,

Introduce the relationship between Boolean vectors, Boolean algebra and Yi Xue. Before introducing these two concepts, we first introduce the concept of operations. "

This chapter also contains a lot of content. In three sections, Zhouyi once again left a lot of exercises.

Without leaving exercises to insult their IQ, Zhou Yi would not be able to express his bad temper.

Only by leaving exercises can they know what the gap is. Zhou Yi suddenly had an idea. Is there a better way for them to ask themselves?

But I couldn't think of anything for a while, so I started working on the inner cylinder at the back.

Immediately afterwards, Zhou Yi began to write the fourth chapter.

The relationship between Zhouyi and group theory.

First of all, there is the connection between the group theory written and the "Book of Changes".

"Group is an extremely important concept in modern mathematics. It was introduced in 1832 by the young French mathematician Galois in the 19th century when he was studying the solution of algebraic equations of more than five degrees.

Groups have very important applications in various branches of mathematics and in many theoretical sciences and technical sciences.

For example, the Lorentz group in relativity and the Lie group in quantum mechanics are common-sense tools in modern science. Today, group theory has developed into a difficult branch of mathematics.

We will see that after properly defining the operations of Yi Gua Set A, Yi Gua Set A becomes a commutative group, which is isomorphic to the modulo 2 additive group.

Therefore, it is natural to apply the basic knowledge of groups to the study of Yi studies.

This chapter first introduces the basic concept of groups, then proves that Yi Gua Set A is a group and discusses some properties of Yi Gua groups and their applications in Yi studies. "

Zhou Yi continued:

"Theorem 4.1.2:

Suppose H is a non-empty subset of group G. The necessary and sufficient condition for H to be a subgroup of G is: for any two elements a and b of H, there is ab^(-1)∈H.

The proof process is skipped here, because many mathematical foundations of group theory have been explained before.

I believe that with the level of masters, you already know that practice makes perfect, and this simple proof should be a piece of cake.

Let's look at a few examples below.

Example 4.1.1: .

example.

Example 4.1.3:

Because the inverse element of element a of Yi Gua group is a itself, a^, =a.

Therefore, according to Theorem 4.1.2, when you want to verify whether a certain subset H of Yi Gua group A is a subgroup of A, you only need to verify that when a, b∈H, ab^(-1)=ab∈H .

That is, just verify that the multiplication of H by A is closed.

According to this, some interesting subgroups of A can be verified.

H_1={干}={1, 1, 1, 1, 1, 1} is the first-order subgroup of A (a finite group with several elements is called a several-order group).

H_2={Qian, Kun}={(1, 1, 1, 1, 1, 1), (0, 0, 0, 0, 0, 0)} is the second-order subgroup of A.

Due to limited time, the fourth-order subgroup of A and the eighth-order subgroup of A are left as exercises for readers to practice.

I believe your wisdom is definitely no problem. "

After Zhou Yi finished speaking the fourth chapter, he took another sip of water and looked at the time. It was already three o'clock in the morning.

Zhou Yi smiled bitterly and said:

"I have to stay up late again, but I can't finish writing even if I stay up late. The most I can do is finish "The Book of Changes" and number theory, "The Book of Changes" and combinatorial theory.

As for the study of the "Book of Changes", probability theory, and the application of mathematics in Yi studies, we will talk about it later. "

Zhou Yi rubbed his head and then continued to talk to Peony.

If Peony wasn't very intelligent, she could help write papers and help with formatting.

It is simply impossible to write a book of more than one hundred pages.

I saw Zhou Yi chanting:

"In the first chapter, we talked about Qin Jiushao's "Gua Gua Fa Wei" and "The Number of Dayan" in "Book of Changes·Xici" both involve the concept of congruence.

The concept of congruence is one of the most basic concepts in number theory.

The contents of the traditional Yi-study are the so-called images, numbers, principles, and accounting. Therefore, there are many places involving number theory in the Book of Changes, such as the number of heaven and earth, the number of 筮, the number of rivers, etc.

However, most of the numbers are relatively simple. This chapter only introduces the relationship between the concept of congruence and Yi Xue.

In particular, the "Zhouyi Xici" method involves multiple data; "its use is ninety-nine", 49

The 2 of ‘divided into two’, the 1 of ‘hanging one’,

The 4 of "Butterflies are made of four", and the 3 of "Three become Yao".

These data have always been regarded as mysterious by Yi scholars. Can changes be made?

Why is the ‘Dayan Number’ 50?

But its use is "nine out of forty" and so on.

These are all long-term unresolved issues in the study of Yi studies.

I will discuss these issues further in Chapter 8. "

I kept writing until dawn. Zhou Yi really didn’t want to write anymore because he was too sleepy.

If you write it all down, it means nothing.

The current five and a half chapters can already explain a lot of problems.

Originally, Zhouyi planned to finish writing "Zhouyi" and number theory, "Zhouyi" and combinatorial theory, but now it seems that it is not necessary.

As long as people who study metaphysics are not stupid, they will carefully figure out its profound meanings.

If you understand the profound meaning, you will learn from the various masters of Yi studies in the Song Dynasty and try to innovate and re-create the "Book of Changes".

For example, Shao Yong of the Great Song Dynasty's "Huangji Jingshi Shu", "Tian Yuan Shu", "Si Yuan Shu" and so on.

The seemingly fantasy name actually refers to the study of mathematics or Yi Xue.

Many authors of fantasy fairy tales have used it for secondary creation.

As for the content at the back of the book, Zhou Yi planned to cut off chapters and let them beg for updates.

Otherwise, it would be too cheap if I wrote it casually.

Zhou Yi felt that he was also a world-famous mathematician, so how could he do something too cheap?

If these people who study metaphysics don't boast themselves to the sky, the contents of a single section of the Book of Changes will not be updated.

Moreover, Zhouyi specifically concluded that the number of Dayan is 50, but its usage is "forty to nine".

Shouldn't this group of people be allowed to kneel and sing about conquest?

After finishing writing, Zhou Yi began to think about how to name it.

This book is sure to be a hit in the metaphysical world.

As we all know, "Zhouyi" was created by absorbing the essence of "Lianshan Yi" and "Guizang Yi".

The book "Book of Changes" has been absorbed by Confucianism, Taoism, Buddhism and other schools of thought, so this book is for many declining schools of thought.

It must be a ground-breaking innovation.

Zhouyi thought about it again and again, and simply called it "Mathematical Principles of Zhouyi".

Hey, this ‘Book of Changes’ is a pun here.

Very beautiful, Zhou Yi thought proudly.

There was no written content, but Zhou Yi still wrote a table of contents.

The relationship between "Zhouyi" and combinatorial theory, the relationship between "Zhouyi" and probability theory, and the application of Zhouyi in Yi study.

Before each missing chapter, Zhouyi still gave a description,

For example, the relationship between "Zhouyi" and combinatorial theory,

[Combinatorics is an ancient discipline, a branch of mathematics that is still flourishing today. Its main research content is counting and configuration.

For example, using the two symbols of Yang Yao "一" and Yin Yao "Yi", take 6 symbols in sequence each time and arrange them into a hexagram. How many different hexagrams can be arranged in total?

This is a typical combinatorial counting problem.

For another example, "Xici" says: "The river produces pictures, Luo produces books, and the sages follow them." After simplifying Luo Shu into "Nine Palaces Pictures\

,"It is equivalent to filling in the nine numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 in a 3*3 square, so that the three rows, three columns and two diagonals The sums of all three numbers are equal.

This is a typical configuration problem. Graph theory is a branch of mathematics separated from combinatorial theory in recent decades and has developed vigorously with the needs of computing technology.

Due to time constraints, I won’t write much here. I’ll write more when I’m happy. 】

Combinatorial theory is also widely used in today's computers, not to mention easy to learn.

For example, the relationship between "Zhouyi" and probability theory:

[Probability theory and mathematical statistics are a science that studies the regularity of random phenomena. It is an important and active branch of mathematics.

The ancients regarded "The Book of Changes" as a book of divination, and used Yi hexagrams to perform divination. When doing divination, one must first obtain a hexagram through a fixed procedure.

But which hexagram is obtained is not known in advance, it is a random phenomenon.

Therefore, when studying "The Book of Changes", you must not understand some basic knowledge of probability theory.

This chapter mainly introduces the relevant knowledge of classical schematics, especially the Bernoulli (1654-1705) schematic that is closely related to the ancient "Die He Cheng Gua".

But due to time constraints, I won’t write it down yet. 】

Probability theory is closely related to robot learning, and Ding Jian is currently researching this direction.

It's already eight o'clock in the morning, and many marketing accounts have already started making videos.

The copywriters are already in place, and all types of copywriting are available.

It depends on the results later.

Happy New Year, cute brothers and sisters!