All-round mathematician

Chapter 113 The Difference Between High Numbers and Low Numbers
Advanced mathematics is so difficult.

Half an hour later, when he arrived at the airport, Feng Yao had already booked two air tickets, and flew from Shanghai to BJ today.

There is no airport in Wuzhou, so it is too inconvenient to make a round trip. After discussing with Feng Yao and Yang Fan's parents, they went directly and left it to Teacher Feng to solve the problem.

Looking at the time, Feng Yao found that there was still an hour before takeoff, and half an hour later the landing procedures began, which was still early.

In the waiting hall, teachers and students are waiting for the flight, and the topic of advanced mathematics is still going on.

Feng Yaodao: "Mathematics learned from university is called advanced mathematics. Elementary mathematics studies constants and uniform variables, while advanced mathematics studies non-uniform variables."

Although Yang Fan has read several advanced mathematics books, he knows them but doesn't know why, and he can't understand them.

Confused, Feng Yao understood and continued to explain: "In layman's terms, for example, π. We learned it in elementary school, and the calculation method directly uses 3.14 as the final answer. In middle school, what we learn is 3.141414... infinite Cycle, or replace it with the character π, this is a uniform variable, which can be accurately measured. The higher mathematics of the university studies 3.1415926...the number has no beginning and no end."

This is easy to understand, there are endless changes between calculation and non-calculation.Yang Fan nodded, feeling that he understood a little bit.

"It doesn't just stop here. When there are hundreds of thousands or millions of decimals, it is infinitely close to 0, so can it be counted as zero?" Feng Yao said.

"This..." Yang Fan hesitated, the number after one hundred thousand million after the decimal point is meaningless, and there is no need to be more precise, "It should be useless, and it doesn't need to be measured."

"No, no, Yang Fan, you still don't understand that if it exists, it cannot be counted as zero. Here comes the concept of limit and differential, which is also the second mathematical crisis in mathematics. Since it is an increment and not zero, The rigor of mathematics must not count as zero. The ε-δ language appears, which is the basic knowledge of advanced mathematics.”

It's so high-end, Yang Fan can't understand the language behind it, but it's still the foundation of advanced mathematics.

"Mr. Feng, you just gave me a few advanced mathematics books at that time, aren't you afraid that I won't understand? I searched, and some of them are mathematics books for graduate students." Yang Fan hid this question for a long time, and he didn't Time to ask, because of the help of the system, it is not wrong to do it anyway.

"This matter..." Feng Yao hesitated, and finally said frankly, "Just remember it, don't say it out. The few books I gave you are all Western translations, and Western natural sciences all started compared to my country In the early days, the system was relatively rigorous, and it was easy to understand from easy to difficult. However, there seems to be a gap in the university books in our country, and it is not clear."

Feng Yao's knowledge has not yet reached the level of writing textbooks, and he is just following others' opinions. Every student says that the span of college mathematics is too large, and there must be a reason for it.

After scrutiny and deliberation, or the knowledge taught is not good, can this be nonsense?Absolutely not.The only remaining reason is that the textbooks are poor.

"The books in middle school are basically universal. In universities, everyone uses their own books. There is always a difference. The only ones who work hard are the students."

Feng Yao is lucky for graduating from Mizuki, the famous school has its own heritage, and generally speaking, the teaching is good.After excluding the top [-] professional schools in China, the education systems of various schools are uneven, and they are crossing the river by feeling the stones.

Yang Fan always thought that all schools in the university basically used the same book, so there are so many ways in it.

If they are not uniform, there is no way to compare them.You say you are the first, what evidence do you have.Universities do not have a unified national examination, as long as they complete the credits of their own school.

"Don't say it's you, I, who have been here, think it's very complicated. Science and engineering students look down on literature and history students who have learned a little-calculus, how difficult it is. Mathematics students despise science and engineering and know something so-called-advanced Mathematics is presumptuous."

"Students in the mathematics department in the real circle, if calculus is divided into mathematical analysis, they can learn more profoundly. Some people call this course Shufen, and they love and hate it, and they gnash their teeth."

Having become more knowledgeable, Yang Fan found that to learn mathematics, he had to ridicule each other for their low IQ, which was unavoidable.

After graduating from literature and history, I have never been exposed to calculus in my life, so what is the use of learning it.The focus of science and engineering is naturally on majors, such as finance, computers, precision instruments, etc. It is not certain whether it is useful or not.

"It can be said that after college students learn mathematics, they will doubt their IQ. It has nothing to do with life. They cannot communicate and apply. They don't know what to do except to cope with the exam. If you are an undergraduate mathematics student, if you want to go to graduate school, you will change your major. This is actually a different kind of escape. I don’t have confidence, I have no confidence, and I can’t see a way out.”

Feng Yao wanted the student in front of him to move forward, but he was afraid that the blow would be too heavy to bear, so he first explained the difficulty to the sky to prepare him mentally.

"Then what's the situation with Tao Zhexin?" Yang Fan refused to accept it, so he was afraid of reading books.

"Talent, hard work, and there is another issue of education. Educational issues include school education and teacher succession. Chen Shengshen taught Qiu Chengtong, and Qiu Chengtong brought up Tao Zhexin. Mathematics is also very important. There is a clever teacher who always reminds us. Let you avoid countless detours."

Speaking of this, Feng Yao felt sorry for his lack of knowledge. The student in front of him was about to be unable to take care of him. He sighed slightly: "Yang Fan, I can't help you much after entering Shuimu. It's a good journey. I'm in Wu Zhou is watching you."

"Teacher Feng, don't worry, isn't it the Fields Medal for the highest achievement in mathematics? Within ten years, I will show it to you."

Yang Fan is still confident, master?Do you need it yourself?No need at all, all the books, as long as you brush up your proficiency, your brain will form a system.

The student vowed, Feng Yao smiled slightly. Many years ago, he was so high-spirited, but the high mountain of mathematics still crushed his spine, and finally he ran around to train mathematicians.

"If you really can, I hope you are a Chinese, not a Chinese, or something else. Otherwise, it's just bragging on paper, meaningless."

Feng Yao got rid of the bloody fact that the two masters and apprentices who won the highest mathematics award are not Chinese nationals.

Mr. Qiu still talked about it because of the political reasons of the civil war that year. Tao Zhexin, who has never eaten a grain of rice in China, grew up abroad.

I don't know Chinese concepts, don't understand Chinese customs, and can't even speak Mandarin.

It is meaningless to put him in the Chinese American, except that the Chinese themselves stick it up to gain popularity.

When he was interviewed and asked about his nationality, he emphasized that he was an Australian.

Yang Fan naturally knew this information, his expression changed, and he said: "Teacher, don't worry. People will only remember me in 20 years. Before I turn 30, I will definitely win the Fields Medal in Mathematics. Let's press it." them."

Yang Fan heard a gossip that Tao Zhexin's IQ is 230.
"Bah." He spit secretly, he is only 140 for the time being, what's so awesome, after a few years of reading books, 320 is fine, it's just a waste of possession, try to use it less in the future, and work hard to improve IQ .

The airport announcement reminded the flight to arrive, Feng Yao said: "Remember what you said today. Let's go."

After a series of rigorous security check procedures, they boarded the flight and arrived in Shuimu in the afternoon.

Before leaving, Feng Yao also made a phone call, it was his teacher, and they made an appointment to have dinner together in the evening.

(End of this chapter)