Advanced mathematics, that's how hard it is.

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

There is no airport in Wuzhou, and it is too inconvenient to go back and forth, Feng Yao and Yang Fan's parents discussed it, went directly, and handed it over to Teacher Feng to solve.

Feng Yao looked at the time, there was still an hour to take off, and it was half an hour before he started to go through the landing procedures, and the time was still early.

In the waiting hall, teachers and students are waiting for their flights, and the topic of advanced mathematics continues.

Feng Yaodao: "The mathematics that I have studied since university is called advanced mathematics. Elementary mathematics studies constants and homogeneous variables, while higher mathematics studies non-uniform variables. ”

Although Yang Fan has read several advanced mathematics books, he knows them but does not know why, and he is a little incomprehensible.

Full of confusion, Feng Yao understood, and continued to explain: "In layman's terms, let's say π. We learned in elementary school that the calculation method was directly 3.14 as the final answer. In middle school, the learning is 3.141414...... Infinite loops, or the character π instead, this is a uniform variable that can be measured accurately. University of Advanced Mathematics, the study is 3.1415926...... There is no beginning and no end to this number. ”

This is easy to understand, calculable and incalculable, endless variations. Yang Fan nodded, feeling that he understood a little.

"It's not just that. When there are 100,000 or 100,000 decimal places behind this decimal point, it is infinitely close to 0, so can he be counted as zero?" Feng Yao said.

"This ......" Yang Fan hesitated, the number after 100,000 and millions after the decimal point is meaningless, and there is no need to be more precise, "It should be useless, and there is no need for measurement." ”

"No, no, no, Yang Fan, you haven't understood yet, since it already exists, it can't be counted as zero. This is where the concept of limits and differentiation comes in, and it is also the second mathematical crisis in mathematics. Since it is an increment and not zero, mathematical rigor must not be calculated as zero. ε-δ language appeared, which was the foundation of higher mathematics. ”

It's so high-end, what language Yang Fan can't understand in the back, it's still the foundation of high mathematics.

"Then Mr. Feng, you directly gave me a few advanced mathematics books at that time, aren't you afraid that I won't be able to understand them? I searched for them, and some of them are still graduate mathematics books. Yang Fan has been hiding this question for a long time, and he doesn't have time to ask, because with the help of the system, he will be able to do it anyway.

"Let's do this...... Feng Yao hesitated, and finally confessed, "Just remember it, don't say it." The books given to you are all Western translated books, and the Western natural sciences started earlier than China, and the system is relatively rigorous, and it is easy to understand from easy to difficult. However, there seems to be a fault line in my country's university books, and it is not clear to say. ”

Feng Yao's knowledge has not yet reached the level of being able to write a textbook, and he is just a crowd, and every student says that the span of college mathematics is too large, and there must be a reason for that.

Either the professor's knowledge is not good, can this be nonsense? Absolutely not. The only reason left is that the textbooks are poor.

"The books in middle school are basically universal, and in the university, there is always a difference between the top and bottom, and the only hard work is the students. ”

Feng Yao is glad for his graduation, the famous school has its own heritage, and the teaching is generally good. When the top 30 professional schools in China are excluded, the education systems of each country are uneven, and they cross the river by feeling the stones.

Yang Fan always thought that all schools in the university basically used the same books, and it turned out that there were so many doorways in them.

If it's not unified, there's no way to compare. You say you're first, what's the evidence. There is no national examination at the university, so you just need to complete the credits of your own school.

"Don't say it's you, I'm a person who has come here and thinks it's complicated. Science and engineering students look down on students in literature and history who learn a little bit - calculus is screaming, and it is difficult and difficult. Mathematics majors despise science and engineering and know a little bit of so-called advanced mathematics and this subject is self-righteous. ”

"For mathematics students in the real circle, calculus is classified into mathematical analysis, and they learn more profoundly. Some people call this course Shufen, and they love and hate it, and they grit their teeth. ”

After gaining knowledge, Yang Fan found that learning mathematics also had to mock each other for the low IQ of others, which was inevitably biased.

After graduating from literature and history, I will not be exposed to calculus for the rest of my life, so what is the use of learning it. The focus of science and engineering is naturally on the profession, finance, computers, precision instruments, etc., it is not necessarily useful or not.

"It can be said that when college students learn mathematics, they will doubt their IQ, have nothing to do with life, cannot communicate, cannot apply, and do not know what to do except for the exam. Mathematics undergraduates, if they still want to go to graduate school, will change majors, which is actually an alternative escape. I am not confident, I have no confidence, and I can't see a way out. ”

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

"What is the situation with Tao Zhexin?" Yang Fan was not convinced, was he still afraid of swiping books.

"Talent, hard work, and an educational problem. Educational issues include school education and teacher training. Chern taught Yau Chengtong, Yau Chengtong brought Tao Zhexin, mathematics is also very lecturer, there is a clever teacher who always mentions, you can 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 it, and sighed slightly: "Yang Fan, I can't help you anything after entering Shuimu, it's easy to go all the way, I'm watching you in Wuzhou." ”

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

Yang Fan is still confident, do you need it? You don't need it at all, all the books, as long as you brush up on the proficiency, the brain will form a system.

The student swore an oath, Feng Yao smiled slightly, many years ago, he was also so high-spirited, but the mountain of mathematics still crushed his backbone, and finally rushed to train mathematicians.

"If you really can, I hope you are a Chinese, not Chinese, not other celebrities, otherwise, it's just bragging B on paper, meaningless. ”

Feng Yao put aside the bloody facts, and the two masters and apprentices who won the highest mathematics award were not Chinese nationals.

Mr. Qiu also said that in the past because of the political reasons of the civil war, Tao Zhexin had never eaten a grain of rice in Huaxia at all, and he grew up abroad since he was a child.

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

Putting him in the Chinese, except that the Chinese themselves stick it to rub the heat, it is meaningless.

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

Yang Fan naturally knew this information, his expression changed, and he said, "Teacher, don't worry." Twenty years later, people will only remember me. Before I was thirty, I would have won a Fields Medal in mathematics, and I would have pressed them. ”

Yang Fan heard a small news, Tao Zhexin's IQ is 230.

"Phew. He spat secretly, he was only 140 temporarily, what is there to be a cow B, he brushed up for a few years, 320 is fine, just to possess and waste, strive to use less in the future, and strive to go to the IQ side.

The airport radio reminded the arrival of the flight, and Feng Yao said: "Remember what you said today." Let's go. ”

After a series of rigorous security procedures, they boarded the flight, and they were able to arrive in Mizuki in the afternoon.

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