I came to the Department of Mathematics as an undergraduate, and I realized that the gap in IQ between people is bigger than that between people and pigs. The Department of Mathematics is really not a place for people to stay. I can say without hesitation that I was the hardest student in our Department of Mathematics when I was undergraduate. As a result, in a class of 60 people, I could not even be in the top 30, the most excessive. It was my roommate who copied my homework every day. In the last analysis course, he passed 90, and I got 60. Then I understood, it’s no good, it’s really no good, so I honestly transferred to financial mathematics, and then The road goes smoothly. Whether it’s gpa or Shenyan or looking for a job, it’s very good, and the salary is also very good. But I really envy those students who continue to go on the road of mathematics and then read the Ph.D. That is my dream that was out of reach. Every one of them is pure and pure in my eyes. I am really very Envy them. The first place in our class was a girl. Later, she went to a well-known overseas university to study for a Ph.D. She may not be very beautiful, but she is really smart and confident. Later, when I was studying metalworking, I met many beautiful girls, but they were not as good as this girl. Smart people really have a special charm. I envy her very much. I want to be a person like her, a person who contributes to the development of mankind in mathematics. It’s a pity that I don’t have this possibility when I’m already 30. I can only make up for it in another way. I married her home.

Talk about your own experience. Before going to university, I was very confident. The six volunteers for the college entrance examination are all the first mathematics, the second physics and the third statistics. He played Jimidovich every day of his freshman year and sophomore year, and he could mix up to eighty or ninety by a few points. Although not very ideal, it is always reasonable. But breaking defense is exponentially accelerated and non-linear. Taking operations research as a starting point, topology has collapsed, number theory has fallen, physical equations are disappointed, and partial differentials are desperate. In the third and fourth years, only 90 points of modeling have been done. The teacher who led me in the back department was very responsible, and took the initiative to enlighten me: the child’s life is still a long way, and the three hundred and sixty lines serve the people. Or you can transfer to study economics and finance, which is a good way out. Not ashamed. After graduating from university for ten years, on the last working day before the holiday when everyone retreated early, I waited for the bank to close and answered questions by the way.

I am a liberal arts student who has been studying mathematics, physics, chemistry and biology for a year in college, and I will tell two short stories. The first one was that there was an Englishman who had a bachelor’s degree in mathematics, but felt that his talent was insufficient, so he switched to philosophy. He became a professor, and when he was about 60 years old, he hand-written a book called “Marriage and Morality”. Twenty years later, in 1950, he won the Nobel Prize for Literature. The second is a South African with a double degree in mathematics and literature. After graduation, he went to IBM in London to become the world’s first-generation programmer. When he chose a graduate major, he weighed it up and felt that his talents were not enough. Supporting mathematics research, he chose literature “unfortunately”. Later, he read a Ph.D. and published a novel. The book published in 1999 was called “Shame”. With it, he won the Nobel Prize in Literature in 2003. The Englishman is Russell and the South African is Couche. The story of the two of them seems to tell us that if you are in the Department of Mathematics and feel that you can’t read it anymore, perhaps this is a call from heaven, calling you to try the way of literature.

Regarding Teacher Zhang Gaofei, there is also a very interesting letter he wrote. Sending station: Shuimu Community (Sat Nov 20 01:53:47 2010), a letter from the station to teacher Mei Jiaoqiang Sending station: Nanjing University Sayuri Station (Thu Mar 11 20:04:23 2010) Strengthening: Hello ! We had a great conversation on the shuttle bus this Wednesday. In the meantime, you told me that last year, the dean of the department, You Jiangong, was named the most popular teacher among students. You said that the two of us should reflect on this matter carefully: We both gave freshman mathematics analysis courses, but why neither of us won this honor? After coming back, I thought about this issue carefully. Now I summarize my own thoughts as follows. Just for your reference. In terms of proficiency in teaching materials and problem-solving ability, I don’t think Teacher You can compare with you and me. Teacher You himself said that his grades in college were very poor, but it was only in his senior year that his grades improved all at once. But we all know that in the fourth year of undergraduate college, except for some music, there are basically no major courses in art and the like. The mathematics analysis class is for freshmen and sophomores. It is conceivable that Teacher You did not learn this course well thirty years ago. But you and me are different. Like our names, you and I belong to the kind of people who are ambitious and strive for perfection. Naturally, both of us are very familiar with basic courses like mathematical analysis. Having said that, you will naturally ask, in that case, why is the class taught by Teacher You most popular with students? This is actually the crux of the problem. Teacher You knows that he is not enough to master this course, so he only talks about those that he is quite sure of when he lectures. For example, if the proof process exceeds ten lines, Teacher You will leave it to the exercises class. For all calculations that require skills, Teacher You will tell everyone in a persuasive manner that he mainly talks about ideas in class, and these skills are left to the exercises class. In this way, not only the lectures of Teacher You are relaxed, but the students also listen to them easily. Even the instructor Yang Jing, who graduated from engineering, said with emotion after listening to Teacher You’s class: It turns out that the mathematics department’s mathematics class is much easier than the college mathematics they had learned at the beginning. Of course, Teacher You will sometimes try a little trick. For example, some students will ask for the exercises after class during the break. When he was convinced that he had complete certainty to win the question, Teacher You would always step up to the stage resolutely and write swiftly. At such moments, the reworked students would carry their schoolbags and leave the classroom quietly. Because they know that in the next class, Teacher You will always focus on this question. Until the end of get out of class the bell rang. However, it is his teaching style that makes Teacher You a great success in teaching. Almost all students felt that Mr. You’s lectures were clear and easy to understand. Even those students who were transferred to the Department of Mathematics at the time of admission have developed a great interest in mathematics. Especially when they witnessed that Teacher You, who had countless auras above his head, was unable to tackle a problem that was not difficult for a long time, they were even more confident. Teacher You’s class is not so much a math class as it is an inspirational class. Everyone stared at Teacher You, full of dreams for their future. However, all of this changed during the second semester of the freshman year. You teach class one, I teach class two. You and I give lectures with a smooth flow, covering everything. Most students can’t digest the content in class. And the thinking questions you write in the corners of the blackboard from time to time, many people haven’t done it at the end of the semester. Last semester everyone thought they were geniuses, but this semester seems to be worse than ordinary people. Before and after comparison, Teacher You formed a sharp contrast with us. While complaining about you and me, everyone missed the teacher Yo who made them full of confidence. At this time, the school launched a competition activity. The results can be imagined. According to Yang Jing, among the 120 people checked, 116 people voted for Teacher You. 3 people voted for me. They are all my fellow in Hebei. Only one person has voted for you. But that person is not your Hubei fellow. Because you never told everyone that you are from Hubei. That person is the counselor Yang Jing. She knows that you have always been serious about your work, and she is afraid that you won’t be able to accept it all at once. Okay, step up, let’s just say so much. We are all still young. As long as we work hard, there will be many opportunities in the future. Hope is just ahead. Sincerely! Goofy

I heard from a tutor that there are several students who studied number theory at the master’s level. They did not learn very well, were not sensitive to the difficulty of number theory, and did not master the basic methods. Then some PhD students went overseas to learn cybernetics, and some I went to learn cryptography, and one learned statistics. The three doctoral tutors surprisingly unanimously responded that these three students learned very well, and now they are all titled faculty. It shows two problems: 1 basic mathematics is indeed better than application It is more difficult to learn and produce results. 2 is that as a student, you should find your own suitable direction. 3 Interest is that you do not have enough or unnecessary conditions to learn a subject. If you don’t like it, you may learn well, and if you like it, you may not learn well. .

I do algorithms, and I liked it because it is combined with mathematics. But now, it’s getting more and more painful, and I feel that this business is just a pit. Many deep learning models are similar to design. There is no reason and cannot be explained. It is designed like this. There is no underlying principle to support it. It only knows which layers should be added behind. It is nothing more than some classic models that are used in this way. of. So the papers in this line are basically 2-3 years old, even if they are outdated. On the other hand, it also shows that there may be no difference between a freshman who has worked for one or two years and a few years of work. There are a lot of assumptions, but the reality is ever-changing, and they are basically not within the scope of the model’s assumptions. So the model has good times and bad times. Each tuning man wants to make the curve more fitting, but at the same time it is over-fitting. Even if the performance on the test set is good, who can guarantee how much the test set can cover? It’s understandable to do this for money, but if everyone’s salary is the same, there is a sense of superiority in the algorithm, which is really letting people.

Four-year undergraduate study of mathematics is not pure mathematics, but information and computing science (mathematics department). Then cross-professional research to management. (Students who have cross-professional postgraduate entrance examinations often have scores of 130+ and 140+ in mathematics.) I feel that the professional courses of management can be completed after reading the book in one month. Why do you have to study for four years? Later, I went to study for a Ph.D. in economics. I didn’t have a foundation in economics, and I went straight to the third high school. Then I found out that it is still very difficult for the students majoring in economics, the junior and intermediate level, to follow along the way (they are very mature in economic thinking, but frown when they arrive at the calculation derivation). There are also classmates who have a better foundation than me. The undergraduate school is handed in by the National People’s Congress, Fudan University, and the same is true for learning. Actually, I am not good at mathematics. I was afraid of mathematics in high school. My scores in mathematics in the college entrance examination were very low, but I went to the Department of Mathematics by mistake. Therefore, I feel that although I am not talented in mathematics, the four years of training in the mathematics department is very helpful for improving my ability and thinking. The limited talent may prevent me from breaking through. I will always be below the ceiling, but I have benefited my life.

Of course, it is necessary to despise the chain. Whether it is the faculty market or the difficulty of changing careers to the industry, statistics, calculations, and counters are much easier than pure mathematics. What’s more, many people in these fields just eat a lot of food, and have no pursuit of mathematics itself. From the perspective of technical difficulty, it is even more incomparable. If you get more practical benefits through some simple work, then don’t expect the idealists who are doing difficult work and facing real troubles such as funding shortages to get equal respect. All day long yelling “Why are we expelled from the number of students”, this is purely a good deal and a bad behavior that disrupts the order of the market.

Those who earn less, despise those who earn more. Those who make less money are ideals, beliefs, and noble people who dedicate themselves to mankind. Those who make a lot of money are all villains who work hard for their own interests. A doctor of pure mathematics, even if one month is 8,000, does not have any extra income, and can not look down on other doctors of mathematics of 500,000 a year. Every pure mathematics student who is not good at it, comforts himself, and can make a lot of money by changing the application. Statistics have been expelled from mathematics because they robbed the civil servants of mathematics.

Regarding how to choose a major in mathematics-Zhang Gaofei, Nanjing University, everyone has seen it and laughed. You don’t have to take this seriously. “As everyone knows, algebraic geometry is the mainstream of modern mathematics. Most contemporary first-class mathematicians work in this field. Therefore, if you feel that you are talented and have a solid foundation in algebra, geometry and analysis Basics, I suggest you never waste your talents: You should choose algebra and geometry as a major. Of course, few people have learned the three basic subjects of algebra, geometry and analysis at the same time. For example, some students have good analytical skills. , But the abstract thinking ability in algebra is relatively weak. If this is the case, I suggest you choose a major in analysis, such as: complex analysis, fractal, harmonic analysis or differential equations. If you are not good at algebra and analysis, But I have a good feeling about geometry. If this is the case, I suggest that you should discuss with Teacher Mei Jiaoqiang. Let him help you judge whether you can learn geometry. In addition to the above three parts of students, there are Some students like this: They are not good at algebra, analysis and geometry, but they have always believed that they can still make a difference in mathematics, and they dream of becoming the mainstay of Chinese mathematics one day. If you belong to one of this group of students If you do, I suggest you choose dynamical systems. The subject of dynamical systems is actually set up specifically for this group of students. Of course, even dynamical systems are not something that everyone can learn. Because dynamical systems require a lot of calculus. But there are always So some students graduated from college before they had time to figure out the concept of the limit. If you happen to be such a classmate, that means you haven’t studied mathematics at all in four years of college, but you still hope that you can study mathematics in the future. In the last big picture, I suggest you choose combinatorial mathematics as a major. The characteristic of this major is that it only uses middle school mathematics. If you participated in mathematics competitions and won awards in middle school, this subject is exactly A place where you can show your talents. I think most of the students have found a major that suits them before seeing this. But if someone shyly says that he fell in love early in middle school, so he didn’t even study math in middle school well, I want to tell Don’t be afraid of this group of students. In our department, there is a specialization for you: Statistics. This subject only requires knowledge of the four arithmetic operations of addition, subtraction, multiplication and division in elementary school mathematics. More importantly, choose this major Most of them are female classmates. When you add up thousands of data accurately and skillfully calculate their average, you have won the hearts of many seniors and sisters: just three years of graduate school life may be able to Once again, you can experience that beautiful, beautiful, and fleeting past… The last one is specifically for those sad characters. They didn’t even learn mathematics in elementary school. Don’t say that adding up thousands of numbers is just adding two. Adding up the numbers is a very laborious task for them. However, all this has not weakened their infatuation with mathematics. They spend day and night in the library. They read all the mathematics literature, but They have never found one that can be read instinctively. But they still persevere in order to find a profession that suits them. Their actions touched God. On One day in the century, God created a machine for them to help them calculate. This is the computer. With the help of computers, they can quickly perform addition, subtraction, multiplication and division operations. This is computational mathematics. “

Full professors in the top 50 schools in the United States> change careers to the industry to mix to the upper middle level> ordinary school teaching positions = change careers to non-popular industries other than the Internet and finance “” “”” “”” “”” “” “”” “” “A half-knoun party full of mathematical terms that I don’t understand, and strong mathematics.” Superiority. It’s boring to despise the chain between directions. No matter what direction you can post the Big Four, it’s better than that. Even if you learn algebraic geometry and number theory, if you can’t post a good article, others will laugh at you. Now those undergraduates who are holding GTM 52 to show off their IQ, most of them still have to switch careers in despair in a few years.