Ever since I was admitted to the School of Mathematics of Peking University eight years ago (2000), the question of what I can do after my math department comes out has been haunting me. No matter my friends or relatives, I have been asked this question once. But every time I give an answer, I feel that the other person is not only not very satisfied with the answer, but also feels that the answer is not clear. Eight years have passed, and on the eve of my doctoral graduation, it is necessary to sort out my thoughts and answer this question well.

Let's talk about what the math department studies first. Generally speaking, basic courses are nothing more than learning calculus, linear algebra, geometry and probability theory. Senior students (juniors and seniors) can choose majors, including basic mathematics, computational mathematics, information science, probability statistics and financial mathematics. Among them, information science majors should study computer-related courses; Financial mathematics majors should take economic management courses. As for the postgraduate stage, it is generally the same as the undergraduate stage, but it is more professional and deeper.

Many majors claim to belong to the category of applied mathematics. Including myself, I also study applied mathematics. So what exactly is applied mathematics? In fact, it is to apply mathematical knowledge and methods to physics, chemistry, biology, finance, engineering and other disciplines. The ultimate goal is to provide mathematical tools and ideas for the research of other disciplines, so as to solve the core problems of this discipline and promote scientific progress. But in all fairness, many applied mathematics researches are still limited to analyzing and solving pure theoretical problems of other disciplines, which is far from the core problems of this discipline, which is also the reason why the influence of magazines such as Theoretical Chemistry and Theoretical Biology is limited. Many people think that the major of financial mathematics has a strong application background. In fact, most of the research results are not useful analytical tools and methods, but printed materials in ivory towers.

At this point, the situation of financial mathematics and theoretical physics is the same, because theoretical physics has been integrated with mathematics, and some physicists are completely mathematicians, so the physical meaning of their theories is actually rather vague. Therefore, we can generally understand that applied mathematics is very different from the applications we talk about in our lives. Few of them can really be transformed into productive forces, and most of them are just explorations and semi-finished products. Probably only computational mathematics and financial mathematics majors will undertake some practical projects, such as product research and development analysis and actuarial science. Most of the papers in the department of mathematics really have no application prospect, at least not for a short time. However, please don't misunderstand that mathematics is just a mathematician's own game. In fact, even if mathematicians entertain themselves, society doesn't know that there is rain in that cloud, which will have great application potential, so mathematicians still play an indispensable role in society.

In addition, the need for mathematical knowledge and the need for professional mathematical talents are two different things. Mathematics required by many disciplines is only the content of freshmen and sophomores in the Department of Mathematics, and it can be skillfully used without recruiting specialized mathematics talents. Therefore, mathematics graduates can only go to those industries that have competitive advantages and need more and deeper mathematics knowledge, and other majors can't learn, such as financial analysis and actuary. Of course, professional mathematics research institutions and schools are also among them.

Students majoring in mathematics, whether they graduate from undergraduate or graduate school, have the following choices:

First, go to scientific research institutes for scientific research and teaching, and stay in the ivory tower. This requires you to get good grades, have certain scientific research achievements, and have good expression skills. At the same time, it can bear relatively low income. Teachers in some departments are well paid, but from the perspective of mathematics department, their income is not high, which is definitely below average among the elite groups in Beijing and Shanghai. Unless you get a scientific research award, it is only rare;

Two, for financial institutions (including securities companies, state-owned banks, investment banks, consulting institutions, stock exchanges, etc.). ), R&D is an insurance company, engaged in professional financial analysis, actuaries and other work. This requires mastering the basic theory of economics and being familiar with the courses of stochastic process, stochastic analysis and statistics of probability and statistics. In addition, you need to be familiar with some important programming software;

Third, go to R&D software company and related enterprise departments to engage in software development. This requires proficiency in programming languages and knowledge of software and hardware. These students are basically students majoring in information science, and may have a slight advantage in the competition with computer graduates because of their good mathematical foundation;

Fourth, a few go to high schools to teach, and go to off-campus counseling institutions to teach. This requires good communication and language skills, and some even need a very good foundation of Olympic mathematics.

5. There are a lot of post-work that has nothing to do with mathematics. In fact, with the proliferation of comprehensive universities in China, it is a common phenomenon that the work is not right, especially in the departments of mathematics and physics, but not in the departments of international relations and philosophy. It is often said that when you are in college, you should make a good career plan and avoid wasting time studying majors that you are not interested in, but in fact, most people can't do it. What you can do is not to choose a major that you are definitely not interested in, and then make full use of the resources of the school to enrich yourself when you get to college. According to your hobbies, you can study hard, read widely, develop your own stylistic expertise, participate in social practice, or strive for internships in various enterprises. When your career plan becomes clearer and clearer, you will find that there is no harm in accumulating before. Maybe some humble knowledge or experience can make your life successful.

Finally, I want to say that as a mathematics department of a comprehensive university, it is impossible to provide vocational training for students, and there is no curriculum knowledge that can be directly applied to specific work. Moreover, the course must be designed for cultivating mathematics professionals, and students who are not interested in mathematics books but have to enter mathematics majors for some objective reasons cannot be treated. If you happen to be such a student, then, as I said above, you can seize the time and make use of all opportunities and resources to enrich yourself. Don't be serious about your grades. It's no big deal if you don't have a scholarship. But if you have no interest in mathematics and force yourself to learn it well, your college life must be dull and even painful in such a predicament. Of course, the plan doesn't change quickly, and interest can be cultivated, as long as you don't keep swinging.