The general direction of mathematics specialty can be roughly divided into basic mathematics, applied mathematics, probability theory and computational mathematics. There are many small directions under the big category, and everyone learns different things according to their own research direction. Everyone takes basic courses, such as functional analysis, advanced probability theory, abstract algebra and so on. Different schools may have different basic courses. Then choose courses according to your own research direction, such as learning the direction of game theory in applied mathematics, then you should learn game theory, evolutionary game theory, nonlinear analysis, nonlinear optimization theory and so on.

There are basically no classes for graduate students in the second year. Every day's work is to read documents, make reports, and consult books for different directions at the same time. By reading the literature, if other people's methods need to be improved, or there are other new methods, they can conduct research, and if there are good results, they can write papers and publish them.