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What is the relationship between the Department of Mathematics of the Graduate School of Chinese Academy of Sciences and the Institute of Applied Mathematics of Chinese Academy of Sciences?
The Institute of Applied Mathematics was founded by Professor Hua, a famous mathematician in China. Mainly based on basic theoretical research, it has little to do with the Department of Mathematics of the Graduate School of Chinese Academy of Sciences, and it is self-enrollment.

If you are strong, I suggest you choose graduate school, because there are too many places to submit, the exam is difficult, and there are relatively more opportunities for practice.

If you are conservative, it is not bad to choose the postgraduate entrance examination.

It's hard to say how to choose a tutor. Generally speaking, good tutors are all gone, so there is no way to recommend them. Leading figures in financial mathematics, such as Ding and Yan Jiaan, are hard to choose and not bad. Other tutors don't know much about it.