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What professional questions are usually asked in the second interview of mathematics major, and how to ask them?
For example, what is your most impressive math class? Why?

Why not explain what curvature is on the blackboard? Why do you define curvature like this?

How many kinds of partial differential equations are there? What is the difference?

What are the equivalent propositions of bounded functional? Give a continuous but unbounded operator.

Tell me about your understanding of mathematics. What is your favorite mathematical theorem? Why?

What do you think is the main difference between complex change and real change?

You can go to the forum of doctors in mathematics and ask.