Do I need to contact my tutor first for the entrance examination of mathematics major? What preparations need to be made? Especially how to prepare for professional courses?
Of course, contact the tutor first. If you don't contact, you can find out the current research topic of the tutor you want to apply for through other channels. Apply first, a tutor usually has only one or two places to apply, so it is also very important to apply first, not just which tutor you want to apply for. What about specialized courses? You should find the bibliography that the tutor will bring in advance and read it several times.