Japanese universities are not difficult to test. Generally, when writing a letter to a professor, you should first explain your research direction. If the professor recognizes your research direction and thinks that you can do a good job in research, you will be admitted, which will be more than half the success.

The research plan is just a wishing material. Personally, I don't feel very valued and there won't be any big problems. I don't even need a research plan when I make a wish in the project. During the interview, professors will not ask any particularly professional and in-depth questions, but will only get a general understanding of what you have learned and some simple life problems. If you have a level of 1~2, it's no problem at all.

With regard to changing majors, it is difficult to change majors from literature, and it is relatively easy to change majors from science. In short, if the landlord wants to transfer to literature, trade, finance, law, business and international cultural exchange, the success rate is relatively high. If the university major is not mathematics, it is hopeless to change to mathematics.