Senior year is basically like this. There are classes in the first semester and classes in the second preschool 10 week. In the last seven weeks, the preparation for the defense was purely done. On the whole, the compulsory courses in senior year are much less than those in junior year, and the compulsory courses are relatively watery, but there are many elective courses, and most of them are deeper. Like Lie Groups and Lie Algebras, they are really starting to burn their brains.

As for some frontier topics of finite group theory, such as the classification of simple groups, the proof of burnside's theorem, the proof and application of Frattini's subgroup theorem and Frobenius's theorem, I really began to wonder if there was something wrong with my IQ.

The study of college algebra.

You need to complete the basic course of Lie Algebra. Lie algebra needs to learn solvable lie algebra, nilpotent lie algebra, semi-simple lie algebra and Cartan decomposition. If you don't learn it later, then the postgraduate mathematics department will learn Lie Groups and Lie Algebras as a start.

Differential geometry must be studied, but the requirements are not so in-depth, because in Russia, higher-order differential geometry is generally taken as a postgraduate course, and undergraduates need to know at least Riemann tensor, hypersurface and Lie derivative. Because learning Lie algebra needs to use many concepts in differential geometry to derive Lie groups.