Transition from introduction to analysis to more advanced analysis

Question

I am currently studying intro to analysis and learning somethings about basic topology in metric space and almost finished the course . I am thinking of taking some more advanced analysis. Would it be demanding to take some course like functional analysis or real analysis only with knowledge of intro analysis course ?Do the courses need more mathmatical knowledge to handle?

Answer 1

Depending on what you mean by "intro to analysis," a real analysis course covering, say, Lebesgue integration would probably be reasonable, but a functional analysis course would often assume you've been through a basic graduate analysis course already. This all depends on where you're studying.

Answer 2

Most of analysis requires very little algebra. If you have covered a course in basic analysis, say using Rudin's Principles of Mathematical Analysis, then you are ready to take a course in more advanced analysis, say using Rudin's Real and Complex Analysis, which covers both measure theory and linear operators as well as holomorphic functions.

Answer 3

I'm currently taking a graduate functional analysis course having only taken introductory analysis (I majored in physics). It's manageable, but knowing measure theory and lebesgue integration would have definitely helped.