Finished Real Analysis (baby Rudin syllabus), what to read next?

174 Views Asked by At

My question is more of a strategic type.

I have recently finished learning about most of the topics in baby Rudin (PMA), but from a different textbook, at my school.

As you can imagine, I haven't mastered those topics yet since I have only done the assigned problems and exercises.

Now, I would like to seek advice about what to do next? My goal is to continue learning Analysis.

I was thinking of reading the entire PMA and doing most, if not all, exercises from it before I move on to Real and Complex Analysis (RCA) by Rudin.

Should I spend some time (perhaps a year) doing PMA? Should I do a little bit of PMA on the side and RCA alongside with it? Or should I just move on to RCA altogether?

And, lastly, would you advise a book other than Rudin? I don't mind the terse and dry nature of Rudin especially because I have heard it contains really good exercises.

Thank you!