Pic related, after going through Abbott, is it worth going through real analysis through Ross's textbook or should I just save my time and start studying complex analysis already.

What do I gain from learning analysis and should I do it or go study complex analysis now?

>>16696306 (OP)
*What do i gain from studying analysis twice

>>16696306 (OP)
>or should I just save my time and start studying complex analysis already.
Complex analysis is not the next thing, they're specific functions that happen to be useful sometimes. Next thing would be measure theory and other more standard graduate analysis topics like integral transforms and functional analysis. You're good with just studying complex variables without getting too deep into it, but you definitely should study measure theory.

And no, you shouldn't study that same course twice unless you need to check some result mentioned somewhere else. That was only an introduction.

>>16696363
So you're saying I should study measure theory, like axler's graduate book on measure theory now that I finished analysis by Abbott?

I can order pugh's book on analysis and attempt it now, but what you are saying is that now i should go straight to measure theory like in axler's text.

Pic related, which one should I go through now, or do i do both?

>>16696363
>you shouldn't study that same course twice unless you need to check some result mentioned somewhere else
Studying the same subject from a different text can offer new perspectives that potentially lead to new insights.

>>16696440
Yes, and I have a lot of books on the same subjects. I'm just saying you shouldn't go back and read it arduously as if it was the first time. Read selectively I guess would be my advice. In fact I must tell him the following.

>>16696372
I don't recommend one single book for any topic. I have found bits I like in different books, and parts that I feel the texts drag and makes me bored. I wouldn't buy books anymore, one because I use an e-reader, and two because you need so many you would break your bank. But regarding your question about a measure theory book, those two don't come up in my mind. I tried reading Axler's but he develops too much of the theory on the real line, and I don't know about Pugh. I checked Pugh, and it seems about the same elementary analysis as Abbott, but I must say Abbott looks even more elementary.

I would check many books. People say Folland's book is the best for graduate analysis, it seems good, I like his fourier analysis book, but I also like Rudin's RCA. The problem with RCA is that it makes some very important theorems as if they were anything, as in "just by the way".

I would check out Probability theory, Fourier analysis, ODEs and PDEs theory. All of those things are related to analysis and would give you a better idea about what you want. I really like this guys books: https://www.mat.univie.ac.at/~gerald/
it only lacks probability theoty. Check those electronic books.

>>16696685
This is good advice. Thanks.

>>16696306 (OP)
Why do you faggots always make these threads? Filtered by Rudin much?

>>16696306 (OP)
Check out Gel'fands "Generalized functions" series or Hörmander's books on partial differential linear operators.