Crossover between mathematical analysis and other subjects?

[mathmonkey]

Hi,

I'm wondering how far one can go in learning graduate level real analysis or functional analysis with only background in undergraduate analysis 1 and 2 and none in algebra or topology? That is, is there any requirement or benefit to taking courses in algebra and topology to understand upper level analysis (beyond the basics that would be covered in an analysis book anyway), and how inter-related are the three topics?

I'm interested in learning more about real analysis and trying to figure out whether my time is better spent concentrating on the subject itself, or taking the time to learn the other areas of math for background knowledge. Thanks for the help!

 

[chiro]

Hey mathmonkey and welcome to the forums.

One thing that I say to people in your situation is to make use of your resources.

In this great age of having the internet, we can ask a question on a forum (like PF!), we can search for similar questions that have been asked and answered, get textbook reviews, and even download a whole set of free complete notes from authors at their university websites.

I can't speak about the relationship between algebra and topology but analysis and topology kind of go hand in hand. The generalization of concepts that help specify continuity are found in topology and of course have very important implications when doing analysis.

So yeah if you have a problem (even a technical problem), it would be wise to search the appropriate math forums to find similar questions or to ask your own highly customized question to the more experienced members who have that knowledge: you will be surprised at the collective amount of knowledge, experience, and wisdom that can found here.

 

[micromass]

If you don't know any topology, then your range of analysis topics you will understand will be quite limited. Sure, you can understand some functional analysis (Kreyszig is a good book tha will not assume any topology), you can study measure theory, etc. But after a while, topology will prove to be necessary.

You say you have no knowledge of algebra? Does that include linear algebra? Linear algebra is used quite a lot in analysis. Functional analysis is basically a mixture between linear algebra and analysis, so knowing linear algebra will be very handy.

If you know linear algebra, but nothing of groups, rings, fields, etc. then you can do a whole lot of analysis. I think you can even do research in analysis without knowing algebra (but I wouldn't advice it). Some things do require algebra: Haar measures, operators algebra's, etc.