Which Branch of Math Should I Study for a Foundation in Functional Analysis?

In summary, the conversation discusses the difficulties of studying functional analysis and the need to have a foundation in set theory and logic before delving into analysis. It also mentions some symbols commonly used in analysis and recommends starting with classical analysis on real numbers before moving on to set theory and logic.
  • #1
houlahound
908
223
looking at notes on functional analysis for self study. the authors I have stumbled across so far launch straight into the formal theory. I can't find any middle ground of intuitive motivations for the theory as yet. I am assuming the following is part of set theory? I can't follow the arguments because I don't know the terminology. are there lists defined for example the symbols in the following. I do not want these particular ones defined I want to know how to do it myself.

what branch of math do I need to read to get a foundation in this language.

any recommended readings.

thanks any leads.
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  • #2
The \ symbol is "set difference" so A \ B = A ∩ BC (the elements of A intersected with the complement of B)

α Fα means ##F_{\alpha_1} \cap F_{\alpha_2} \cap \dots F_{\alpha_n} \cap \dots##, where the ##\alpha_i##s are some indexing set.
α Fα is similar, but is the union over some indexing set.

Books on analysis usually define these symbols in an appendix.
 
  • #3
Mark44 said:
α Fα means ##F_{\alpha_1} \cap F_{\alpha_2} \cap \dots F_{\alpha_n} \cap \dots##, where the ##\alpha_i##s are some indexing set.

Correct, but this gives the impression that the number of ##F_\alpha## is countable, while it can be much more general. In any case, it seems the OP will need to look at some basic set theory before he can handle analysis.
 
  • #4
micromass said:
Correct, but this gives the impression that the number of ##F_\alpha## is countable, while it can be much more general.
Yes, I realize that the ##\alpha##'s are some indexing set, not necessarily a countable set. My intent was to expand the notation somewhat.
 
  • #5
Does analysis solve problems or just prove theorems and provide tools for solving problems?

ETA, I am going to do classical analysis on real numbers first re calculus. Seems like the logical thing and apparently I am already familiar with many of the content eg limits, series, real numbers etc.

Then set theory/logic then analysis.

Sound sound?
 

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