Real Analysis/Measure Theory Required?

[gterr]

Are theoretical courses such as Real Analysis/Measure Theory required for MFE admission? Will the Applied (explicitly named Applied Real Analysis) courses make up for these requirements?

Thanks in advance,

- Statistics/Finance Double Major

 

[euroazn]

Not required but as I understand highly recommended.

 

[Swayum]

How much do universities care about stuff like this? Will they really pay close attention to what you COULD have studied (e.g. measure theory)? How would they even know that a courses titled just "real analysis" does not include any measure theory? Maybe some universities have it in theirs?

Or when you say "highly recommended", do you mean in order to survive the Masters course itself, as opposed to getting in?

 

[gterr]

Well, they are usually requirements for undergraduate Mathematical Finance majors, so I'm assuming they should also be emphasized in the master's programs.

 

[bigbadwolf]

How much do universities care about stuff like this? Will they really pay close attention to what you COULD have studied (e.g. measure theory)? How would they even know that a courses titled just "real analysis" does not include any measure theory? Maybe some universities have it in theirs?

Don't stress yourself out over measure theory. Real analysis without measure theory should be fine. You can teach yourself the measure theory you need as you go along -- it's not a difficult topic. Albeit it is a boring one, with the ratio of definitions to interesting theorems abysmally poor. Pay more attention to the motivation: Why is measure-theoretic probability necessary? Why is classical probability -- as expounded in the books by Feller -- not sufficient?

 

[gterr]

Don't stress yourself out over measure theory. Real analysis without measure theory should be fine. You can teach yourself the measure theory you need as you go along -- it's not a difficult topic. Albeit it is a boring one, with the ratio of definitions to interesting theorems abysmally poor. Pay more attention to the motivation: Why is measure-theoretic probability necessary? Why is classical probability -- as expounded in the books by Feller -- not sufficient?

What's your opinion on Applied Real Analysis vs. Real Analysis? (Applied Real Analysis is considered Applied Math at my university, whereas Real Analysis is Pure Math).

 

[bigbadwolf]

What's your opinion on Applied Real Analysis vs. Real Analysis? (Applied Real Analysis is considered Applied Math at my university, whereas Real Analysis is Pure Math).

Dunno. What are the topics for each and what precisely are the differences other than those of topics (e.g., differences in emphasis, in rigor)?

 

[gterr]

Applied:

Topology of Euclidean spaces, continuity, norms, completeness. Contraction mapping principle. Fourier series. Various applications, for example, to ordinary differential equations, optimization and numerical approximation.

Pure:

Normed and metric spaces, open sets, continuous mappings, sequence and function spaces, completeness, contraction mappings, compactness of metric spaces, finite-dimensional normed spaces, Arzela-Ascoli theorem, existence of solutions of differential equations, Stone-Weierstrass theorem.

 

[bigbadwolf]

Pure:

Normed and metric spaces, open sets, continuous mappings, sequence and function spaces, completeness, contraction mappings, compactness of metric spaces, finite-dimensional normed spaces, Arzela-Ascoli theorem, existence of solutions of differential equations, Stone-Weierstrass theorem.

I prefer this one but from the surface I don't see anything wrong with the first (applied).