# Proofs and Analysis Course

#### mez

I wana take a Proofs and Analysis course in the summer but I am not sure how useful that course would be for me in an MFE program, does anyone have any insight?
Topics covered include: the elements of set theory, mappings, basic ideas of metric spaces, continuous mappings and sequences. Text: Elementary Theory Of Metric Spaces Robert B. Reisel

#### Daniel Duffy

##### C++ author, trainer
yes and no.
More important in my opinion is to understand the symbols an to applications. It should not descend into dry theorem proving alone.
Metric spaces are a small part.

See my hands on + exercises approach here. And is geared to finance.

mez

#### josephron

Just great to take for learning and opening up a new world of mathematics, even if not for MFE

#### m_s

Just great to take for learning and opening up a new world of mathematics, even if not for MFE
I agree, it could also signal something on your application when you apply, especially if you Ace the class

#### Daniel Duffy

##### C++ author, trainer
Just great to take for learning and opening up a new world of mathematics, even if not for MFE
Mathematics is for ever. An example: I studied and researched in Functional Analysis and Hilbert spaces almost 50 years ago, now it is a new wave in Machine Learning.

I wana take a Proofs and Analysis course in the summer but I am not sure how useful that course would be for me in an MFE program, does anyone have any insight?
Topics covered include: the elements of set theory, mappings, basic ideas of metric spaces, continuous mappings and sequences. Text: Elementary Theory Of Metric Spaces Robert B. Reisel

At some stage (even for MFE) you will have to take some course on functions of several variables. Metric space theory will be indispensable there.

mez

#### noether-skolem

Can't really go wrong with having some analysis background, even if just a little bit. Knowing some concepts in set theory, sequences/series, convergence, continuity, normed and inner-product spaces etc. would help you along the way. I've seen some of these used in MFE courses too. On top of my head, L^p norm, and Holder continuity were briefly touched in some ML courses, a bit of measure theory in time series courses (different types of convergence, Borel-Cantelli lemmas).

If nothing else, knowing more proof techniques could make some homework problems less problematic for you.

#### Daniel Duffy

##### C++ author, trainer
And complete metric spaces. Cauchy sequences. And more Constructive Analysis ... prove existence and uniqueness of a solution by actually constructing it. Good example is Banach's fixed point theorem in metric spaces .. it can even be done in C++.

Another *constructive* existence proof is Picard iteration fr ODEs

Functional Analysis is the new wave in ML applications. Question is, are data scientists aware of this?

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mez

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