Is analysis course helpful?

[ethan.wen]

I am facing a choice between second year analysis and normal multiple calculus course. I am taking Analysis I now, but someone told me that Analysis II (which covers analysis on manifolds) is extremely difficult. On the contrary, normal calculus course would be quite easy and more possible to obtain 4.0 GPA. So I was wondering whether it is more helpful to take rigorous analysis course than normal calculus course in quant area. And is there a close relation between mathematical analysis and math fin?
Thank you so much!

 

[Daniel Duffy]

The advantage of rigorous analysis (a la Rudin's book) is that it is a foudation. Calculus is useful but essentially applying formulae.

Not sure if learning manifolds is relevant in this context.

 

[ethan.wen]

The advantage of rigorous analysis (a la Rudin's book) is that it is a foudation. Calculus is useful but essentially applying formulae.

Not sure if learning manifolds is relevant in this context.

How about topology?
I heard that you can apply topology and real analysis in statistics, is that true?

 

[Daniel Duffy]

How about topology?
I heard that you can apply topology and real analysis in statistics, is that true?

Topology is needed a bit in analysis. In general it is _not_ on the critical path.

Edit: Topology for its own sake is fun and you need it if you want to be called a mathematician.

 

[Jedison]

Analysis IMO is always useful. In my experience, these courses have challenged me the most, and where I saw the greatest growth in my mathematical abilities. Will you directly apply the information you learn during an MFE? Probably not. But indirectly, yes. Having a strong set of analytical skills is always useful in any sort of problem solving environment.