Need help on math courses selection, preparing for MFE/MF

[Mensa]

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[bigbadwolf]

1. I whatched a thread before, many peple said the "Real Analysis" is really important, but I cannot find this course; is "intro to modern analysis" similar to "real analysis? (The course description is: Real numbers, metric spaces, elements of general topology. Continuous and differential functions. Implicit functions. Integration; change of variables. Function spaces. )

It's a real analysis course. Description is vague but seems to be "Real Analysis II" or "Intro to Real Analysis for Grad Students." If you've already taken basic real analysis as an undergrad you'll be fine -- otherwise you may still be able to follow the course, get a good grade in it, but still be wondering about the motivation behind the generalisations to metric and topological spaces, and to function spaces (there won't be enough time for applications).

 

[Mensa]

It's a real analysis course. Description is vague but seems to be "Real Analysis II" or "Intro to Real Analysis for Grad Students." If you've already taken basic real analysis as an undergrad you'll be fine -- otherwise you may still be able to follow the course, get a good grade in it, but still be wondering about the motivation behind the generalisations to metric and topological spaces, and to function spaces (there won't be enough time for applications).

Thank you!

Is this course necessary? How about computational linear algebra, I think I should choose one from them, or take both?

 

[Daniel Duffy]

Take courses that improve your analytical skills, not just recipes.
e.g. write your own QR, LU algorithms from scratch.

And if time permits

http://en.wikipedia.org/wiki/Dedekind_cut

 

[bigbadwolf]

Is this course necessary? How about computational linear algebra, I think I should choose one from them, or take both?

I have a personal bias against computational/applied linear algebra courses -- linear algebra for dummies. If it involves some non-trivial coding, go for it, otherwise give it a miss. I presume you've already taken linear algebra (the real thing) at some time -- up to the spectral theorem and rational and Jordan canonical forms. That's more than enough.

 

[Mitor]

I have a personal bias against computational/applied linear algebra courses -- linear algebra for dummies. If it involves some non-trivial coding, go for it, otherwise give it a miss. I presume you've already taken linear algebra (the real thing) at some time -- up to the spectral theorem and rational and Jordan canonical forms. That's more than enough.

I believe that most of the meat of linear algebra in qfin comes from the applied/computational part. In physics it is representation theory as used by physicists. Having abstract math skills vs computational ones are partially disjoint skillsets. See for example this "Applied Linear Algebra" http://persson.berkeley.edu/18.335/course that essentially is a computational methods course using Liner Algebra.

 

[Mensa]

I believe that most of the meat of linear algebra in qfin comes from the applied/computational part. In physics it is representation theory as used by physicists. Having abstract math skills vs computational ones are partially disjoint skillsets. See for example this "Applied Linear Algebra" http://persson.berkeley.edu/18.335/course that essentially is a computational methods course using Liner Algebra.

I see the course is similar to Columbia's computational linear algebra. So do you think it is necessary to take for quant fin preparation? I cannot take all courses at a time, so I must trade-off...which is why I was asking for advice.

 

[bigbadwolf]

I believe that most of the meat of linear algebra in qfin comes from the applied/computational part.

You are right -- but I just can't summon any enthusiasm for this kind of math.

 

[Daniel Duffy]

You are right -- but I just can't summon any enthusiasm for this kind of math.

There are several phases

Vector spaces (pure) --> Numerical Analysis (see Golub/Van Loan) --> Numerical Recipes

The middle phase has all but disappeared. The last phase has become mind-numbing if done without background.

The analysis has been taken out of NA.

 

[Daniel Duffy]

Actually, students should be able to do any numeric algorithms. first manually on a 2X2 case etc. before automating it.

That would be a super interview Q, e.g. Cholesky decomposition for 3X3 matrix using quill and vellum.


Or a 3x3 lattice to do polynomial interpolation.

So you map the maths to an algorithm; then code it up in the general case.

 

[mhy]

Actually, students should be able to do any numeric algorithms. first manually on a 2X2 case etc. before automating it.

That would be a super interview Q, e.g. Cholesky decomposition for 3X3 matrix using quill and vellum.

We just learned that in my Monte Carlo class...I guess at least one person thinks it could work as an interview question!

 

[Daniel Duffy]

We just learned that in my Monte Carlo class...I guess at least one person thinks it could work as an interview question!

It's also a good technique when coding.