Leftover Undergrad subject choices in pure maths after all relevant applied/stats are done

[AutumnWater]

So I realised I should focus on applied and stats units as I read through other posts in this forum.
To save words, after I've filled my degree with all the appropriate applied and stats units, plus real analysis to help with measure theory and probability.

What other pure maths subjects should I do?

At my current school, algebra 1 and algebra 2 are both mixed with number theory 1 and number theory 2, group theory is also included in algebra and number theory 1, at a different institution, there is a subject called metric and hilbert spaces that's a pre-req to measure theory and group theory happens to be a pre-req to metric and hilbert spaces, so I'm assuming algebra and number theory I should be mildly relevant to measure theory if not completely? What branch of pure math is that metric and hilbert space course by the way?

So at my school I have a total of 5 subjects I can do in pure maths, if neither of the two leftovers are of any concern to quant then I might as well fill up the rest two with CS units instead:

These are:
Real analysis (will do)
Complex analysis (will do, relates to signal processing right?)
Algebra and Number theory I (Should I do it? it contains group theory)
Algebra and Number theory II*
Differential Geometry*
Functional analysis*

Which two should I pick out of the asterick ones and if none, should I be focussing on computational science units (numerical analysis and data structures) or coding units or even just chill and keep some of my past credit points in finance from being revoked?

 

[MarekSabata]

...so I'm assuming algebra and number theory I should be mildly relevant to measure theory if not completely? What branch of pure math is that metric and hilbert space course by the way?

I don't really think you need any number theory to take measure theory courses. In general, these two fields have very little in common.

Metric spaces and more generally topological spaces (including normed linear spaces, Banach spaces and Hilbert spaces = really nice Banach spaces, where the norm is induced by inner product) are topics in Functional analysis.

My personal advice would be take Functional analysis. It might not have direct applications in finance, but it's the most interesting and beautiful math field there is. (Though I might be little biased... )

 

[AutumnWater]

My personal advice would be take Functional analysis. It might not have direct applications in finance, but it's the most interesting and beautiful math field there is. (Though I might be little biased... )

Sweet, I'll keep that in mind when I get to that level

 

[bigbadwolf]

The two CS options -- numerical analysis and data structures.

 

[AutumnWater]

Cool, what about sequence of units?
Apparently these same year leveled ones don't have each other as pre-requistes and all can be taken at the same time, in which order should I take them:

Am doing multivariable calculus, Linear algebra, and discrete maths atm, will do DE, stats and probability next semester, but don't know what order to take the rest next year:

2nd year:
Probability, Stats, DE, Real analysis

3rd year:
linear random processes: ARIMA/ARMA/Spectral analysis, financial mathematics, random processes in physical sciences: poisson/martingale/randomwalk, Advanced ODE, Applied Modelling, PDE, Computational maths, Complex analysis, Baye's theorem, financial econometrics, Contingencies in insurance, Econometric theory,

and which ones are quite heavy so I should mix with some easy ones during the same semester?

 

[Daniel Duffy]

Functional Analysis is cool. It forces you to think like a mathematician.

At my current school, algebra 1 and algebra 2 are both mixed with number theory 1 and number theory 2, group theory is also included in algebra and number theory 1, at a different institution, there is a subject called metric and hilbert spaces that's a pre-req to measure theory and group theory happens to be a pre-req to metric and hilbert spaces.

Hilbert space is not really a prerequisite to measure theory as such nor is group theory, which is a closed project unto itself.

 

[bigbadwolf]

Hilbert space is not really a prerequisite to measure theory as such nor is group theory, which is a closed project unto itself.

Agreed. Just more stupid hoops to jump through, and designed no doubt by some bureaucratic shithead who knows no math himself.

 

[Daniel Duffy]

Agreed. Just more stupid hoops to jump through, and designed no doubt by some bureaucratic shithead who knows no math himself.

I agree. It's one of the weirdest descriptions I have ever read.

 

[Smullyan]

Take as much analysis as you can fit in, the heavier on the proofs and rigor the better.