Another coursework question

[GoPackGo89]

Fall schedule is out and it will probably be my last semester as an undergrad. I'm deciding between:

A. 2nd semester in linear algebra: Vector spaces; duality, direct sums; linear maps: eigenvalues, eigenvectors, rational and Jordan forms; bilinear maps, quadratic forms; inner product spaces: symmetric, skewsymmetric, orthogonal maps, spectral theorem.

B. Grad level analysis- Metric spaces, abstract measures, measurable functions, integration, product measures, Fubini Theorem, topological measures, Haar measure, differentiation. Radon-Nikodym Theorem, linear spaces, Hahn-Banach Theorem, Riez Representation.

C. Grad level stochastic models- Stochastic process models with applications. Analytic and computer modeling techniques for Markov chains, Poisson processes, Markov processes, Empirical processes, Brownian motion, and special topics

I have 2 semesters of intro real analysis, 1 semester of functional analysis so I'm wondering if there are diminishing returns on these analysis classes or the more the better. Thanks!

[Dora the Destroyer]

Grad schools love it when you can pull that ruler out of your backpack backpack and measure some things!

[abstract_art]

You can't really go wrong with either 2nd semester linear or measure theory (there's probably not diminishing returns if you're doing well in all of these analysis classes). I don't know which an admissions committee would look more favorably at (maybe measure theory?), but I'd try to take both if you can. The stochastic models models class sounds interesting but it might be something you'd end up taking again in grad school (so maybe sit in on it, take it pass/fail, etc).

[chisquare]

If I were you, I would go with the measure theory. I didn't take it when I was an undergrad, and now I am a master student and had a really bad time with measure theory. I am planning to take it in the first semester of my PhD program. 

 

As both my master supervisor and undergrad supervisor told me, 99% of the time you probably won't need the knowledge. However, as my current supervisor added, once or twice in your life, you might need to proof something with measure theory.