Real / Abstract Analysis Vs Multivariate Analysis

As per the title, I need to choose between the two above courses to take in my last year of an MMath, looking to either A) Pursue a PhD in Maths/ FinMath/ Stats or B) Go into Quant Research.

For some added background: so far I have chosen a selection of Measure and Probability Theory, Stochastic Dynamics, Functional Analysis and Advanced Analytical Techniques (Think Fredholm/Volterra Integrals and Variational Calculus). I have one more module I am allowed to take: Real and Abstract Analysis (Metric Spaces, Differentiation in R^n, Contraction Mapping, Weierstrass Approx and Inverse Function Theorems), or Multivariate Analysis ( Principal Component Analysis, Multi-dimensional Scaling, Cluster Analysis etc).

I think MVT Analysis may be more useful regarding QR in terms of actually applying to proposed models. Whereas, I think R/A Analysis would help go into metric spaces, as no prior analysis course really delves into it (Have done Analysis, Complex Analysis, and Real Analysis which just introduced them by definition). On the other hand, this course seems to be pretty much all about metric spaces, and introduces Measure Theory near the end.

Since I will be taking Measure Theory and Functional Analysis, I was wondering perhaps R/A Analysis would almost be superfluous. But I also have no experience in QR space, so don't know if MVT Analysis is actually used or is helpful at all.

I also understand one choice of a course won't make or break my career, but just looking to gain insight into where people think there is more value. Thanks :)

Daniel Duffy

C++ author, trainer
Thanks for the link, really interesting stuff. I know Functional Analysis really helps tie things together but what are some of the numerical applications of Functional Analysis that you mention?

1. Finite Elemensts, PDE
2. Machine Learning e.g. RKHS
3. Generalised Numerical Analysis.
4. You can define a prori error estimates in convergence processes

FA is so cool.
Abstract analysis is used when the data set is very large (use cases, requirements, etc). Abstract analysis finds a happy medium in the middle of the two variables. The analysis provides a good balance of the data. On the other hand, Multi-variate analysis identifies the relationship between the two variables and helps to minimize the impact of the relationship on the dependent variable.