To the Wilmott community, 

May I seek your opinion on which electives should I take over the course of my 4-year undergraduate degree? 
TLDR: Should I pursue the measure-theoretic probability path or the Statistics/Computer Science path? 

Some context about myself:
I am currently a freshman attending a university in Singapore and my major is Quantitative Finance (QF). (Some of you may irk at the sight of a bachelor's degree in QF, I get it...)
A detailed list of my major requirements (the modules I MUST/HAVE/AM/WILL take) includes: 

1. Calculus (the contents are similar to the United States' Calculus 1 content, plus a tiny bit on Real Analysis)
2. Linear Algebra 1 (the usual undergraduate linear algebra stuff; eigenvalues, diagonalization, rank, linear transformation between Euclidean spaces)
3. Accounting
4. Python programming 
5. A module on finance which covers: financial statement analysis, long-term financial planning, time value of money, risk and return analysis, capital budgeting methods and applications, common stock valuation, bond valuation, short-term management and financing.
6. Multivariable Calculus (the equivalent of US' Calculus 3)
7. Real Analysis. Major topics: Basic properties of real numbers, supremum and infimum, completeness axiom. Sequences, limits, monotone convergence theorem, Bolzano-Weierstrass theorem, Cauchy's criterion for convergence. Infinite series, Cauchy's criteria, absolute and conditional convergence, tests for convergence. Limits of functions, fundamental limit theorems, one-sided limits, limits at infinity, monotone functions. Continuity of functions, intermediate-value theorem, extreme-value theorem, inverse functions
8. Numerical Analysis
9. Probability (calculus-based probability) 
10. Investment Instruments: Theory and Computation which focuses on the basic paradigms of modern financial investment theory, to provide a foundation for analysing risks in financial markets and to study the pricing of financial securities. Topics will include the pricing of forward and futures contracts, swaps, interest rate and currency derivatives, hedging of risk exposures using these instruments, option trading strategies and value-at-risk computation for core financial instruments. A programming project will provide students with hands-on experience with real market instruments and data.
11. Mathematical Finance 1 covering: the basics of financial mathematics and targets all students who have an interest in building a foundation in financial mathematics. Topics include basic mathematical theory of interest, term structure of interest rates, fixed income securities, risk aversion, basic utility theory, single-period portfolio optimization, basic option theory, emphasizing on mathematical rigour. 
12. Regression Analysis
13. Ordinary Differential Equation, that includes the mathematical analysis of ODE
14. Linear and Network Optimization or Nonlinear programming
15. A couple of Business oriented modules
16. Financial Modelling: which equips me with the knowledge of modelling financial process for the purpose of pricing financial derivatives, hedging derivatives, and managing financial risks. The emphasis of this module will be on numerical methods and implementation of models which includes: implied trinomial trees, finite difference lattices, Monte Carlo methods, model risk, discrete implementations of short rate models, credit risk and value-at-risk.
17. Mathematical Finance 2: which provides me with in-depth knowledge of pricing and hedging of financial derivatives in equity, currency and fixed income markets. Major topics include fundamental of asset pricing, basic stochastic calculus, Ito’s formula, Black-Scholes models for European, American, path-dependent options such as Barrier, Asian and Lookback options, as well as multi-asset options and American exchange options.

The list continues for a while more but I will stop here because we should have had some sensing of my course curriculum.
Anyway, with this context, what are your opinions on the elective (unrestricted) modules I should take to complement my studies? 
Option 1: Follow up with 3 more mathematical analysis modules, which covers differentiability, Riemann integrals, metric spaces, an analysis treatise on multivariable calculus, measure theory? 
OR 
Option 2: Follow up with more statistics and computer science modules which exposes me to mathematical statistics, applied time series analysis, statistical learning, machine learning, designing/ analysis of algorithms, data analysis etc.  

I also plan to pursue postgraduate studies, either a Masters in Financial Engineering or PhD (that's quite some time away but I want to be in a position best suited to further my studies).

Correct me if I am wrong, but from my premature understanding of QF, I understand that stochastic calculus/ stochastic analysis are used for areas such as option pricing and model validation whereas one can apply his/her knowledge of statistics and Computer Science on algorithmic trading/ HFT. Currently, I am interested in algorithmic trading - I'm working on a mean reversion theory project in university. However, since I am unsure of which area of QF I am interested in, I do not want to close my doors unnecessarily.... 

I think I have already said quite a bit so I'll stop here for now. 

Nevertheless, thank you for reading and I would like to hear what you have to say!

Galvinator

7. is the foundation for everything else. It is analysis while some of the others are 'robotic' methods/tricks but still needed of course (e.g. calculus, ODE)
Functional analysis maybe as well.

13. why numerical ODEs?
PDE?

C++/C#/Python

If you were reasonably certain that you wanted to go on to do a PhD in a very quantitative area, then maybe option 1. Under most other circumstances, option 2, since that will improve your employability both within and outside quant finance, and will also be useful in most relevant directions of graduate school.

@Cuchulainn:

One module I excluded from that long list is, in fact, a module on numerical PDEs.

The contents include: various numerical integration schemes for solving ordinary differential equations, and (2) finite difference methods for solving various linear partial differential equations. Major topics: (ODE) One-step and linear multistep methods, Runge-Kutta methods, A-stability, convergence; (PDE) Difference calculus, finite difference methods for initial value problems, boundary value problems, and initial-boundary value problems, consistency, stability analysis via von Neumann method and matrix method, convergence, Lax Equivalence Theorem.

I'd look for a survey course in what's traditionally called "engineering mathematics" that uses, say, Kreyszig. That combines a bunch of things. Then, add a stochastic calculus course. Plus do Option 2. Leave the measure theory, functional analysis, etc for grad school. 

Other nice things:
Mathematica/MATLAB/R/LaTeX/WordPress

A useful book we used to call KKOP contains a lot of useful stuff and some protean Functional Analysis

@Cuchulainn:

One module I excluded from that long list is, in fact, a module on numerical PDEs.

The contents include: various numerical integration schemes for solving ordinary differential equations, and (2) finite difference methods for solving various linear partial differential equations. Major topics: (ODE) One-step and linear multistep methods, Runge-Kutta methods, A-stability, convergence; (PDE) Difference calculus, finite difference methods for initial value problems, boundary value problems, and initial-boundary value problems, consistency, stability analysis via von Neumann method and matrix method, convergence, Lax Equivalence Theorem.

Looks pretty good. Convection-diffusion PDE is what universities leave out
Here is an introductory article on FDM for such an equation.

Measure theory and functional analysis should be done ASAP IMHO before the brain goes to pot
I did about 4 courses on MT from 2nd year one and I hated them. Functional Analysis is much more important.

@Cuchulainn, 

I perfectly agree with your comment on understanding measure theory/ functional analysis ASAP because time isn't our brain's friend. 

On the other hand, Alan and bearish are more inclined towards option 2... for reasons I can agree with.. 

I am still caught in between these two paths...