Maths course choices

Hello all,

I am doing a Maths and Stats undergraduate degree and hope to be a statistician. I have to choose one of the courses below. I would be very grateful for advice from statisticians as to which is more useful, all things considered; not just in direct terms of similarity-of-techniques, but helping to get a deep understanding of the mathematical stuff statisticians do etc.

a) Group theory, Linear algebra, Analysis

b) Vector algebra, Differential equations, Matrices and Numerical methods

If it's relevant, in the final year I will do probability modelling, mathematical statistics and linear modelling.

Thankyou very much.

Sorry, I see how I was unclear. Yes I have to pick only one of these two. So option (a) which covers the three topics listed. Or option (b) which covers the four topics listed.

(a) is classed as Pure mathematics and (b) is classed as Mathematical methods, models and modelling.

(b) includes a mathematical software package but it is not a programming language, and I will already use 4 statistical software packages in the stats courses anyway.

Option (a) is all pencil and paper (this actually counts as a plus for me, since it will make a nice break from the computer work in the stats courses).

As far as enjoyment goes I think I will enjoy both the same, maybe pure a bit more. So my choice is ultimately driven by career matters.


Probably A Mammal
While I find the first 2 in (a) to be quite interesting--I have a math degree--you'll benefit from real analysis if you want to go on in mathematical statistics because you'll have to study measure theory. This typically coincides with studying more analysis (beyond real valued spaces) and metrics defined on those spaces (which is what probability is).

When it comes to (b), you can benefit greatly from learning numerical methods, if you plan to go on and want to do computational data analysis. That's sort of the route my applied skills have developed, because a lot of my analysis revolves more around how to manipulate and analyze data through programming. While I'm not sitting here writing integration functions, depending on how they teach it, the matrix techniques and monte carlo simulations can be useful. With that said, vector algebra is typically studied in stats, for the obvious reasons that a lot of stat formulas are expressed in the language of matrices. Differential equations hasn't always been too significant, but I'm finding in certain areas (time series, fourier analysis), it has its place. It's really the one thing that's kept me from studying signal processing.

If I had to choose, I'd probably go with (a) if I wanted to be more theoretical and (b) if I wanted to be more applied. I love pure mathematics, so I'd have chosen (a), which is sort of the boat I'm in now, but for work, most of my skills are derived from (b). Honestly, though, the best education has been experience for me, and that's been through work. Therefore, I find it a good choice, in my case, that my education has been largely theoretical. I have a solid foundation from which I can build upon in applied settings.
Hi bryangoodrich,

Thanks for your reply, very interesting. That's a good point (if I've read you rightly) that a lot of the directly-job-relevant stuff you pick up on the job, so getting a solid theoretical grounding in school is wise. I actually have no programming experience so computational data analysis is not something I know about.

Sounds like that's an investment for long-term career, focussing on theory. It's a tough balancing act: age and money worries (I've two arts degrees and am now penniless and trying to change career direction) mean I need lots of stuff on my CV that will jump out at an employer who has no interest in spending any time training anyone to do anything. But I imagine depth sets the foundation for length in terms of a statistical career.

I still have a year to decide by which time I would have had an introduction to medical stats, time series, multivariate and Bayesian, so hopefully that will make the choice clearer.

Thanks again.