I am writing this, as I am a currently an intern at an aircraft manufactur. I am studying a mixture of engineering and applied math. During the semester I focussed on numerical courses and my applied field is CFD. Even though every mathematician would say I have not heard a lot of math, for myself I would say that I get the “most amount of math” you can get while not studying math.
In my courses I have done deep theoretical analysis for numerical concepts and application in CFD. But currently I am starting to wonder, how much the e.g. Calculus of Variation course really helps me in my future career. The theory you learn at university seems to get only a little application in the real word.
Example: In my numerics for PDE class I have spent (wasted?) so many hours on trying to figure out the CFL number of certain schemes, but what I am doing right now has nothing to do with that. Oh your simulation does diverge? Well let’s take 2 instead of 4 as our CFL number.
Furthermore, I am not really programming stuff as I hoped I could, but I am rather scripting. Fact is, 99 out of 100 people are not going to program a CFD solver. You rather use the code and apply it to your needs.
I am aware that university always follows a way more theoretical path than industry, but I am actually disappointed how little math I am really doing. Okay you might, say that’s due to the fact that I am an intern and of course you are right. But I am in the lucky situation, that my team comes really close to research. Most of the members hold a PhD and studied engineering or math, and the focus is definetely on research ( in this departure of the company). But if the amount of math is that small in such an environment, where are you really able to make use of what you have learned at university.
So here comes my question
How much math are you actually doing at your job?
And I don’t mean, how much math is helping you to understand things, but how often does it happen, that you sit down and really do math in your non-academic job?
Personally I get the impression that I could do the exact work without having heard most of my courses. Don’t get me wrong, I really enjoy the theory, but currently I am rather frustrated.
Note: As this is my first Question, I hope I did not screw up completely. I did not found similar questions on this side. And feel free to edit or ask questions if thinks are not clear.
I’ve spent the past twelve years as a professor. However, for five months last spring I spent part of a sabbatical working in the long-term forecasting group of an investment firm. I used a lot of math in those five months. (Admittedly, it was mostly a research-type position, and I gravitated toward the math-heavy problems.) Here are some problems I tackled on this job that required me to use math.
We have huge gaps in our set of stock prices because countries change currencies or come into existence or cease to exist or stocks move in and out of major indexes or name your reason. We need to know how these stocks rise and fall (or don’t) with each other. How do you calculate a covariance matrix in the presence of missing data? The best solution often results in the matrix becoming singular. This is a big problem because your model requires you to invert it. Do you try one of the other solutions to avoid the singular matrix problem and accept the resulting drawbacks, or do you try to “fix” your matrix somehow? If the latter, what are the best ways to do that? Answering this question required a great deal of understanding of (well, to be honest, learning about) numerical issues in linear algebra.
We have a model that we’re happy with that makes short-term predictions, and we have a model that we’re happy with that makes long-term predictions. How about the medium term? How do we smooth our short-term predictions into our long-term predictions? To answer this question for us I had to, among other things, solve a couple of differential equations that resulted from trying variations on the logistic curve as models.
- Our model is giving weird, erratic results. Why? Does it have some
fundamental economic flaw? It takes me a couple of days to
determine that the answer to this one has to do with the eigenvalues
of the covariance matrix at the core of the model. Linear algebra
- I’m analyzing a set of economic indicators to determine their
predictive value. Are they random walks of some sort, or do recent
values have something to do with slightly less recent values? This
requires time series analysis.
- The woman sitting next to me is having trouble with her linear
regression. I can’t remember now exactly what the difficulty was,
but I needed some statistics to solve the problem for her.
The job wasn’t all math; I spent more time coding than anything else. But I did use linear algebra, numerical methods, optimization, statistics, differential equations, and even some calculus on this job.
So don’t give up hope yet. Maybe they are in the research arm of a company, or maybe they require an advanced degree, but there are some jobs out there that require a good deal of math.