Applied Mathematics and its many uses!

Greetings seething masses of qt3! I am crawling out of the lurker woodwork to toss out some (probably ignored) questions. There appear to be some math-minded folks out there, so these questions are aimed right at you!

So, to preface, I am a graduate student in (Pure) Mathematics currently. I am running the gauntlet of basic required grad Algebra and Analysis classes. However I am finding that the courses I WANT to take are offered in the Applied Math department. Essentially dynamical systems in its many shapes in forms. My first exposure to it was in my ODEs classes, where we modeled assorted biological systems. And hot damn if it wasn’t fascinating as hell.

So my questions, to you select smart folks still reading, are thus: Do any of you fine folk know much about dynamical systems, especially as used in the sciences? Also, does anyone have any general experience with mathematics in an applied capacity? If so, do you have any advice/wisdom/tips? The sexiness of applied mathematics is more alluring than the wonky abstractness of the pure stuff!

Thanks in advance for any input on my rambling thoughts/questions.

The only thing I know about math beyond the class room is seeing it in action in NUMB3RS. Math formulas pop up all over the screen and create neat pictures and meld in to other pictures on the screen, and then Charlie Epps magically helps them catch the bad guy with his math wizardry.

Though to be honest I know nothing about math in an applied term except engineers using it to figure things out and/or analysts using it to figure things out.

EDIT: Would it be helpful in code breaking? I must say whenever I read some books if they had code breaking happening in it I’ve always wondered what kind of education the code breakers have. I would guess that mathematics would be a good background for algorithms and what not.

As someone who went to grad school for the sorta-pure stuff (philosophy), got my Ph.D. and then left to do the less-than-pure stuff (design videogames), my only advice is to not seek advice and do what truly inspires you. As my dissertation director told me while I was hanging around in Toronto trying to get a job in film, “find something you’d love to do, then find someone willing to pay you to do it.” Three months later I was working in the games press. So if you are more interested in applied rather than pure math, I wouldn’t wait around for a few qualified remarks from strangers on a message board, I’d start the gears in motion for changing your focus. Of course, this is a qualified remark from a stranger on a message board, so I’m also recommending you ignore me, but there ya go.

A good question for Math Professor Dave Perkins.

If you’re thinking in career terms, having a grounding in financial maths will not hurt you. Stochastic calculus & tree modelling, say.

A lot of our space radar guys have advanced degrees in applied mathematics. It gives you a lot of tools (such as various paths to function maximization) which are helpful in untangling SAR geometries.

If you’re looking to specialize in a domain like that, applied math is critical.

This better not be a hidden ploy to get us to give you help with your homework.

Pure Math and Applied Math are not the same thing at all. If you plan on staying in academia, you should choose one and stick with it, the sooner the better. If you plan on working in industry, they probably won’t know the difference.

And one more thing. Why do people ask for advice like this from game related forums? Why don’t you consult with your academic adviser about this? After all, I wouldn’t ask a math professor which he thinks is better, lolcats or loldogs.

hi Brinstil,

I’m a couple years ahead of you in grad school it sounds like. I’m firmly in pure math but I know a ton of people in math biology, which I would consider applied math. That area is exploding right now with no signs of slowing down, there is tons of money for grants and tons of problems to work on if you choose to go that route.

I have a question for both Ezdaar and Brinstil:

How do I stop sucking at modern algebra?

Is it all algebra or one particular part?

You might try a different book or a couple different books. I find something like Dummit and Foote to be a really great reference but incredibly hard to learn from since everything is done in the absolute most generality and you lose all the nice intuition along the line. My first algebra course was with Herstein, which I think can be a very good book but the notation is at odds with the rest of the world sometimes.

You might also try finding something to put it in context, like algebraic topology, geometry, combinatorics, representation theory, etc. Getting my hands on something like the symmetric group and counting things or playing with permutations gave me a much better understanding of groups in general. Rather than being just some abstract creation you see why the group properties need to be the way they are and as a bonus you are playing with a noncommutative group.

Damn! I was too transparent!

I already have meetings set up with advisers and professors (including the head of the applied math dept.). Asking here is purely supplemental. And as for why a gaming forum? There are smart people in here, and different perspectives are always useful (or interesting at least), no matter how deluded or psychotic!

I’m in neuroscience, and I can confirm what Ezdaar said, in that computational biology is a burgeoning field. Using ODEs and PDEs to model systems is increasingly useful, and a good way to determine how much you know about a system. A lot of physicists switch into neuroscience after getting their PhD since there’s more funding, and they actually know math.

Well, I am only now starting to not suck at that, haha. The key for me has been a professor that finally is passionate about the subject. As for practical advice, what Ezdaar said is all good stuff. And for me personally, I HAVE to do lots of examples and problems for concepts to sink in. Lots. LOTS.

Ezdaar, what area of research are you going towards? And awesome on the math biology info. I think my university is really starting to pick up steam there, so I might be able to hop on in the early stages, yay!

And so another question popped into my head. Is it a pain in the ass to switch majors at the graduate level (between similiar majors, ie Math to Applied Math)? And note, I already have appointments set up to officially answer this question, but if anyone has dealt with this it’d be nice to know what to expect.

My research is in algebraic combinatorics. I can’t imagine it would be that hard to go from pure to applied, especially if you have already passed quals/comps/etc.

I almost took a dynamical systems class this quarter (long with group theory) but here, the dynamical systems class is offered through the computer engineering graduate department. It’s a real application with real results definitely worth looking into.

The professor keeps his lectures online, so if you want a preview, I can PM you a link.

I give this thread a “meh”.

I’d be interested if possible, fire.

(As for the original question, applied math has a lot more viability than pure math for career paths. However, be aware that there’s a lot of “science” background that you’ll eventually need to pick up for any specific application of applied math. Much of the applied math in academia at least still comes from people who’ve tacked the advanced math onto the science, rather than the other way around, and you’re going to need to be able to communicate with those people.)

I started my undergrad work in pure math but when I transferred to UC Davis (which does not have a pure math undergrad program) I went into general math, tossed a bunch of skill points into applied courses, and finished. I now work in market research for a financial investments company.

I use the pure math stuff like graph theory, set theory, etc. for thinking about how to solve problems, and it also gave me a good foundation for databases (normalizing, logical structure, etc). But then once I’ve thought out an approach, I find that the lower-level applied stuff like series and sequences, derivatives and basic integrals, error estimation, etc. is how I end up solving it. So far I’ve only had to actually use pure math stuff once in proving that an approach to a problem solved for the entire possible space of answers, but everything else has been applied.

Cool, my math professor who taught ODE’s does research in mathematical neuroscience.

Nifty, a friend of mine at another college is thinking of doing research in that area. I am pretty amazed at people who can get a solid grasp on the high level algebraic stuff (and combinatorics no less!). Its a helluva lot more digestible than topology though, oi vey!

For sure! I’ll send you a PM.

Yeah, I’ve heard as much. I don’t mind playing a bit of catch-up.

Haha, I went to UC Davis for undergrad as well! When did you graduate?

UC Davis had a pretty good selection of applied courses. And from what I’ve checked out since graduating, they’ve added a bunch more.