Mathematical modeling: physics degree or math degree

vicsmithvic

I am currently a double major in biology and math, interested in mathematical modeling of ecosystems and physiological systems.

The math portion involves modeling and pure math, but there isn't a lot of concentration on knowing physical laws. I'm not sure if I would miss all the knowledge about waves, electricity, statistical mechanics, fluid mechanics, etc., and I don't know if that'd be a disadvantage for when I apply to grad school for applied math. Also, given that I'm a junior, I will only be finishing the bare minimum that allows me to get a physics degree, while I'm already into the math major.

Still, I'm doing well in my pure math classes and enjoy them, but I don't know if being unable to take stat mech/fluid mech/etc. will be a disadvantage when it comes to mathematical modeling of say, cardiovascular systems, for research (that would show up for my grad school transcript). I'm already self studying programming, so I have limited free time.

What is the best option when it comes to mathematical modeling? A math degree (most of it is proofs, which I see in texts like smale's dynamical systems) or a physics degree?

Mépris

Just gonna go out on a limb and put this out there: have you considered an *applied math* major? If your university does not offer it, take a look at the programs of those who do, and see if these are the courses you'd need/want to do.

I've seen a few applied math courses aimed at modelling/computation.

http://maths.anu.edu.au/study/bcomptlsci/

deRham

Do not chain yourself to what a major expects of you. If you are interested in something interdisciplinary, you should choose the assortment of courses and other activities you pursue yourself. Major requirements are just a guideline.

I think some physics, and other courses directly related to modeling should be very good training.

Coto

Hi vicsmithvic,

deRham is right, don't let the requirements of a degree confine what you take. The field you're looking to get into is quite well established and there may be professors in the math department that can advise you on courses that would be useful to take.

An applied math degree in your case would probably be more directly applicable, however, there are some invaluable skills taught through the physics program that you may find useful in modelling. For this reason, it makes sense to ground yourself in a few physics courses--in particular, classes grounded on mathematical methods for physicists, and something like an advanced classical mechanics course to get a good sense on conservation laws and methods of approximation.

In terms of the mathematics courses, you'll want a very strong background in:

• (ordinary and partial) differential equations
• dynamical systems
• linear algebra
• computational methods
• analysis
• statistics and probability

In terms of a biology background, you'll want to take a survey of courses that give you a general understanding of:

• ecosystems;
• cell bio, and;
• physiology (animal or human).

Other physics courses you've listed (waves, electricity, fluid mechanics, etc.) may add some implicit understanding to natural processes, but this is something you can develop as you come to understand differential equations and their applications to biological systems.

The short answer: do the applied math/bio majors, but consider a couple of mathematical physics courses/advanced classical mechanics. You will not be any worse off than a guy coming out with a physics degree.