# Geometry, Differential Equations, or Differential Geometry

## Main Question or Discussion Point

I go to a small liberal arts university that only offers certain math classes at certain times. Due to the way my schedule has worked out, I only have the option of taking ONE of the following: geometry, DEs, or DG. What should I do? By the time I HAVE to chose, I will have taken the calculus series (three semesters, including multivariable), introduction to proofs, and linear algebra (and introductory physics as well). I am leaning towards DEs but I am not completely sure.

nicksauce
Homework Helper
Can you maybe provide more information? What program are you in? (I'm assuming phyiscs) What year are you in? Can you provide descriptions of these courses?

Can you maybe provide more information? What program are you in? (I'm assuming phyiscs) What year are you in? Can you provide descriptions of these courses?
Certainly. I'm a math and biology major at a small liberal arts college with good math and biology programs. I'm a junior by credit standings (aka no GURs) but am only in my second year of college. I took BC and AB calculus in high school, which covered the basics of single variable calculus. I came in as a Freshman taking multi-variable calculus, and then just took proofs last spring (we covered direct proofs, proof by contradiction, proof with the contrapositive, proof by induction, and then some set theory and some complex numbers stuff), and I'll be taking linear algebra in the fall. I'm currently doing the pre-med program with hopes of doing something medical in the future (pharmacy, medicine, research, etc).

Here are the course descriptions:

Geometry Math 321: Foundations of geometry and basic theory in Euclidean, projective, and non-Euclidean geometry.

Differential Equations Math 351: An introduction to differential equations emphasizing the applied aspect. First and second order differential equations, systems of differential equations, power series solutions, non-linear differential equations, numerical methods.

Differential Geometry Math 480: This class is a one-time offer, so there is no course description. One professor went on sabbatical and studied up on DiffGeometry and is going to teach a class on it. It has been described to me by some professors as "the mathematics of curved space and time."

differential equations is your best bet. Comes up a lot in the sciences, and is pretty fundamental

nicksauce
Homework Helper
I will second ekrim's response. Taking differential geometry if you want to go into medicine areas seems a little excessive. Differential Equations is much more practical.

By far and wide differential equations. Much more fundamental than the other two, and you will see a lot of applications to biology. Differential equations are used everywhere to model things, many of which are medicinal in nature.

The Euclidean geometry stuff is pretty much useless to you. While an interesting subject in its own right, compass constructions do not go hand in hand with medicine. Differential geometry is highly abstract and used only in heavy-duty physics. Unless you intend to major in physics and study GR or do higher math, it won't be of any use.

If you were doing physics I'd say diff geom. For maths for it's own sake, I'd say whatever looked interesting. But if you want something applicable to medicine, pharmacology, etc do differential equations. It's probably maths overkill tbh, but better that than something completely irrelevant.

If you were doing physics I'd say diff geom. For maths for it's own sake, I'd say whatever looked interesting. But if you want something applicable to medicine, pharmacology, etc do differential equations. It's probably maths overkill tbh, but better that than something completely irrelevant.

I'd say differential equations should supersede differential geometry for anyone regardless of major

Differential Equations for sure, it's the bread & butter of any physical sub-discipline.

Geometry and topology is something you can easily study in your own time should you need it later on.

If you were doing physics I'd say diff geom. For maths for it's own sake, I'd say whatever looked interesting. But if you want something applicable to medicine, pharmacology, etc do differential equations. It's probably maths overkill tbh, but better that than something completely irrelevant.
I second this, differential equations is by far the most applicable of your options. And it might not even be overkill - for example, have a look at Pharmacokinetics http://en.wikipedia.org/wiki/Pharmacokinetics

(I'm no expert at all in this, but somehow the word came to my mind when I read about the combination of math and pharma/medicine stuff). Differential equations with an emphasis on applications might be exactly the right preparation for this, and pay close attention to the numerical methods !