Difference between an applied math and pure math degree.

Intervenient

From what I've heard, both do theory, but applied math has a lot more computational and applicable electives, vs. the theoretical based electives of pure math.

chiro

The focus is completely different, but things do overlap.

In applied math, we take results from pure math to solve actual problems in the real world.

I'll give you a concrete example.

Take for example linear models in statistics. The goal of linear models is to use linear equations (think matrices) to measure various statistics and use them to draw inferences.

Now the framework uses a lot of results from linear algebra including idempotent matrices, least squares, psuedo-inverse matrices, and so on to calculate something useful.

Contrast this to pure math, where if you were say a research in linear algebra, you might have been working on the theory of pseudo-inverses and its calculation for generic square matrices. You probably don't care that (or least don't have the perspective that) a statistician needs your work to estimate a linear model. You are likely to be more interested in studying some generic situation and trying to use the existing work of pure mathematicians to extend their work to a more generic situation.

Maybe you have come across some problem that was a previous thought experiment of a previous pure mathematician and you become interested in it. It may have no immediate scientific application, and may just be a curiosity, but what it may do is lead to further results, and maybe results that form an analytic framework for some analysis of a more generalized model.

One thing you should remember is that a lot of applied math nowadays is using the pure math that was developed before. Think about all the stuff that engineers use in their daily work from signal analysis to optimization, to cryptography, it's all there.

Sometimes it's hard to distinguish between pure and applied, but if a particular topic is used to solve a particular problem in some applied science, then it is applied.