I just finished my freshman year at a very highly esteemed LAC. I started off wanting to do physics but I did not continue with it like I probably should have. I am on track to be a math major. I was wondering if I got a math major and got a phd in applied mathematics, what kinds of fields could I go into? Could I go into certain aspects of physics? Or maybe intelligence (another thing ive always been interested in). I'm just not exactly sure what applied mathematics is.
Applied mathematics - as the name says - is a global cover of all possible ways to apply the mathematical knowledge. To give an example - each time we have a differential equation in physics (ordinary or complicated, linear or not, involving only constant coefficients or not...) the theoretical mathematics tries to either find a solution, or to insure the existence and uniqueness of it (under boundary data), or at least to know qualitative common issues (e.g. growth) for solutions of a given class of such equations. One usually works with Banach spaces and with very theoretical spaces of functions and distributions.
In applied mathematics, the differential equation has to be solved for practical needs, e.g. it is related to the orbit of a comet and we really want to have the numerical solution, and to compare it with the present position of the comet.
(The differential equation may come from elasticity, then the values should correspond to those expected by the specific car producer, etc.) The numerical approximation is obtained by applying the theorems most suited for the given situation.
Getting a phd is not so important, just fix the field first, find the person next, then try hard to understand the framework some years, then solve the problem.This page is free of commercials. Please respect this and no longer insert links to unrelated material.