Dear PF members, I am about to begin my junior year as a math major, and I feel like I made one observation. That is, if I want to study math at advanced level, I need to choose either pure or applied mathematics. I have also noticed that if I get a title of "mathematician," that implicitly implies that I am a pure mathematician, and if my research is leaning toward applications, I would be rather referred to as applied mathematician than just a mathematician. Notice that this is only my observation, and I could be wrong about this, so feel free to give me a counterexample to my observation. For me, if I am going to study math in graduate school, I would like to study both pure and applied math. To me, applications interest me a lot--I find it cool that something like linear algebra, for example, can have so many applications outside of mathematics even though what you're learning in class is somewhat abstract (e.g. vector space with >3 dimensions, inner-product space, etc.). I find it really fascinating, especially because I was originally a science major (biochemistry) when I first entered college. And of course, I find the theory of mathematics to be beautiful--I just took a class in abstract linear algebra, and I really enjoyed that class. I also find some of the stuff in number theory to be beautiful as well (e.g. Fermat's Little Theorem, Chinese Remainder Theorem, etc.). So to be honest, I really like the theoretical and applied aspects of math, and in fact, I am afraid that I would get bored if I could only study one of those two. So I was wondering what to study in grad school (if I am going to one), and looked up some of the websites of applied math departments. What I found out was that most of the applied math departments (in U.S.) seem to recommend taking ODE, PDE, numerical analysis, and etc during undergrad, but not many of them recommend taking courses like analysis, algebra, topology, or those types of rigorous math courses (in fact, I think Cornell was the only school that explicitly stated that they recommend analysis and algebra before grad school). This made me think that maybe I won't see many pure math in applied math department, which is disappointing to me. But as I stated before, if I go to a grad school, I would be only studying the pure math and not much applications (based on my observation). So my ultimate question comes down to this: If I want to study both pure and applied math, what should I do? Any thought is appreciated--you don't really need to answer to my last question as long as you're replying me with something related to this topic in general.