How well does "Applied Mathematics" cover "pure math?" Ill be going into my first year of college fairly soon, with a prominent interest in studying and researching (as a career) pure/theoretical mathematics (especially number theory). However, the college I'll be entering only offers an "Applied Mathematics" major, which I understand may be more suitable for engineers, economists, physicists, etc (but my perception on that point may be incorrect). Given this conflict, I have been considering transferring to another university.

My question is: Is an Applied Mathematics major still satisfactory for my interests in pure math, or should I transfer to pursue a major more closely connected with these interests?

Thank you kindly!
For undergraduate math, programs tend to be really similar. You do calculus, then multivariable calculus, then linear algebra and differential equations, and you move on to an elementary analysis course and abstract algebra. These are usually what a student does through their freshman year for any math degree (and many for sophomore year depending on how prepared you were).

After you go through these, there will be upper division courses in PDEs, dynamical systems, manifolds/geometry, complex analysis, numerical analysis, etc. I assume that the main difference would be that an undergraduate program with only applied math would have less algebra courses (more courses in ring theory, Galois theory, etc.), one or maybe no upper division number theory course (except maybe a cryptography course in a CS department), and more courses based in modeling, numerics, and differential equations (numerical linear algebra, finite element methods, etc.). 

But there's really one way to know for sure: look at the courses they offer. It's always online. Don't look at just one year since the upper division courses tend to be every other year, so look at maybe the last 3 or 4 years. Look at what they offer and ask "are there 3-4 courses a quarter here that interest me?". Look at some syllabuses, crack open some books, look through Wikipedia. Then do the same for places you are wishing to transfer to.