<p>I don’t know much about math competitions. But AMS (Applied Math and Statistics) teaches you how to USE math. Here, you’d be more likely to learn how to solve a certain problem in, say, science or engineering. Proofs would pretty much consist of “because a mathematician said so, Google it if you don’t believe me.” MAT (Mathematics) is math for the sake of math. You go deep into theories, proofs, and the like. Said proofs that your AMS professor told you to Google might more likely be on your homework in MAT. I don’t know the full details, but that’s the best I understand of it. Obviously, there’s enough difference in the material for one to be able to double major in AMS and MAT.</p>
<p>Also, AMS has statistics, MAT not so much. And AMS has “Applied Calculus X” (where X is the number in the sequence), while MAT has “Calculus X” or “Calculus X With Applications”.</p>
<p>If you’d like to know more, maybe shoot an e-mail to some staff in both departments. They can help you more than I can.</p>