<p>So, I'm planning to major in physics. I was wondering what level math will be most useful for me to study further? I can either study for AMC/AIME math or Calculus. Would you guys recommend I study Calculus in depth since it was pretty much discovered for applications in physics or should I get really good at the basic contest prep material? Thank you.</p>
<p>I’m not familiar with the former, but I would say that calculus would be a good thing to develop a strong foundation in. However, Calculus is just the starting point for physics. My university requires 2 individual physics courses that are a crash course in useful higher level math concepts.</p>
<p>Calc is much more useful than studying for the USAMO…</p>
<p>Depends on your interests. Calculus, differential equations, and linear algebra would suffice for most experimental and computational physics. As for theoretical and mathematical physics, you’ll need topology, differential geometry, and some analysis wouldn’t hurt either.</p>
<p>For mechanics it’s good to have a background in first year calculus and multivariable calculus and some ordinary differential equations (for the harmonic oscillator), for Electromagnetism you rely on vector calculus a ton. Later on I am told you will need to be comfortable with ordinary and partial differential equations and linear algebra/some group theory, and real and complex analysis. If you want to go into theoretical physics (which is me) I’ve been told that it’s great to know more abstract algebra and algebraic topology. It seems that quantum field theory entails a lot of ideas in group theory and other areas of abstract algebra.</p>