<p>What math classes should be taken in order to study plasma physics and quantum field theory?</p>
<p>For QFT, the math required is of a pretty decent amount (vectors, vector-spaces, eigenvalues, eigenvectors, complex analysis, multidimensional calculus, and a little bit of differential geometry).</p>
<p>For plasma physics you need complex analysis and group theory.</p>
<p>I don't seem like I know all the answers so I will do what I USUALLY do...</p>
<p>...I'll just look up a few grad programs in the top 10 and come back with an answer.</p>
<p>For QFT...add on Functional Analysis, Partial Differential Equations and Probability.</p>
<p>For Plasma Physics....add on Partial Differential Equations and Hilbert Spaces which is usually in more advanced Linear Algebra courses</p>
<p>If you pursue a PhD in plasma physics, you will probably learn more math than that, whether in a course or on your own. We spent so much time talking about plasma flows and electric and magnetic fields in my algebraic topology class that I'm having a hard time imagining how you could get a PhD in plasma physics without some background in topology.</p>