I am entering my final year as a physics/math double major undergrad and have hopes to continue onto a PhD program where I can do optics research, either through a physics or ECE department. That being said, my interests lie in experimental work rather than computational or theoretical, but I have one upper level math class left required for my degree and I'm looking to take the one that will help me most to carry on with optics. I've narrowed my choices down to the two following courses. Advanced Differential Equations (w/ ODE's as a prereq): "Development and application of advanced topics in differential equations. Topics may include foundational theories of differential equations, partial differential equations, perturbation theory, calculus of variations, distribution theory, transform theory, or other advanced topics" and Dynamical Systems Theory: "Development and application of the theory of dynamical systems. Topics include phase plane analysis, bifurcation theory, and chaos theory. Basic applications relevant to each topic are included. Additional topics may include fractional dimensions, differential equations, and cellular automata."