never thought i'd be making one of these threads but my directed independent study professor dropped me at the last moment and now im stuck trying to fill a hole in my schedule. so between these classes what should i take? background: i'm a senior math/physics major. im already taking advanced calc 1, abstract algebra 1, advanced physics lab, spanish 4. if i go to grad school it'll be for math, applied math at that. the catch is i like pure math and despite swearing up and down that i hate physics im still drawn to it out of shear masochistic curiosity. here are my options: Fun Analysis Spectral Theory - Grad Class – applications to differential equations – duality of norm spaces and operators, in particular Hahn-Banach, Open mapping and the principle of uniform boundedness. – basic introduction to generalized functions (distributions) – spectral theory for compact operators on a Banach space i have not taken a grad math class before no do i have the advanced calc prereq for this class but i could still get in and am very curious about functional analysis. i have all the linear algebra prereqs and have met a lot of this stuff before in my qm class. Game theory and it's applications Nash equilibrium and other solution concepts for noncooperative games Evolutionary stability and other criteria for equilibrium selection Cooperative games in strategic form Cooperative games in characteristic function form The prisoner's dilemma and the rationality of cooperation Population games Further applications, as determined by student needs or interests something i know nothing about so naturally im interested. Topology I Grad Class I took the undergrad version a summer ago. It was easy I got an A. Can't find much about this class but I know it'll be taught out of Munkres. Quantum Mechanics A - Grad Class I. The physical basis of Quantum Mechanics II. Schrodinger equation. One-dimensional potentials. III. Operators, eigenfunctions, and symmetry. Expectation values. IV. Discrete eigenvalues, bound states. Harmonic oscillator and hydrogen atom. V. Continuous eigenvalues and collision theory. i've taken the undergrad QM sequence. hated it. it was the straw that broke the camel's back as far being a physics major goes for me. I got Bs in both classes. I won't say im the best quantum mechanic ever but i've peaked at the hw for this class and it looks pretty doable. why would i take this even though i ostensibly hate physics/qm? cause im stubborn and up for a challenge. Phyiscs DIS A former physics professor has approached me about doing research with him. nice guy. the research might even keep me occupied/interested but i don't know how useful it would be as far as learning new skills/grad school for math. i could also do something crazy like take german 1 or arabic 1 which i would really enjoy but wouldn't be useful at all. or even crazier would be to take QM and do the research on the side.