Sorry I keep posting about this. I had settled on Probability (Probability in discrete and continuous sample spaces; conditional probability; counting techniques; probability functions; binomial, Poisson, normal distributions; and transformations of variables.) based off of previous answers to posts on here, but my differential equations professor this semester just told the class today and sent us an email about a directed study class he is running on advanced differential equations next semester. The description is "A focus on boundary value problems with topics such as the Shooting Method, Green's Functions, Sturm-Liouville Problems, and the Contraction Mapping Theorem. Phase portraits with an emphasis on limit cycles will be explored." It sounds really interesting and I have heard references to Green's Functions and Sturm-Liouville equations when reading about quantum mechanics, so I was wondering whether anyone had any advice on whether Probability is more useful for quantum mechanics or the advanced differential equations course? (I only have room for one of the courses next semester otherwise I would take both.) Thank you so very much for any advice!