what math class should I take?

what math class should I take, to help me as an Engineer?:

Probability and Statistics II: (Random variables; distribution functions; expected value and moments; sampling; point estimation; interval estimation; hypothesis testing)

Partial Differential Equations: (Classification of linear second order partial differential equations (PDE), diffusion-type problems, Fourier sine and cosine transforms. Laplace transform solutions, method of characteristics, elliptic-type problems, Green’s functions, numerical and approximate methods),

Applied Math II: (Topics include complex analysis, Laplace and Fourier transforms, vector calculus, ordinary and partial differential equations and special functions of mathematical physics),

other classes I’ve already took or are proof based math classes at my school

@deltax2 You haven’t provided us much info. What type of engineering are you in? What courses specifically have you taken, and are any of those courses required/recommended for your major?

chemical engineering, ive taken calc 3, diff equations, linear algebra, and prob and stats 1. I’d prefer the class that would help me with ChE (doesn’t have to apply to degree).

Really it’s your choice; they could all be useful at some level in engineering. The probability class will be useful if you want to do modeling and reliability type work, and for statistics which is useful in general. The PDEs class will be useful for better understanding the fundamental equations behind engineering concepts, especially within the transport phenomena series which uses a lot of the differential equations you learn in that class. The other class seems like a survey of different higher-level math topics, which will give you a cursory understanding which is more than enough for most engineers but far less-than-rigorous by a mathematician’s standard. Which might not be a bad thing since it doesn’t sound like you really want to do proof-based math.

Pick one; they’re all useful but not strictly necessary, and if you plan to go to grad school you will probably have to learn all these topics sooner or later.