So, I can take 4 technical electives in my chemical engineering program, but one of them is pretty much required (so much for being an elective). I am interested in using at least one of the remaining on upper level math classes. The interesting options are: Partial differential equations (leaning towards this one, because of its supposed utility) Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks Introduction to analysis ii (I think i is Real analysis, which I guess is also an option, but it's for some reason not on my school's curriculum guide for elective options). Which is better if I had the option? Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem Numerical methods Solution of nonlinear equations in one variable. Interpolation, polynomial approximation, numerical integration/differentiation, numerical solution of initial-value problems. Probability and Statistics (theory) Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. Applied linear algebra Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. Which ones do you guys think I ought to take/not waste my time with? The two classes that most intrigue me are the first two. How crucial is it for a guy to know his probability and statistics? I give you the open-ended question: which of the above upper level math classes ought I to take as a chemical engineering major? (Keep in mind that I plan to use this degree to enter into a health-related field, which may or not influence your opinion on how rigorously I should strive to stay within the bounds of purely chemical engineering related courses). Would it be better for me to take more strictly chemical engineering courses if I were to enter into industry?