Here is a very condensed list of a list that I got somewhere. Can't remember where, but I have condensed....
Programming Experience:
C++ Programming and use of computers as a computational and management tool
Quantitative Background:
Calculus – intro to differential and integral calc with transcendental functions; Techniques and application of integration; Infinite sequences and series; First and second order differential equations; Oscillation and damping; Series solutions of ODE’s.
Multivariate Calc – Parametric equations and polar coordinates; 2 and 3D Euclidean space vectors; Partial Derivatives; Multiple integrals, Vector Calc, Theorems of Green/Gauss/Stokes
Linear Algebra and Diff EQ’s – Basic linear algebra, vector spaces, eigenvalues and eigenvectors, linear transformations, determinants, quadratic forms and Rayleigh’s principle. Jordan canonical forms, application of linear algebra.
Partial Differential Equations – second order diff eq’s, elliptic and parabolic equations, solving IVP’s for hyperbolic equations, existence and uniqueness theorems, Fourier transform…
Statistics – Everything that you learn in the basic stats classes… hypothesis testing, descriptive statistics, test of significance, controlled experiments vs observational studies, correlation, and regression analysis.
Advanced Stats – Intro to theory of probability; random variables and distributions; central limit theorem; applications of statistics; multivariate distributions and use of computer applications.
Probability – application of probability. Discrete and continuous variables. Central limit theorem. Poisson process, Markov chains and characteristic functions..
Concepts of Stats – In depth study of stat theory and methodology. Descriptive stats, max likelihood estimation, G.O.F. tests, analysis of variance and least squares regression estimation. All of this with an emphasis of computer based applications.
Numerical Analysis – Programming for numerical calculations, round off errors, approximation and interpolation and solutions of ODE’s. Again, with emphasis on use of computer applications.