At least the following:
-- Probability Theory Course
-- Stats Course (basic decision theory, parameter estimation, moment generating functions, sampling, etc.)
-- A rigorous linear algebra course (at should get through SVD at the very minimum, and hopefully to some other factorizations like QR and Cholesky)
-- Real Analysis with some basic topology mixed in (hopefully covering a touch of Lesbesgue integration if possible)
Also, I'd learn a vector-based programming language (i.e., Matlab) and know generally how to program well, as well as learning some basic data structures and search algorithms, etc. Courses beyond the above that probably every PhD applicant has:
-- Stochastic Processes
-- One other stats class: Theoretical Stats (Decision and Estimation), Analysis of Variance, Time Series.