For almost all areas of math, we want to see real analysis (epsilon-delta proofs, compact sets, Cauchy sequences, etc.) and a theoretical linear algebra course (not just row operations on matrices; there should be linear independence, diagonalization theorems, minimal polynomials). For pure math, a good course in abstract algebra is recommended. For more applied areas, some partial differential equations or complex analysis is good. Generally, the more math, the better. If you are at a school that offers grad courses, then taking a grad course (and doing well) increases your chances. If your school doesn't offer grad courses, then take as many upper-level courses as possible.

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All of our accepted students (except a few who are supported by employers) are offered support by the University, usually in the form of a Teaching Assistantship.