Mathematical prerequisites for beginning graduate student in robotics

Other answers are correct: It depends on where you are focusing, and what your topic will be. However, there are some common themes. I would say that a minor in mathematics from a decent university should cover the bases.

I would strongly recommend the following, based on my experience:

1. Linear Algebra, at least one or two semesters. Plan on taking refresher courses and specializing if necessary. Because robots operate in the world, and the world is defined by coordinate frames, knowing something about matrix multiplication, inverses, rank, affine and projective transformations, etc is extremely helpful.
2. Calculus, at least 3 semesters.
3. Some numerical analysis, because robots use computers.
4. Probabilities and Statistics, at least 1 semester, though this is becoming increasingly important

For my subfield (Algorithmic Robotics), the following things are very helpful:

1. Algorithms and Data Structures, at least 2 semesters
2. Formal Theory of Computation (Hardness and mappings of problems), at least one semester
3. Matrix Theory, (another semester of a specialized linear algebra)
4. Discrete Math (graphs, counting and enumueration), at least 1 semester,