You must be enrolled in either the Department of Mathematics or the Department of Physics for this program. Basic preparation should include courses in advanced calculus, linear algebra, modern algebra, complex variables, classical mechanics, electromagnetism, quantum mechanics, modern physics, thermodynamics, and statistical mechanics. Knowledge of the following fields is desirable: real analysis, differential equations, probability, topology, differential geometry, and functional analysis.

(Some Master degree students are later admitted to the Ph.D. program based on a record of academic excellence.) at https://math.indiana.edu/student-portal/graduate/conditions-for-financial-support.html