I am just curious to know as to what are the course requirements to get a PhD in Mathematics. Is there is a standard set of courses required or does it vary according to the university? Also, does it matter if it is pure math or applied math? I simply googled and found that there is a list of courses that is listed as the requirement for Caltech. Kindly let me know if this list changes for other universities. a. Logic, Set theory, Calculus, Analysis, Measure theory, Measure theoretic probability b. Algebra (including Linear algebra), Representation theory c. Topology, Algebraic topology, Geometric Topology d. Linear differential equations, Partial differential equations, Non-linear differential equations e. Number theory, Combinatorics, Computability and Complexity Algebra, Analysis and Topology were considered as mandatory courses and the rest were like electives. 9 of the above on top of the mandatory courses are required.