The course layout for the first two years consists of three courses in each core sequence in Algebra, Topology, and Analysis. The Analysis one consists of two semesters of Real Analysis (Measure & Integration) followed by one semester of Complex Analysis. In the second year the student adds intermediate-level courses.

Elective—or topics‐courses—are more advanced courses that are taken by students who have progressed past the first four semesters.

The course layout is:

= PhD qualifier course; =Intermediate level; = Elective course option

Four-semester grid:Course layout for the first two years.

1st Fall	1st Spring	2nd Fall	2nd Spring
Measure & Integration I	Measure & Integration II	Complex Analysis I	Functional Analysis or Fourier Analysis
GRV I	GRV II	GRV III	Algebraic Geometry or Number Theory
Topology I	Topology II	Topology IIIa* or Topology IIIb*	Differential Geometry or other Geometry/Topology course

*Topology IIIa (Algebraic Topology) and Topology IIIb (Differential Topology) are offered an alternate years.