Courses

An active introduction to limits, derivatives, and integrals, plus a preview of Taylor series.

Algebraic and analytic combinatorics — counting with matrices and power series.

Weekly training for the William Lowell Putnam Mathematical Competition: one technique per week, a short lecture, then problems.

Counting, graphs, recursion, and number theory — a first course in reading and writing mathematics.

Point-set topology. The schedule is a skeleton for now — one row per meeting, waiting to be filled in.

Limits, derivatives, integrals, and a first glimpse of Taylor series, taught from Active Calculus.

Fourier series and Hilbert spaces, with side trips to Weyl equidistribution and values of the Riemann zeta function.

Linear systems, vector spaces, bases and dimension, and the maps between them.

Lie groups and Lie algebras, vector fields, flows, and the Lie derivative.

Covering spaces, monodromy, the classification of coverings, and a first look at homology.

Topological spaces, manifolds, connectedness and compactness, and the fundamental group.