A brief introduction to real analysis in one-variables, covering properties of real numbers, infinite series, uniform convergence, and power series.

Elementary topics in abstract linear algebra, including vector spaces and linear transformations, canonical forms of matrices, elementary divisors, invariant factors, and applications.

An introduction to the formal Theory of Computation, covering computability, complexity, the Church–Turing Thesis, undecidability, reducibility, completeness, and time/space complexity.

An introductory course to abstract algebra on the elementary theory of groups, rings, and fields. Content covers up to the construction of the algebraic closure.

A rigorous course based in Riemann integration on the convergence of Fourier series, Hilbert spaces, the Fourier transform on the real line, the inversion, Plancherel, and Poisson summation formula, and applications.