Course Archive
Notes
Course notes, proof writeups, implementation notes, and technical summaries from mathematics and computer science coursework.
Modern Algebra I
Abstract algebra through arithmetic and congruence in the integers, modular arithmetic, rings, polynomial rings, ideals, quotient rings, groups, normal subgroups, and quotient groups.
Modern Algebra II
More advanced abstract algebraic structures and concepts. Further study of group theory, including finite abelian groups and the Sylow theorems. Field extensions. Further applications of group theory, including Galois theory and geometric constructions. Arithmetic in integral domains. Additional topics such as public key cryptography or algebraic coding theory, as time permits groups.
Real Analysis
Metric spaces and continuity; differentiable and integrable functions of one variable; numerical sequences and series; and sequences and series of functions.
Introduction to Algebraic Geometry
Affine and projective varieties, regular and rational maps, Nullstellensatz, Veronese and Segre varieties, Grassmannians, algebraic groups, quadrics, smoothness, tangent spaces, singularities, and tangent cones.