(Graduate) Math Courses
- Math 504/505/506—Algebra
- Groups, modules, rings, fields, Galois theory, representation theory, homological algebra, etc.
- Math 507/508/509—Algebraic Structures (notes on github: 508, 509)
- Advanced commutative algebra, Lie groups and algebras, and homological algebra.
- Math 534/535/536—Complex Analysis
- Complex variables, contour integration, conformal maps, harmonic functions, the Dirichlet problem, etc.
- Math 544/545/546—Topology and Geometry of Manifolds
- Topological and smooth manifolds, algebraic topology, covering space theory, differential geometry, etc.
- Math 561/562—Combinatorics
- Counting, posets, generating functions, inclusion/exclusion, graph theory, etc.
- Math 567/568/569—Algebraic Geometry (notes on github)
- Affine and projective varieties, rings of functions, the Nullstellensatz, localization, dimension, algebraic curves, divisors, cohomology, genus, and the Riemann-Roch theorem.
- Math 581B/582B—Algebraic Groups and their Representations (notes on github)
- Group schemes, Hopf algebras and representations; the Barsotti-Chevalley theorem, existence of quotients, descent, etc. Infinitesimal theory, the Borel fixed point theorem, parabolic subgroups, representations and highest weight theory.
- Math 582H—Hopf Algebras (notes on github)
- Hopf algebras, quantum groups, duality, actions, and representations of Hopf algebras and tensor and fusion categories.
- Math 583H—Cohomology Theories, Triangulated Categories, and Applications (notes on github)
- Hochschild cohomology, group cohomology, homotopy and derived categories, dualizing complexes, and Artin-Schelter regular algebras.
- Math 600—Directed Reading
- Group Schemes and Representations Autumn 2018-Winter 2020 (with Prof. Julia Pevtsova)
- Abelian Categories Spring 2018 (with Prof. James Zhang)
- Representation Theory Winter-Spring 2017 (with Prof. Julia Pevtsova)
- Algebraic Topology Autumn 2016 (with Prof. Steve Mitchell)
Computer Science Courses
- CSE 143x—Accelerated Computer Programming I/II
- CSE 373—Data Structures and Algorithms
- CSE 517—Natural Language Processing
- STAT 509—Introduction to Mathematical Statistics
Thanks to the following for their contributions to this site:
- Background: "What the Hex" - Angel Micevski
- Website fonts (unicode fonts based on Donald Knuth's Computer Modern font family) provided by Andrey V. Panov