(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

Statistics Courses

  • STAT 509—Introduction to Mathematical Statistics