Yuval's Notes

Lecture notes from some courses I've taken over the years. Feel free to reach out if you find a typo (big or small).

Fall 2026 (In Progress)

MATH730: Algebraic Topology I CW complexes; fundamental group; covering spaces; simplicial, singular, and cellular homology. Instructor: Or Hershkovitz Book: Algebraic Topology, Hatcher
MATH606: Complex Algebraic Geometry Riemann surfaces; elliptic functions; the Riemann surface of an algebraic function; Čech cohomology; vector bundles; divisors; Riemann–Roch; Serre duality. Instructor: Harry Tamvakis Book: Compact Riemann Surfaces, Narasimhan
STAT410: Intro to Probability Theory Basic facts about σ-algebras and probability measures; conditional probability; random variables; expectation; central limit theorem; law of large numbers. Instructor: Mestiyage D. Gunatilleka Book: Intro to Probability, Anderson

MATH601: Abstract Algebra II Exterior powers; FGMs over PIDs; bilinear forms; categories; Yoneda's lemma; projective, injective, and flat modules; homological algebra; Ext and Tor; Galois theory; solvability by radicals; representations; Schur's lemma; character tables and orthogonality relations; Burnside's theorem; additional topics in rep. theory. Instructor: Harry Tamvakis Book: Abstract Algebra, Dummit and Foote

MATH600: Abstract Algebra I Vector spaces; universal properties; groups; the class equation; Sylow theorems; finite simple groups; semidirect products; free and Coxeter groups; rings; various types of domains; CRT; Noetherian rings; classical algebraic geometry; Nullstellensatz; ideal-variety correspondence; modules and algebras; tensor products; tensor and symmetric algebras Instructor: Harry Tamvakis Book: Abstract Algebra, Dummit and Foote
MATH407: Advanced Number Theory Finite fields; Chevalley-Warning; quadratic reciprocity; p-adic numbers; Hensel's lemma; the Hilbert symbol; characters; Dirichlet's theorem Instructor: Niranjan Ramachandran Book: A Course in Arithmetic, Serre