Topics in Number Theory

Despite the broad catalog blurb, this graduate course is really a focused dive into modular forms as a bridge between complex analysis and number theory, using the geometry of the modular group's action on the upper half-plane to extract arithmetic information. You'll work through fundamental domains, multiplier systems, and the valence formula, then apply Fourier expansions and theta functions to classical problems like partition identities and representations as sums of squares, with most of your time spent on weekly homework and an independent component. It sits at the entry point of a much larger landscape (L-functions, Galois representations, Iwasawa theory) that the catalog hints at, giving you the analytic toolkit needed before tackling automorphic forms or arithmetic geometry seriously.