Undergraduate honors analysis: sequences and series, continuity, differentiation, and the Riemann integral, with a focus on proofs and problem solving.

Discrete and continuous dynamical systems: fixed points, stability, bifurcations, and qualitative behavior of orbits.

Holomorphic functions, Cauchy theory, residues, and conformal mappings, based on the Math in Moscow complex analysis course.

Curves and surfaces, curvature, geodesics, and the geometric side of analysis on manifolds, together with associated exercise sessions.

Notes corresponding to a playlist on measure spaces, integration, and convergence theorems.

Problem reviews and solutions from Chapters 1–5 of Rudin’s Principles of Mathematical Analysis.