Jacobson structure theory, density theorem, Jacobson radical, Maschke's theorem. Artinian rings, Artin-Wedderburn theorem, modules over semi-simple...
Lebesgue measure on the line, the Lebesgue integral, monotone and dominated convergence theorems, Lp-spaces: completeness and dense subspaces....
General measures, measurability, Caratheodory Extension theorem and construction of measures, integration theory, convergence theorems, Lp-spaces,...
Banach and Hilbert spaces, bounded linear maps, Hahn-Banach theorem, open mapping theorem, closed graph theorem, topologies, nets, Hausdorff spaces,...
An introduction to the geometry of algebraic curves with applications to elliptic curves and computational algebraic geometry. Plane curves, affine...
An introduction to differentiable manifolds. The tangent and cotangent bundles. Vector fields and differential forms. The Lie bracket and Lie...
Review of general topology, quotient spaces, scissors and glue constructions. Basics on homotopy and topological manifolds. The fundamental group....
Prereq: Not open to General Mathematics students
