Affine and projective varieties, coordinate rings and function fields, birational correspondences, sheaves, dimension theory, regularity. ...
Banach and Hilbert spaces, dual spaces, annihilators, Hahn-Banach theorem, Riesz representation theorems, bounded linear operators, adjoints, closed...
Review of differentiability in Euclidean space, inverse and implicit function theorems, integration in Euclidean space, Fubini's theorem, partitions...
Moebius transformations; local behavior of analytic functions, open and inverse mapping theorems; Schwarz's lemma; harmonic functions, solution of the...
Entire and meromorphic functions, infinite products, canonical products, the Weierstrass factorization and Mittag-Leffler theorems, the Hadamard...
Set theory: axioms, ordinal numbers, transfinite induction, cardinality, the axiom of choice. Foundations of mathematics: construction of the real...
Laplace transforms and their application to solving differential equations. Sturm-Liouville systems; eigenvalue problems, expansions, Fourier series,...
First order vector systems and nth order single equations; adjoint systems and boundary value problems; Green's functions and self adjoint eigenvalue...
Antirequisite(s): Prerequisite(s): Permission of the Department. Corequisite(s): Pre-or Corequisite(s): Extra Information: 3 lecture hours, 0.5...