ANALYSIS I

MATH 522

Special functions, power series, Fourier series, approximation, contraction principle, characterizations of compactness in metric spaces, applications to differential equations. Differential calculus in normed spaces, including implicit and inverse function theorems. Course is essential for graduate work in mathematics.

MATH 721

Real analysis concentrating on measures, integration, and differentiation and including an introduction to Hilbert spaces. Knowledge of undergraduate analysis (e.g. the sequenceMATH 521and522) is strongly recommended.

MATH 921

Selected topics in Analysis.

MATH 725

Continuation ofMATH 721. An introduction to further topics in real analysis: Banach spaces, Fourier transforms, elements of distribution theory, and applications.

MATH 551

Topological spaces, connectedness, compactness, separation axioms, metric spaces.