School of Mathematics School of Mathematics
Course 321 - Modern Analysis 2002-03 (Optional JS & SS Mathematics, SS Two-subject Moderatorship )
Lecturer: Dr. D. P. O'Donovan
Requirements/prerequisites: 211/221

Duration: 21 weeks

Number of lectures per week: 3

Assessment: Regular assignments.

End-of-year Examination: One 3-hour examination


Measure theory
Measurable sets and functions, definitions and properties of the integral. Convergence theorems. Carathéodory extension theorem. Sigma measures, decompositions and the Radon-Nikodym theorem. Fubini theorem.

Banach Spaces
Bounded linear maps, finite dimensional spaces, quotient spaces, Hahn-Banach theorem, dual spaces, Riesz representation theorem, Stone-Weierstrass theorem, open mapping theorem, closed graph theorem.

Hilbert spaces
Orthonormal bases, orthogonal projection, self-adjoint and normal operators.

Apr 9, 2003

File translated from TEX by TTH, version 2.70.
On 9 Apr 2003, 18:18.