This course presupposes MATH 339 (Real and Functional Analysis) as the background and aims to give

students a solid foundation for further study in Pure and Applied Mathematics. Some topics are treated

with certain depth. We will study Lebesgue integration, positive Borel measures, and the all important

function spaces Lp. Then we will study the elementary Hilbert space theory and Banach space techniques.

We also plan to discuss bounded and unbounded linear operators together with their spectral properties.

Prerequisite: MATH339

Text books: Rudin Real and Complex Analysis (topics 1-5); Reed & Simon Functional Analysis (topic 6).