To provide students with a strong foundation in functional analysis, focusing on spaces and operators, fundamental theorems; to strengthen students understanding of this theory through applications of functional analysis; to develop students skills and confidence in mathematical analysis and proof techniques.

This first course in functional analysis will focus on:

• spaces and their operators
• metric spaces and metrics (Chapter 1)
• vector, normed and Banach spaces, and norms and linear operators (Chapter 2)
• inner product and Hilbert spaces, and inner products (Chapter 3)
• fundamental theorems (Chapter 4)
• applications (Chapter 5 and 6, plus extra examples throughout the semester)

There will be a significant component of the class the comes from daily homework assignments and longer take home assignments, as well as tests.