Course outline

Some facts and definitions

Proofs of some Lemmas

A proof of Hahn-Banach Theorem

Hahn-Banach Theorem in the complex case

Two more applications of the Hahn-Banach Theorem

A proof of Banach open mapping theorem

On Gram-Schmidt orthogonalization procedure

Fixed pointn theorems

Solutions of some exercises

Homework Assignments:

• Assignment 1, due September 18, 2009. Solutions.
• Assignment 2, due October 2, 2009. Solutions.
• Assignment 3, due October 16, 2009. Solutions.
• Assignment 4, due October 30, 2009.     Solutions.
• Assignment 5, due November 13, 2009. Solutions.
• Assignment 6, due November 27, 2009. Solutions.

MIDTERMS (OLD and RECENT)

Midterm 2006         Solutions.

Midterm 2007         Solutions.

Midterm 2009         Solutions.

Second Midterm 2009         Solutions.

Additional exercises