Meets: MWF 11:15 to 12:20
in 004
Kemeny Hall

First Meeting: Monday, January 4, 2010

There will be no class on Friday, January 15th.

- A course in functional analysis by Conway
- Functional analysis by Rudin
- Real and complex analysis by Rudin
- Real analysis
by Folland

Please note that at this point, your work should be correct. Turning in work you don't believe in is inappropriate at this level. Of course, students do make conceptual mistakes from time to time. However, when you turn an assignment in, you are asserting that you believe that whatever parts of the problem you have attempted are correct and articulate.

- Homework #1: Due Monday, January 11th. [Corrected version posted 1/6/10.]
- Homework #2: Due Wednesday, January 20th. (Selected solutions: here.)
- Optional Assignment on Nets.
- From now on, homework should either be LaTeXed in 12 point type or handwritten on one side only of 8.5" x 11" paper with smooth edges. In the case of handwritten work, please start each problem on new page.
- Homework #3: Due Wednesday, February 3rd. (Selected solutions: here.)
- Here is a proof that a norm satisfying the parallelogram law is induced by an inner product. The result is often called the Jordan-von Neumann Theorem.
- Homework #4: Due Wednesday, February 17th. (Selected solutions here.)
- Some thoughts on taking an advanced graduate course. Everyone learns differently, so I don't tell students -- well graduate students anyway -- how to manage their courses. But I have noticed that a few of you don't take notes. I find this surprising. I am well aware that most of the time the course follows the book pretty closely. But I certainly say more than is in the book, and often I say it differently or expand on points that Pedersen skips over. But that is not the point. I find that taking notes really forces one to mentally process the material. Also, material at this level can't be absorbed in one sitting. When I took courses in graduate school, I not only took notes, but tried to find the time to sort though them and actually copy them over filling in the bits that puzzled me and sometimes even fixing bits that I will charitably say that I copied down incorrectly. I still have those notes and have referred back to some of them during my career. This process is even more important in an advanced course like Math 113 where I feel the emphasis should be on learning as much as you can and NOT just enough to do the homework. Going though your notes, filling in the gaps, and seeing if my "it is easy to see that''s are actually easy to see should be, in my opinion, as much a part of learning the material as doing the homework.
- Homework #5: Due Wednesday, March 3rd. (Selected solutions here.)
- Once we finish with the Spectral Theorem for normal compact operators, we'll be following sections 2-4 of my notes on the Abstract Spectral Theorem from my web page.
- Homework #6: Due Wednesday, March 10th (in my mailbox or via email if you have a pdf).