Math 175: Elementary functional analysis

Course Info

Office hours	Mon 3:15--4:10 and Friday 11:00--12:00 in 382F, or by appointment. (Fridays office hours are shared with my 103 course) Note: Should course enrollment exceed 25, then we will have a grader in addition to a course assistant. This means you get about six extra office hours! (If this is something you want anyway, send me an email).
Email list	math175-win0607-students or math175-win0607-guests All registered students should be automatically subscribed to the students list. If you're auditing (or are not subscribed by error), then subscribe yourself to the guests list. Any email announce made by me will be made to both the above lists.
Midterm	You will have a take home midterm due in class on Friday 5^th week. The midterm will be posted online (here) exactly 24 hours before black Friday's class. To compensate, your homework due in 5th week will be marginally shorter than usual.
Final	Take home (due sometime in finals week).

Grading and other policies

Grading Your final grade will be the average of your homework, midterm and final with the midterm counting as 30%, final 50% and your homework 20%.

Homework Homework will be assigned every week on Wednesday, and due in class on the following Wednesday at the beginning of class. Late homework will NEVER be accepted. However to accommodate for unusual circumstances (e.g. too much beer), one homework will not count towards your grade. Working in groups is encouraged, but blindly copying will certainly guarantee miserable performance on all exams.

Extra credit There is NONE! Homework problems marked with a * are optional. Do NOT turn them in, as you will receive no credit for them. Homework problems marked with two stars (**) are 'interesting' challenge problems. If you manage solving these, come show it to me. Do not turn these in with regular homework. Three star problems are Ph. D. Thesis material. Remember that these problems are worth no extra credit. They're only there for betterment of your soul.

Homework Assignments

Note If you download the tex sources, you also need the calculus.sty style file.

Assignment 1 (Assigned Fri 04/06, Due Wed 04/11): pdf tex
Assignment 2 (Assigned Wed 04/11, Due Wed 04/18): pdf tex
Assignment 3 (Assigned Wed 04/18, Due Wed 04/25): pdf tex
Assignment 4 (Assigned Wed 04/25, Due Wed 04/02): pdf tex
Assignment 5 (Assigned Fri 05/04, Due Wed 05/09): pdf tex
Assignment 6 (Assigned Wed 05/09, Due Wed 05/16): pdf tex
Assignment 7 (Assigned Wed 05/16, Due Wed 05/23): pdf tex
Assignment 7 (Assigned Wed 05/23, Due Wed 05/30): pdf tex
Assignment 7 (Assigned Wed 05/30, Due Wed 06/06): pdf tex

Handouts

Equivalence of norms on finite dimensional spaces pdf tex
A few solutions. pdf tex
A short proof showing the unit ball in C^\beta is compact in C^\alpha. pdf tex

Solutions

I've created a directory in /afs/ir.stanford.edu/class/math103/WWW/solutions which is writable by all students. Since some of you type your solutions, it would greatly help your fellow students if you used this directory to upload your solutions. Upload both your tex sources and solutions, so that others can modify your solutions if needed.

You can browse the contents of this directory online here, but will have to mount the above directory (via AFS) to upload files to it. See the online help about Stanford's AFS if you don't know how.

References

I will not use a "textbook" per say. Here are a few references you might find helpful (listed in approximate order of difficulty).

N. Young An Introduction to Hilbert Space. (This should be the correct level for this class).
W. Rudin Real and Complex Analysis. (The first few chapters have a rapid, terse treatment of Hilbert spaces)
K. Yosida Functional Analysis. (Graduate level)
W. Rudin Functional Analysis. (Graduate level)

If you don't know the Spectral theorem, then read enough of any of the following so that you understand the theorem and proof.

Hoffman and Kunze Linear Algebra.
Sheldon Axler Linear Algebra done right.

If you don't know the Bolzano-Weierstrass theorem, then read enough of any of the following so that you understand the theorem and proof.

W. Rudin Principles of Modern Analysis
Apostol Analysis
Simmons Topology and Modern Analysis
E. T. Copson Metric Spaces

Feedback

Feedback at any time (either anonymous or signed) is always appreciated. You can use this form to send me (or your course assistant) anonymous (or signed) feedback. [Note: Evil spammers have been using this form to clutter my inbox. Thus I have restricted access to this form to within stanford.edu domain.]

Questions? Comments? Send me hate mail? gautam@math.stanford.edu.

"I'm sorry I couldn't turn in my homework. I was watching the world series and got tied up proving it's absolute convergence."

Last modified: Thu 31 May 2007 12:06:20 AM PDT