Qualifying Exams Material
This repository is, for the most part, a work-in-progress. You are welcome to browse around and take an online look at things---but I ask that you heed my demands below about what may be distributed in the form of a printout.
Shorties but Goodies:
[Feel free to make a printout!]
Some notes on product measure and the Fubini theorem, and how to understand the different versions of this theorem presented by various books and teachers:
- productMeasureFubini.dvi (size:) [landscape page orientation]
- productMeasureFubini.ps (size:) [landscape page orientation]
Summary of relationships between various properties of functions (like differentiable, Lipshitz, bounded variation, etc.):
The remaining material below is unfinished and in flux; it is being placed online at this time solely for the benefit of students studying for the exams. These documents are not ready for distribution.
There is way too much stuff here to be read from front to back. You might want to take a quick look right now, perhaps skim through the notes on various topics---that way you'll know, for future reference, what is available. Then maybe, during some pre-exam panic, you might restore your sanity by looking up some solution appearing here. (Admittedly, many solutions are missing, and some are incorrect.) Please do not blindly trust any material that appears here, as I find (and correct!) mistakes in these documents from time to time. (Send me corrections, and I'll include them.)
Solutions to old qualifier problems:
[Please don't distribute printouts! (See above.)]
Algebra:
Analysis:
Geometry/Topology:
Miscellaneous notes:
[Please don't distribute printouts! (See above.)]
Some basic facts on modules (written back when I barely knew what a module is):
Some notes on complex analysis organized around the Churchill/Brown book; mostly has additional comments section-by-section, or summarizes the important points from a particular section:
Some notes on calculating residues of complex functions, and some exercises on solving indefinite real integrals via complex analysis.
People sometimes wonder why I am paranoid about printouts of unfinished work making the rounds. Have you ever had an idea for how to solve a problem, perhaps written the idea down, been willing to show your solution to a friend, yet considered it too rough to turn in to a professor? The stuff here might look nice because it is typeset and all, but really it is quite rough!