Qualifying Exams Material

This repository of study aids for the mathematics qualifying exams is, or the most part, a work-in-progress (that is seldom progressing). You are welcome to browse around and take an online look at things, but keep in mind that many items are unfinished, and some exercise solutions contain mistakes.


Product measures and the Fubini theorem

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:

DVI15K
PS95K

Relationship between function properties

Summary of relationships between various properties of functions (like differentiable, Lipshitz, bounded variation, etc.):

DVI3K
PS40K

Solutions to old qualifier problems

This unfinished material is online solely for the benefit of students studying for the exams. There are likely mistakes. These documents are not ready for distribution. Just because it is typeset nicely does not mean it is of high quality.

Algebra:

DVI232K
PS627K

Analysis:

DVI173K
PS535K

Geometry/Topology:

DVI204K
PS641K

Miscellaneous notes

This unfinished material is online solely for the benefit of students studying for the exams. There are likely mistakes. These documents are not ready for distribution. Just because it is typeset nicely does not mean it is of high quality.

Some basic facts on modules (written back when I barely knew what a module is):

DVI20K
PS112K

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:

DVI50K
PS237K

Some notes on calculating residues of complex functions, and some exercises on solving indefinite real integrals via complex analysis.

DVI16K
PS90K