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:
15K
95KRelationship between function properties
Summary of relationships between various properties of functions (like differentiable, Lipshitz, bounded variation, etc.):
3K40KSolutions 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:
232K627KAnalysis:
173K535KGeometry/Topology:
204K641KMiscellaneous 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):
20K112KSome 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:
50K237KSome notes on calculating residues of complex functions, and some exercises on solving indefinite real integrals via complex analysis.
16K90K