Summer 2026 Analysis SEP Materials
materials for the analysis SEP at UW Madison.
The materials are listed in reverse-chronological order.
Week 1: Basic analysis—advanced calculus and topology
Recommended reading
This unfortunately covers a very large amount of material; supposedly, this portion of the qual is commensurate with what students learn in Math 521+522 (“an introductory sequence in analysis”). Andreas Seeger (who often is on the qual writing committee!) has compiled a helpful course outline for 521 and 522 which lists all the topics (allegedly) covered in this course sequence. There is also a complementary list of practice problems related to this material.
In terms of what to read: go through the course outlines and familiarize yourself with as much of it as you can. There are Math 522 notes written by Andreas Seeger and Joris Roos that are a helpful reference. I recommend taking a look at the notes and supplementing with a textbook.
For topology, Folland’s Real Analysis book technically covers most of the topics from point set topology (in chapter 4) that you need to know. An additional reference containing a ton of exercises is Munkre’s Topology book.
Worksheets
coming soon :~)