Analysis SEP Materials
Worksheets
Click the title for a pdf copy of the worksheet / materials for that day. Solutions will be provided to registered participants. (to be posted online at a later time.)| Day | Date | Topic |
| 1 | Monday, July 13 | Advanced calculus (part I) |
| 2 | Tuesday, July 14 | Advanced calculus (part II) |
| 3 | Wednesday, July 15 | The Arzela-Ascoli Theorem |
| 4 | Friday, July 16 | The Banach Fixed Point Theorem + Contraction Mapping Theorem Quiz |
| 5 | Thursday, July 23 | Topology |
| 6 | Friday, July 24 | Measure Theory (part I) |
| 7 | Monday, July 27 | Measure Theory (part II) |
| 8 | Wednesday, July 29 | Modes of Convergence |
| 9 | Friday, July 31 | $L^p$ spaces |
| 10 | Monday, August 3 | The Lebesgue Differentiation Theorem |
| 11 | Wednesday, August 5 | Basic Functional Analysis / Complex Integration |
| 12 | Friday, August 7 | Distribution Theory (part I) / Cauchy Theory |
| 13 | Monday, August 10 | Fourier Analysis / Singularities and Residues |
| 14 | Wednesday, August 12 | Distribution Theory (part II) / Conformal Geometry |
| 15 | Friday, August 14 | Sobolev Spaces / Harmonic and Global Theory |
Additional References for the Qualifying Exam
These are some resources that I am aware of for the qual. If you find other resources, please do not hestitate to let me know so I can add them to this list!
- Math 522 Notes by Joris Roos and Andreas Seeger - notes for Math 522 written by Joris Roos and Andreas Seeger. Andreas is frequently on the analysis qual writing committee. Many people, including yours truly :'(, are coming from backgrounds that did not necessarily cover all the topics which are taught in the undergraduate sequence here at UW Madison. In addition to the textbooks recommended on the qual study topics webpage, this is a great quick reference for most of the content in the "basic analysis" portion of the qual.
- Analysis SEP Course Notes (2021-2022) by Jacob Denson and Max Hill - I referenced these frequently when I was studying for the qualifying exam. They do a great job of breaking down several of the recurring topics on the real analysis exam and providing solutions to several common qualifying exam questions. Good reference for additional problems' solutions and alternative solutions to those that I provide.
- 2024 Analysis SEP Material by Sam Craig - I admittedly have not looked through these solutions thoroughly, but we will be following a similar schedule as outlined here. Feel free to reference these for solutions to more problems or alternative solutions to mine.