Analysis Qual Solutions
compilation of solutions for the analysis qual at UW Madison
Before reading through solutions, I implore you to familiarize yourself with the following webpages.
- Guide for Topics for the Qualifying Exams : this outlines all the topics you can expect to see on the qualifying exam. The topics list for the analysis qual is pretty accurate, in my experience.
- Quals Study Strategies : General study recommendations for the qualifying exam.
- Mathematics Practice Exams : Repository of historical mathematics exams; scroll to the bottom for the past qualifying exams. Maintained by the Steenbock Library.
Everything you (objectively) need to know can be found on those pages.
On the exam itself, you need to be able to write complete—fully justified and coherent/comprehensible—solutions to six (6) of nine (9) given exercises. Here are some references to help you develop an idea of what that will look like.
I would like to emphasize that I do not recommend memorizing these solutions! Try a problem on your own first, and if you can’t figure it out, then take a glance at these to help you get started. However, keep yourself honest: how much did you rely on the solution? Did you just need something to help you get started, was there some clever little ‘trick’ that you weren’t aware of but helped you overcome an obstacle in the proof, or did you have to write your solution while reading through the entirety of someone else’s solution?
Others’ solutions and references
I have not verified the contents of these documents—as with anything, exercise caution and judgment! There may very well be typos, mistakes, etc., and some ‘solutions’ may only be very rough sketches (i.e., not a full argument/justification).
- Analysis SEP Notes by Jacob Denson and Max Bacharach. The document is long, but excels in breaking up the exam topics into digestible sections with a brief introduction followed by different exercises.
- Analysis SEP Materials by Sam Craig. I have not personally referenced these materials (sorry, they were written after I passed the qual!), though others have told me they are quite helpful.
- “Things to know for the analysis qual” by Allison Byars. A compilation of useful facts to know when preparing for the analysis qual. This is a great reference for getting started with writing your own flashcards/reference sheet.
- Random document about the analysis qual that the department provides. I have not read this. I’m including this in case this is a helpful reference for someone.
My solutions
:~) a work in progress