Algebra Qualifying Exam
Here is some assorted material related to the Algebra Qualifying Exam. This page has been created by graduate students, so, as always, you should consult the official graduate program page for official information. The list of exam topics can be found here.
Summer 2025 SEP
Below are the notes and worksheets that will be used during the Summer 2025 SEP, run by Caroline Nunn (cnunn@wisc.edu) and Ivan Aidun (aidun@wisc.edu).
Schedule
July 15: Jordan Normal Form (Worksheet, Solutions, Cheat Sheet)
July 17: Exact Sequences (Worksheet, Cheat Sheet)
July 22: Localization and projective modules (Worksheet, Solutions, Modules Cheat Sheet, Localization Cheat Sheet)
July 24: Tensor products (Worksheet, Solutions, Cheat Sheet)
July 28: Field theory (Worksheet)
July 31: Galois theory (Worksheet, Cheat Sheet)
Resources
List of topics covered on exam
Online repository of past exams
Write-up of past qual problems: Problems, Solutions
Ivan's full 2024 notes in one document
Evan Dummit's notes: Linear Algebra, Rings and Modules, Group Theory, Field and Galois Theory
Summer 2024 SEP
Below are the notes that were be used during the Summer 2024 SEP, run by Ivan Aidun.
Ivan's study guides:
Summer 2023 SEP
Below are the notes, worksheets, and solutions that were used during the Summer 2023 SEP, run by Owen Goff and Ivan Aidun.
Schedule
5 Weeks: July 18 - August 17
Meetings on Tuesdays and Thursdays 10:15am-12:30pm in VV B203.
Week 1 - Linear algebra: Notes, July 18 (Worksheet and Solutions), July 20 (Worksheet and Solutions)
Week 2 - Groups: Notes and Ivan's notes about some uncommon but important group constructions, July 25 (Worksheet and Solutions), July 27 (Worksheet and Solutions)
Week 3 - Fields: Notes, August 1 (Worksheet and Solutions), August 3 (Worksheet and Solutions)
Week 4 - Rings & Modules: Notes, August 8 (Worksheet and Solutions), August 10 (Worksheet and Solutions)
Week 5 - Misc./Review: August 15 (Worksheet and Solutions), August 17 (Worksheet and Solutions)
Summer 2022 SEP
Below are the notes, worksheets, and solutions that were used during the Summer 2022 SEP, run by Caitlyn Booms and Ivan Aidun.
Schedule
5 Weeks: July 19 - August 18
Meetings on Tuesdays and Thursdays at 9:45am-12pm in VV B333.
Week 1 - Linear Algebra: Notes, July 19 (Worksheet and Solutions), July 21 (Worksheet and Solutions)
Week 2 - Fields: Notes, July 26 (Worksheet and Solutions), July 28 (Worksheet and Solutions)
Week 3 - Rings & Modules: Notes, August 2 (Worksheet and Solutions), August 4 (Worksheet and Solutions)
Week 4 - Groups: Notes, August 9 (Worksheet and Solutions), August 11 (Worksheet and Solutions)
Week 5 Misc./Review: August 16 (Worksheet and Solutions), August 18 (Worksheet and Solutions)
Past Qualifying Exams
- Summer 2019
- Winter 2019
- Summer 2018 ( Solutions)
- Winter 2018 ( Solutions)
- Summer 2017 ( Solutions)
- Winter 2017 ( Solutions)
- Summer 2016
- Winter 2016
- Summer 2015
- Winter 2015
- Summer 2014
- Winter 2014
- Pre-2014 exams are available here
SEP Notes
https://kb.wisc.edu/math/internal/122251 is the new repository for any SEP content from previous semesters.