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 that will be used during the Summer 2025 SEP, run by Caroline Nunn (cnunn@wisc.edu) and Ivan Aidun (aidun@wisc.edu).

List of topics covered on exam

Online repository of past exams

Write-up of past qual problems: Problems, Solutions

July 15: Jordan Normal Form (Worksheet, Solutions, Cheat Sheet)

Summer 2024 SEP

Below are the notes that were be used during the Summer 2024 SEP, run by Ivan Aidun.

Ivan's study guides:

Basic Linear Algebra

Advanced Linear Algebra

Ring Theory 1

Ring Theory 2

Module Theory 1

Module Theory 2

Module Theory 3

Group Theory 1

Group Theory 2: Group Actions

Group Theory 3

Fields and Galois Theory

Evan Dummit's notes: Linear Algebra, Rings and Modules, Group Theory, Field and Galois Theory

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.