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 syllabus can be found here.

Summer 2022 SEP

Below are the notes, worksheets, and solutions that will be used during the Summer 2022 SEP, run by Caitlyn Booms (cbooms@wisc.edu) and Ivan Aidun (aidun@wisc.edu).

List of topics covered on exam

Online repository of past exams

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, there is also a file with 1991-2013 quals on Atrium.

Guillermo Mantilla's SEP Notes

https://kb.wisc.edu/math/internal/122251 is the new repository for any SEP content from previous semesters.

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In the summers of 2008, 2009, 2010 Guillermo Mantilla ran a well-regarded summer enchancement program in algebra preparing for the qualifying examination. Guillermo wrote up a set of notes covering the material that appears on the qualifying exam. Links appear in the order presented in class, not the order of the respective problems on the exam.

Note: the links below are broken. The files themselves are available on Atrium, there are also 2016 SEP notes by Eric Ramos.

• Linear Algebra
  • Linear Algebra I
  • Linear Algebra II (inner products)
  • Linear Algebra III (Jordan Form)

• Group Theory
  • Group Theory I
  • Group Theory II (group actions)
  • Solvable & Nilpotent Groups
  • Theorems for non-simplicity
    • Non-simplicity proofs for groups of order < 1000

• Field Theory
  • Field Theory I
  • Field Theory II

• Ring Theory
  • Modules
  • Commutative Rings