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.

Guillermo Mantilla's SEP Notes

In the summers of 2007?, 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.

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

• Ring Theory
  • Commutative Rings
  • Modules

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

• Field Theory
  • Field Theory I
  • Field Theory II