The preparatory course for the Algebra Qualifying Exam will treat, among others, linear and multilinear algebra, group theory, rings and modules, category theory, field theory, and Galois theory. The primary goal for this course is to work through old qualifying exams, and to see as many fully solved problems as possible. The prerequisites required for this course are graduate Algebra I and Algebra II.

The course will have weekly classes on

• Tuesdays and Thursdays in Zoom Meeting 937 1949 6348, from 2:15 to 5:45 pm.

The recommended reference books are Algebra by Thomas W. Hungerford and Algebra by Larry C. Grove. We will be covering the material required by the Syllabus.

The participants are expected to completely work through the material to be covered in class beforehand. The participants are expected to share their progress, even if their solutions are not perfect nor complete. Multiple solutions to the same problem, as well as suggestions and ideas on how to tackle problems, are welcome.

Here are some materials that are helpful for this course:

• The solutions to many of the old algebra qualifying exams organized by subject are:
  • Finite and simple groups,
  • Group theory,
  • Ring theory,
  • Modules,
  • General Galois theory,
  • More Galois theory,
  • Linear algebra,
  • Tensor products,
  • Finite fields and random problems.
  These were typed up by Alexander Ruys de Perez.
• Some general advice on qualifying exams, as well as a set of notes for the algebra qualifying exam, can be found here. This was made by Kari Eifler.
• Many expository papers about results of interest for the qualifying exam can be found here. This was made by Keith Conrad.
• Four standard tricks to show that a group is not simple can be found here. This was made by Tai-Danae Bradley.
• An isomorphism between a module and its direct sum can be found here. This was correspondence between Matt Papanikolas and Pablo Ocal.
• A solution to Problem 7 of the January 2014 exam can be found here. This was made by Erik Davis.

Please keep in mind that you will only learn how to do the exercises if you try them on your own: without trying, looking up the solutions is absolutely useless.

The instructor would like to thank Erik Davis for the solution to Problem 7 of the January 2014 exam, and Jordy Lopez for invaluable help with note-taking during technical difficulties.