Algebra Qualifier Prep Seminar

The seminar will meet Thursdays, Noon-3pm in Skye 284 starting the week of July 29. The qualifying exam will Monday, September 23, 9am-Noon.

Aside from the seminar, my utility to you in studying for this exam is to have someone to direct your questions to, whether those are questions about algebra or about the exam itself. My email address is . If there’s an exercise you’d like to know how to do, of if you’d like someone to read over your solution to an exercise, or if you’d like guidance as to what you should study next, or if you need a shoulder to cry on or a drinking partner because you’re freaking out, just ask.

Exercises & Resources

The algebra qualifying exam is just another exam, so naturally it will consist of some finite list of algebra questions for you to respond to. And your responses to these questions will be the basis by which your worth as an algebraist will be judged. So, when studying for this exam, your time is best spent doing exercises and solving problems. Here are a bunch of good exercises and problems to focus on, and resources to help with that.

• Fundamental Exercises in Algebra — This is a list of those ubiquitous algebra exercises that pop up on many exams, and are in every algebra textbook. You should know how to answer all of these.
• Algebra Problems on Which to Chew — These have got a bit more meat than the fundamental ones.
• Mock Exams — As the seminar goes on, I’ll create some mock exams and post them here, along with solutions to the problems written by me or by other grad students where indicated. The earlier exams most closely resemble past exams from the committee members.

  One · Solutions       Two · Solutions       Three · Solutions       Four · Solutions

• Past UCR Algebra Qualifying Exams — This is the official list of past algebra qualifying exams posted to the department website. But here is a list of all the past qualifying exams up to 2018 annotated with the names of the test authors.
• Just Write it Down — The hardest part of responding to these questions is just writing it down. None of these require that you know a theorem or trick, but only that you verify an algebraic gadget has a desired structure.
• Notes on Modules & Linear Algebra — Notes, exercises, and solutions I typed up relevant to Part B of the qualifying exam.
• John Dusel’s Notes — Notes and exercise solutions that John Dusel wrote up when he ran the preparatory seminar. Email me for a copy of these.
• Kayla Murray’s Binder — A 283 page document of past exams, and Kayla Murray’s solutions to some of those exams. Here’s a few past exams that might be of particular interest:
  • Part A:   Greenstein 2015,   Chari 2011,   Greenstein 2010,   Greenstein 2008,   Chari 2005
  • Part B:   Chari 2016,   Greenstein 2011,   Chari 2010,   Gan 2009,   Gan 2008,   Chari 2006
  • Part C:   Gan 2015,   Chari 2012,   Chari 2007

Stuff from the Summer 2018 Seminar

• Here are the mock exams I made for the Summer 2018 seminar. The exam committee consisted of professors Rush, Greenstein, and Ran for parts A, B, and C respectively. The earlier exams most closely resemble past exams from these committee members.

  One           Two           Three           Four           Five

• Exercises to do in a Field — Solutions to some of Professor Ran’s Galois theory exams.
• Math201B 2017 — Documents from when Professor Greenstein taught 201B in 2017.
• Some relevant past qualifying exams of interest from Kayla Murray’s notes.
  • Part A:   Rush 2012   Greenstein 2010   Greenstein 2008   Rush 2007   Rush 2004
  • Part B:   Greenstein 2011   Greenstein 2007   Rush(?) 2004   Rush 2003   Rush 2001
  • Part C:   Ran 2008   Ran 2006 (#3 is false though)