Abstract Nonsense

Crushing one theorem at a time

Qualifying Exams

Having most of my friends being in graduate school, I am exposed to quals a lot. In particular, in helping them study I have found myself taking a lot of quals. Considering I write most of the quals down, I thought it would be useful to put them here on my blog for anyone interested.

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Please feel free to contact with me comments, questions, or corrections.

Maryland Quals

Considering that I am at UMD, it makes sense these would be the one’s I’d do first. That said, I haven’t been doing them long and so, as of now, I have roughly a sixth (by total problems) of the UMD Algebra quals. I shall periodically update the algebra ones as I progress through them (I’m jumping around, but mostly drying to do group theory, then linear algebra, then ring theory, then module theory, then representation theory). You’ll note that some of the problems I have started but not finished. Don’t worry, I probably was interrupted, got bored, or got stuck. I’ll complete them eventually.

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Maryland Algebra Quals (Last Updated: 5/12/2012)



  1. Hi Alex, I’m very interested in your blog. I wanted to ask a word of advice. I am 24 and at community college and currently in Calculus 2, Physics 1, and CS 1. Could you share any insights on the relationship between age and learning math? I want to transfer as a Math major, but I know that lots of students started university level education sooner than I did, and will already have taken classes like Real Analysis and Abstract Algebra in their Freshman/Sophomore years. I will be Junior and will have only finished Calculus 1, 2, 3, Linear Algebra, Discrete Math, and Differential Equations. Will I still be able to get in to grad school for math? Will I have time to learn what I need to learn to be prepared? Thanks!

    Comment by Ben | June 5, 2012 | Reply

    • Dear Ben,

      I’m glad that you like my blog! There’s always a debate about whether age is an important factor in one’s math career. I have encountered many older grad students/undegrads who have (for some reason or another) convinced themselves that being X years old means you can’t do math. In general I really disagree with this. Theoretically I don’t think you’re ever too old to learn math. The only real issue is a practical one. People who are older tend to be more focused on non-academia things (a family, paying off a mortgage, etc.) and do not always want to have to deal with the rigmarole that is grad school. If you don’t think that this is going to be an issue for you then, by all means, go for it!

      This all said, I am probably not the best person to ask–you should consider e-mailing/meeting your advisor to discuss this in full.

      I hope that everything works out for you!


      Comment by Alex Youcis | June 10, 2012 | Reply

    • Dear Ben,

      I am currently a Master’s student. I know another Master’s student in my program is 35, which makes him one year older than our algebra instructor. Also, I once went to an Number Theory conference where I met a Ph.D. student preparing to graduate who start math at the College Algebra level after finishing 4+ years in the military. Based on this, I think you will be perfectly capable of succeeding in graduate level mathematics. Just focus on learning as much math as possible.

      Comment by William | September 25, 2012 | Reply

      • Thanks for your response, this was definitely reassuring!

        Comment by leapingleibniz | October 5, 2012

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