I got partway through a graduate degree in math and I'm now doing something "completely different," but it bothers me that my skills are fading away. I don't have a lot of time, but I would like to devote 15 - 30 minutes a day to working on a problem, or some problems.

I'm curious where you'd look for problems if you were in a similar situation...

Here are some ideas to get started:

  • Martin Gardner books
  • Project Euler (but do the problems without computers)
  • Measurement by Paul Lockhart

I wonder about textbooks. It's hard to push oneself through textbooks outside of a class, peers, deadlines. Maybe there are some which would be friendlier than others in this regard...?


The 15 - 30 minutes thing is a bit arbitrary. I'm just saying I can't count on having lots of time to spend. I started reading Munkres's Topology again, and Gleason's analysis book, intending to take my time, do most of the exercises, etc..

I suppose there aren't any specific skills I'm most interested in maintaining, but I was just looking to see if you had some ideas for ways to keep my head in the game.

  • 1
    $\begingroup$ What skills are you concerned about sharpening? $\endgroup$ – Don Thousand Dec 18 '18 at 21:13
  • 4
    $\begingroup$ I think Marvin is actually called Martin! (I can't make a 1-character edit to correct it, but as the post author you can.) $\endgroup$ – timtfj Dec 18 '18 at 21:32
  • 1
    $\begingroup$ I do not make a habit of Project Euler problems, but I would not recommend trying to really answer them without a computer. The problems are designed with programming in mind; they are meant to be such that even getting a computer to do it requires ingenuity. So they are presumably designed to require huge computations; definitely not a 15-30 minute thing! That said, if you wanted to then you could try to think about what the best algorithm would be; but then imo you might as well implement it to make sure it works the way you want it to. $\endgroup$ – Will R Dec 18 '18 at 22:16
  • $\begingroup$ So similarly I studied math and now I am doing something that does not at all use my studies, though I did get the PhD. I use this site. It seems that when school is out, good problems are few and far between, but during the fall and spring semesters there's lots to do. I also still do my research as a hobby, with no plans of publishing unless I hit the jackpot. $\endgroup$ – Matt Samuel Dec 19 '18 at 2:38
  • $\begingroup$ Fixed that spelling blip. Thanks timtfj. $\endgroup$ – user3050028 Dec 20 '18 at 19:45

I find that training problems for mathematical competitions are a good exercise to keep your mind sharp. For example there are

An exercise-rich textbook is Atiyah's & McDonalds Commutative Algebra. Depending on your background their exercises might be challenging or the daily 10-15min exercise for you.

P.S.: I have been actively collecting problems involving a "trick" for a couple of years and am sure others have done so as well. Maybe you will find some of these by a google search?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.