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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...?

EDIT:

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.

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    $\begingroup$ What skills are you concerned about sharpening? $\endgroup$ – Don Thousand Dec 18 '18 at 21:13
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    $\begingroup$ 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
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    $\begingroup$ 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
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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?

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