# Sources of Math Problems to Maintain One's “Chops”

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.

• What skills are you concerned about sharpening? – Don Thousand Dec 18 '18 at 21:13
• 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.) – timtfj Dec 18 '18 at 21:32
• 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. – Will R Dec 18 '18 at 22:16
• 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. – Matt Samuel Dec 19 '18 at 2:38
• Fixed that spelling blip. Thanks timtfj. – user3050028 Dec 20 '18 at 19:45