Ways to study mathematics while commuting

I spend approximately 3 to 4 hours on public transport everyday. I try to maximize the usage of this time by checking email etc on my phone. Are there any tips to study mathematics while commuting? Thanks for sharing! Just want to make full use of the time spent commuting!

When going to uni I would spend 5 hours on a train every day. I would use that time to solve lots of problems, individual ones, such as the ones found at the end of each chapter in the book. Studying concepts while commuting is too hard as the train is too distracting an environment. So I would just do problems after problems on the train, and save the studying of the concepts themselves for another time.

I used to do a similar commute—a 10-minute drive to the local parking garage, a 65-minute train ride to New York City, and a 25-minute subway ride to my office—then in reverse, every weekday.

These are general techniques not specific to studying math (but it could be that such general techniques may have more of an impact than ones specific to studying math):

1. Always have at least 3 similarly-challenging things you could do.

   For example,

   • reading Baby Rudin,

   • a real-life problem to wonder about (as @fromGiants suggested), like, "What's the actual value of walking faster to catch a train, given that trains arrive at discrete intervals?"

   • and an unsolved (or formerly unsolved) problem in math.

   I read about a PhD student who, for months, struggled to lift even a finger toward his thesis. In the meanwhile, he embarked on other projects—learning languages, freelance web design, and so on. ("I'm not procrastinating; I'm being productive!") However these new projects didn't turn out to be as glorious as he first imagined, and to his advantage! Because suddenly, he found himself working on his thesis, and gladly. It was simply more rewarding to work on his thesis, than to redesign the navigation bar for the 3rd time on his fickle client's website.

   In the same vein, whenever I can't fall asleep, I think about how I'm going to get out of bed, log into my work computer, and get a head start on tomorrow's work... I usually fall asleep instantly.

   So by "similarly-challenging" I actually mean "similarly-demotivating-at-some-point" so that, hopefully, 2 options will always demotivate you toward gladly working on the other :-)

2. Set easy-peasy goals.

   If you have a natural enthusiasm for something, then 99% of the time (yes, a made-up statistic), it's not the doing of it that's the problem, but the starting of it.

   Set goals like

   • get through 2 pages of Baby Rudin,

   • make one minor breakthrough regarding the train intervals problem,

   • and briefly describe one potential strategy or starting place for this unsolved problem.

   Aim to achieve that and no more, and most of the time, your enthusiasm will carry you further. On days your enthusiasm brings you nowhere, your body's trying to tell you something. Maybe you need more sleep—so nap, if you can. Maybe some emotional burden is holding you down—so space out and meditate on it, if you can.

   A long commute is seldom realized for the luxury that it is.

I'm not going to make up a third item just to have three items—at the moment these are the two most important techniques I can think of. Besides, I'm here because I don't want to be doing what I'm supposed to be doing ;-) I'd better get back to work.