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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!

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Switch off that phone. Grab your book and/or notepad. Start thinking... – Jyrki Lahtonen Jun 27 '14 at 7:29
You can also watch (downloaded) video lectures on a tablet or laptop, and the headphones will even shut out distracting conversation, if any (unlike when you're reading a book). I do this while travelling, and even walking. – M. Vinay Jun 27 '14 at 8:56
3-4 hours of math a day should be enough to learn enough to earn a bachelor's in 4-5 years, depending on whether you have a table available in the train (at least I can't properly study without a table to work on) and whether the environment distracts you little enough. I personally need to have stuff in front of me in pretty print, so I'd go for either picking up a really good book on a topic I'm interested in, or maybe lecture notes from some uni course. Many professors make their entire material available in PDF form nowadays. – G. Bach Jun 27 '14 at 15:16
Next question: what is the best way to study mathematics on a boat? – ᴡᴏʀᴅs Jun 27 '14 at 21:09
If you're commuting, then you are some sort of mathematics: $A\times B = B\times A$. – Kaz Jun 28 '14 at 2:24

15 Answers 15

up vote 20 down vote accepted

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,

    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.

    With that in mind, whenever I can't fall asleep, I think about getting out of bed, logging into my work computer, and getting a head start on tomorrow's work. I 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.

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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.

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+1, This is how I started learning number theory. – Antonio Vargas Jun 27 '14 at 7:41

I know this answer is a bit off-topic, but...

My friend, what you really need is to rent (buy?) an apartment in that place you're commuting to. Whatever it is you have back home - it's not worth it. You're wasting your life and ruining your health. If it's your family - ask them move with you to your commute destination, or seriously consider only coming home to them on the weekends.

If you do that, you'll be a lot less tired, a lot more focused, a lot less grumpy - and you could devote actual leisure time to studying math the usual way, whatever that may be... you could even take a university course or two and rearrange your work schedule since you'll be more flexible.

Do it. I mean it. I was in your shoes during part of my life - and in retrospect I completely regret not having done something about it.

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Money is a limiting factor for some. – Alexander Gruber Jun 28 '14 at 14:23
@AlexanderGruber, For "many" you mean. – Pacerier Jul 12 '14 at 8:21
@AlexanderGruber: If his job is important enough to commute for so long, then he can probably afford to rent something, if only a room. – einpoklum Jul 12 '14 at 8:57
@einpoklum Depending on what part of the world OP's in, it might not be possible. For example, if he commutes from a suburb of Chicago to work at the city center, a room could be close to $1000/mo. Maybe it's different in other places, but where I am from, many people deal with long commutes because the cost of an apartment is prohibitive. – Alexander Gruber Jul 12 '14 at 13:22

The most important tip I have: Think about mathematics. Remember that you are NOT reliant on any phone, computer or even books - all you need are your thoughts. They can serve to be very useful tools, however. Then comes the question what to think about.

I'm sure you run across plenty of interesting problems during your days. What I would do is to get a notebook and write down all such problems, which you then bring along while you commute. Examples could be problems from textbooks, assumptions that are made but never proved (always be sceptical and try to convince yourself of what is true, this is an approach that will be infinitely rewarding in an academic/research career!), famous historical problems, or problems that you come up with yourself. Be creative and have a curious mind!

Then while commuting, go through your list and pick some problem that you find appealing at the moment.

Try to have the habit of always writing down the solutions as well. This will serve to help you remember the problem and the solution better. It is also easy to take short cuts (which could prove to be wrong) if you only solve the problems by thinking. Some of the most successful problem solvers in physics (Feynman and Dirac to name a few) were known to be very strict about writing all solutions down and saving them.

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My friend, who is Ph. d now, and I were classmates back in the old days. He has the habit of carrying pens and scrap papers in his pocket. While commuting, he always takes them out and starts drawing sketches and thinking about the maybe possibles.

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It depends on whether the environment around is too distractive for you; I'm able to study books (resp. printed pages) when commuting. In fact, sometimes I'm able to study more concentrated in trains and cafes than at home, especially if there is no wifi there. But you must find your own ways of spending time efficiently that are most suitable for you.

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+1, "... no wifi there...". – fermesomme Jun 28 '14 at 14:50

It depends partly on why you're studying, but if you're studying for some reason other than simple personal pleasure... Use a delayed repetition application (Anki or SuperMemo or many others) to memorize formulas, theorems, and any patterns or insights that you spot while studying (if I see x pattern, try using y theorem first). Memorization isn't a substitute for understanding, but the speed gain vs looking things up can be significant, giving you more time to focus on the real work. Also, I find that the process of writing things out in a way which is optimum for delayed repetition memorization can lead to insight in a way that you don't get from passively reading. Finally, delayed repetition memorization is perfect for public transit because it is best done in short-ish bursts and is enough like a game to keep you fully engaged during that time.

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Buy an e-reader (one with an e-ink screen). It's cheap, much easier reading than from a tablet or computer, can last more than a week on one charge, and you can put many books on it. It's lighter than a heavy math book, easier reading, and you can put it in your jacket pocket and take it out easy everywhere. The downside is that formatting may become problematic, especially for formulas.

That e-reader, put a nice novel on it, and take some time to read something just for fun, something completely different than math. You need to put your mind off math from time to time, and reading a novel for 30-45 minutes can help a great deal giving your brain the time to put things in the right order. Sleeping does the same, and making sure you get enough sleep will help you even more.

Read your mail the first or last 15 minutes. Disable automatic loading of mail so it won't distract you.

Download videos or podcasts and listen to them on your phone or tablet.

Find a nice problem or challenge, and try to solve it while on the train.

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The other big advantage of some e-readers such as Kindle (not Fire) is the battery life - many laptops, even if you can find the space, and some tablets will not last for your round trip, let alone if you forget to charge them. – Steve Barnes Jun 29 '14 at 18:19

I would rather say that instead of studying something from texts or doing serious writing down stuffs, it would be much better to think about stuffs that you read the night before or sometime recently. The idea is that amid all the noise and shaking around you would get distracted again and again if you are reading something but when you are in thought it is easy to get lost.

During a summer I had to attend a institute which was an hour and half away from the place of stay. So I started to read in the bus but after sometime I realised that it is a great place to think about problems that keep nagging you, than to open a textbook and read something new. Just lay back and think about problems or concepts that need sinking in. Often I reserved many tough problems to do there only.Of course sometimes you do get really excited and have to scribble some things to check some answer but keep reading and writing to the minimum. In fact best make a list of problems on sheet of paper and one by one, solve them mentally on the go. Good luck!

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Whatever you do depends on how you think. Your Body-language and you academic-performance are highly influenced by your way of thinking.

$\bullet$ Always try to think critically for a question. Once you get the feeling from your self that it is much important to understand the concepts rather than solving the problems, then you will automatically understand how to use the time while commuting.

$\bullet$ I always ask my friends (specially juniors) to use the time in studies rather than on social networking websites. Now-a-days, Social Networking Websites are also used for Educational-Purpose which is actually a great move. If you think you're addicted to a specific site like Facebook, Twitter etc. then you may just simply discuss your problems with your friends and in other groups.

For example, I know that it may not be possible for me to stay away from Facebook,so, I started using it to clear my doubts by discussing my problems with my friends and some experts in a group named StudyIsland. I don't mean to publicise it, but, I'm just stating this as an example.

$\bullet$ Try to understand the concepts behind each and every move of Nature. When you work on Mobile/PC/Tablet then, you may just search for some interesting concepts and theories like, today, I studied a bit about Quantum Mechanics which is in fact, a great thing to learn.

$\bullet$ Planning is the key role for success. While Time-Management and hardwork also play a vital role but the first step of the protocol to study is Planning. Set a target of your week/day and be determined to complete it at time. Once you decide what you have to study, then you come to how to study? and which books to refer to?

Remember that no one else can influence your thoughts and opinions unless and until you are determined to improve yourself. Think about the birds flying (there is much Physics behind this also), mobile running, you breathing etc. Each and every thing has a Scientific Concept behind it. Mathematics is defined as the language of Physics. It has its own existence though, but still, many consider it as the language of Physics. You have to think critically in order to start something.

Have you ever thought what is the significance of Integrals and Differentiation in Real life?

Remember that, life is the Reality and what we study is theoretical. It may or may not be true for the real life. Try to be Practical, and apply the concepts in the real life and notice the differences.

Once you develop your interest in Mathematics or any subject, then nothing will be difficult for you in that particular field.

Good Luck for your future!

May God Bless You!

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Go to Amazon and search for whatever branch of mathematics you're looking for. Then change the order of the books to "average customer review" and you'll have a massively curated list of the best books in that topic.

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I have quite a bit of commute time and I like to use some of it for mathematics. But I have a problem: the bus shakes about far too much to use pen and paper. But I can type on a laptop. I could scribble notes using TeX. But although TeX produces beautiful final quality documents, it's horrible if you want to read your notes as you scribble them down, or if you want to manipulate expressions directly in the text editor.

My solution was to define a set of macros for my text editor vim. It consists of lines like:

:map! \<=> ⇔
:map! \leadsto ↝
:map! \supset ⊃
:map! \vdash ⊢
:map! \cong ≅
:map! \~= ≅

These are convenient enough that I find I can manipulate expressions reliably in vim.

Some branches of mathematics work well this way. For example logic and group theory often have single-line formulae without too many complicated subscripts and superscripts. But multivariate calculus (and hence a lot of physics) don't work well as they require formulae that span multiple lines.

I've placed my current set of macros here:

The nice things is that you can have a permanent searchable record of your solutions to all exercises without acquiring the clutter of many scraps of paper.

It's still not ideal. I find myself occasionally using a drawing package to draw diagrams. I'm using a Mac so to enter mathematics into those I also use a custom input method with the same definitions (

(Emacs also has a TeX mode that you could use if you're that way inclined.)

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I see a lot of great suggestions here.

What came to mind first for me, is writing down some relevant problems before-hand, and try solving them while commuting. Some of them would of course require deep concentration, so certain types of music might be preferrable to the ambient noise on the bus/train/whatever.

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Reading online about maths or anything is fairly easy these days with phones, tabs etc. I think you can use the time to solve problems during your commute.

There was an Indian mathematician Late Shakuntala Devi. She wrote books that have pure mathematical puzzle and just easily fit into pocket. The puzzle revolve around many aspects of mathematics like trignometry, permutation & combination etc. Good for a start!

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IF you want to apply mathematics, e.g. increase your command of algebra: use khan academy. THe courses for math a re simply great: I am doing this right now for my daily 2 hour commute. THe caveat: you need internet access, at least sporadically.

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This might be good in some cases, but once you start studying mathematics explicitly, Khan Academy will more often than not, fall short. They have very little in terms of university-level mathematics like group theory, abstract algebra, topology, differential geometry,... You get my point. – Alec Jun 27 '14 at 17:36

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