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This is not a math question per se, but I think that it is relevant to a number of people. I am currently in the process of applying to graduate school, but not feeling super confident that I will get in. In the case I do not, I plan to get a job and try again next year. The job is something that requires problem solving and a little math, but not at the level that would be required of a PhD program.

My question then is what sorts of things can I do to stay competitive in my time off if I do not get in? The things I do now are (besides actual classes)

  • Project Euler (when I have time)
  • Perusing this site way too much
  • I have recently begun reading papers of the faculty at the schools to which I am applying

What more can I do to make sure I don't lose that insight and "sophistication" while working at a full time job that may not be entirely relevant to my career goals?

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I've always found that, if given the opportunity to, explain something math related that you know very well to someone who doesn't. That has always been the best way for me to stay "sharp" and also a test to see how well I truly understand something. –  Patrick Dec 5 '12 at 21:39
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Study now what you would have studied if you got in. Most of the math I know I taught myself long before I reviewed it in any classroom. The same is true for many mathematicians. –  Bill Dubuque Dec 5 '12 at 21:53
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6 Answers

up vote 9 down vote accepted

If you don't get into a graduate program this year,

Find some ways to keep yourself accountable.

When enrolled in classes, one usually has homework that is required in some way (due dates, deadlines), and exams to prepare for. While it is clear that you are motivated, and that you are willing to keep actively engaged in "doing" math as well as reading it, try to stay connected with professors you have worked with whom you can "answer to", to help monitor your progress. If nothing else, set your own deadlines/goals for completing problem sets. Create or find exams to take, set a dates when you plan to take them, and limit the amount of time you have to complete them.

Also, as Patrick suggested, commit yourself to tutoring, e.g. tutoring upper-level undergrads, so that you'll need to keep "a step ahead" of their progress and will need to have a good enough grasp of the subject areas to be able to teach them well.

Finally,

Keep it fun, as well!
Be sure to explore and engage in areas about which you are most interested, even as you push yourself to tackle areas of less interest.

Good luck!

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Pick a book on a subject you are interested in and that isn't too difficult to do without support, and work through it, possibly keeping a blog on additional examples and interesting exercises. If you are not used to doing this, plan the week with your book out in advance, create your own assignments, etc. because the structure that you had at school will no longer be available. If you can't understand something, then this site is the obvious choice.

Unfortunately, time management will be difficult with a full-time job. You will have less time than you think, because even though you will have time after work, you will need downtime to recover from the pains of repetitive labour that occurs in most jobs. It may be helpful to read an overview of what you need to do in the coming week so that when you do get down to serious work, the transition from job-downtime-math will be less jarring.

Ultimately I think you should consider this as a last resort and apply to more graduate schools, even if they are not quite the calibre you envisioned. On the bright side, even if you do not get into graduate school, one year off probably won't make too much of a difference since there isn't too much undergraduate material to forget in the first place; in contrast, taking a year off after finishing your PhD would be far more harmful I think.

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+1 for mentioning blogging. Teaching is a great way to stay sharp, and blogging allows you to teach on a flexible schedule . You can commit to monthly entries if you want to make sure you actually do things on time as well. –  Gordon Gustafson Dec 6 '12 at 1:56
    
Thank you for all of this. Your and amWhy's answers together would be perfect. I wish I could accept both! –  Jeremy Dec 7 '12 at 21:37
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I took a two year break after undergraduate and even though I used some math & programming skills at work, my actual math knowledge dwindled very rapidly, despite me reading articles and skimming some books in my free time.

In my opinion if you want to stay mathematically active, you must do problems. Math is not a spectator sport so just reading articles texts or this forum will only keep you interested in math. To be able to retain the skills you possess you must actually DO it.

Since I did very little doing while working, and mostly stuck to reading, returning back to school this semester after 2 measly years off was quite a challenge and I found myself having to work very long days every day just to get back to the level I was before I left school. Luckily it comes back faster each time you relearn it, but practice and active learning is key!

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My experience was a bit different. The draft forced me to take a two-year break between my 1st and 2nd years in grad school. I was lucky: I ended up with a desk job that left me some free time, albeit scattered, and I used some to work problems from Dugundji’s Topology. I got out several months before school started, and I remember doing some programming, but I did not (so far as I can recall after ~40 years) make any effort to brush up on what I’d studied my first year. While in the army I felt a bit rusty, but as it turned out I had no trouble getting back into the swing of things. –  Brian M. Scott Dec 5 '12 at 22:39
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Bedtime reading, engaging with sites like this, and some of the great blogs (Gowers, Tao and their links), searching out problems to solve, testing yourself on questions on this site. I've made a complete idiot of myself a couple of times, but I did that when I was an active student too.

Searching the web for the bits which extend my interest.

This is the greatest generation for a couple of hundred years in which an amateur enthusiast can enjoy maths in public. Who knows whether it will ever be possible for such to make real contributions at the frontiers. I am content to enjoy my passion.

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If you already know the specific postgrad area of research you want to pursue, you could start reading relevant research papers. It could not only keep you entertained, and help you really make up your mind with it, since postgrad is a big commitment both time and $ wise.

I have a postgrad in applied math, and realized afterwards that I could've learned everything on my own...

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I would strongly suggest learning up on machine learning. It is a great field to be in for folks are adequately mathematically inclined but not that willing to go all the way and be a theoretical person. Here is a set of books worthwhile to read, especially the last one on the list which is on the subject of machine learning. HTH

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