What are some good math specific study habits?

Here's something I didn't do until grad school, but wish I had started earlier. Depending on my schedule each quarter I find one hour every single morning that I set aside for "basics."

I find that I absolutely must specify this hour for that and only that if I'm going to psychologically get myself to do this. Otherwise I'll just keep putting it off for later and later in the day until I just don't get around to it. Everything else will seem more important, but I've found this time to be extremely useful.

Here's what I use the time for. Take a textbook on a subject you're learning (presumably the assigned textbook, but certainly others work to get a variety of perspectives). Start going through it. By going through it I mean you have a huge stack of paper (usually from the recycling next to a public printer). You read the book, and after every single sentence make sure you can justify why it is true.

Paragraphs from the book will sometimes transfer to many pages of your own writing. Also, don't let the topics get too fancy. This time is set aside for basics.

What I find odd in math compared to practically everything else is that this type of thing isn't emphasized. Even the top musicians in the world set aside time for scales everyday. It is easy to forget while struggling to play a hard piece of music that the basics are what makes it easy to put together (what am I talking about again?).

Maybe everyday is excessive for an undergrad class, but I think a few times a week will really get your brain in gear to understand the harder topics, and it will certainly help you fill in the details of proofs on quizzes/tests if you've already carefully thought through why the steps of the big theorems are true.

Here are some suggestions:

1. Solve problems

2. Look at what good schools tell their students, for example:

• http://students.berkeley.edu/apa/staff%20training%20and%20development/handouts/math_study_skills.html
  (link aged away: from archive.org)

• http://www.maths.cam.ac.uk/undergrad/studyskills/text.pdf
  (link aged away: from archive.org)

• http://mathcs.slu.edu/undergrad-math/success-in-mathematics
  (link aged away: from archive.org]

• http://sun.iwu.edu/~lstout/HowToStudy.html
  (link aged away: from archive.org)

• http://academic.cuesta.edu/acasupp/as/701.htm
  (link aged away: from archive.org)

• http://www.dartmouth.edu/~acskills/success/learninglinks.html#math
  (link aged away: from archive.org)

In addition, I would recommend learning a Computer Algebra System (like Mathematica) and learn to explore problems and find various avenues to solve problems.

Please see: http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems

I hope that gives you some ideas and things to research further.