In other words, don't just read the material. After each example, after every proof, close your book and try to reconstruct it from memory. You will probably not be able to. Do not look in the book right away! Instead, think about the example, and try to do it yourself, perhaps in a different way than is done in the book. Give yourself some time to think about it, even if it seems you're not making any progress. Note that thinking does not mean spacing out. It is much, much better to try something, even if it seems unlikely to help, than to sit and wish for a solution. No solution drops out of the sky in perfect form; instead, write something wrong down first, and then try to tweak it a bit at a time until you force it into a good solution.

For example, one can ask about any potential ambiguity in a definition. (π is the ratio of the circumference of a circle to its diameter. But of which circle?) Or one can ask about whether every condition given in a theorem must be there. In other words, if you remove one of the assumptions, is the theorem still true? (Does the intermediate value theorem hold on open intervals?) Etc. There are always questions you can ask. Find them!

The best way to do this is to try to explain to (a potentially imaginary) someone what happened in lecture. A worse, but still OK, alternative is to (actively!) read over your lecture notes.

There are several reasons for this. For one thing, there are only so many hours on a given day which can be used for creative thought. Second, if you work a little bit every day, you potentially run across conceptual difficulties much earlier. This gives you more chances to talk to me / your TA / other students. Moreover, this gives more time to reflect on some of the more challenging questions. Also, when you have a whole day ahead of you all devoted to one task, it's easy to fall into the trap of thinking you're not in any rush, and to start procrastinating. By contrast, if you only have an hour or two left to work on math, you will force yourself to focus, and get a lot more done.

• Get really frustrated, stomp your feet, and pout. The effect can be enhanced by rolling around on the floor, screaming, and letting a few unstoppable tears well up.


• COME TALK TO ME. Seriously, I'll always be happy to see you. There are plenty of opportunities to talk to me:
  • Before lecture.
  • During lecture.
  • After lecture.
  • During my office hours (see the course homepage for times and location).
  • By email. (Note that I will only reply on Mondays, Tuesdays, and Thursdays.)


• Communicate with your TA, either in tutorial or by email.


• Check out the resources offered by the Centre for Teaching and Learning. Among other services they offer:
  • Writing Centre: free help with your writing.
  • English Language Development: free help with the English language.
  • Math Learning Centre: free help with math.


• Here are a few other resources:
  • The Health and Wellness Centre provides medical advice and care, including counselling. If you're going through some hard times emotionally and feel you have no one to turn to, you should seriously consider contacting them.
  • The AccessAbility office can help you if you're having a tough time academically.
  • The Academic Advising and Career Centre can help you figure out what courses you need to take to achieve your career goals. They can also help you figure out your career goals!

*Graphic courtesy of Hiro Tanaka.