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
Force yourself to generate questions -- of me and of
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
Review the lecture later the same day.
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.
It's much better to do a bit of math every day, than to do a lot of
math all in one day.
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.
Things to do if you're stuck:
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:
English Language Development: free help with the
Math Learning Centre: free help with math.
Here are a few other resources:
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
AccessAbility office can help you if you're having a tough