Reading a Mathematics Text
Here are some suggestions we have compiled
for reading a math textbook:
**LEARN BY DOING: Mathematics is not a
spectator sport. We learn
mathematics by participating, so "participate" while you read. When
you read your textbook, you should do so with a paper and pencil.
* Take notes on
definitions, theorems or key concepts in your notebook. You should try to state
the material that you read in your own words. If you encounter an unfamiliar
term, look it up and make a note of it.
For definitions,
find examples of the defined objects and examples of objects that do not fit
the definition.
Figure out why
each piece of a theorem is necessary or sufficient.
* When you come to
an example or theorem, work through it carefully step by step. Try to
understand and follow how the author is progressing through it. After reading
it, cover it up and try to work through the details on your own. Authors often
omit steps. Fill in the gaps to deepen your understanding of the material.
* When you can work
through an example, try to think of other examples that would fit the idea
being discussed. Think of other relevant problems and try to solve them.
* Make a note
of those things you do not understand and discuss them with your study group,
in class, via email or during office hours.
* Discuss the text
with other students. Even a short discussion of a concept or example may help
deepen your understanding.
* Ask questions as
you read: Why are the topics presented in this order? What may be a better
order? What’s coming up next? Does this make sense? Is this a sound argument? If something does
not make sense to you, explore it further.
You may find mistakes. Keep
track of mistakes/typos you find.
**SLOW DOWN!! Math is dense.
The flow of a math book is not like the flow of a novel. Reading a mathematics
textbook requires slow and careful reading of each word. A typical novel might
be read at the rate of a page a minute. Expect to spend 30-60 minutes
working through the few selected pages for each reading assignment thoroughly
for the first time.
* Every word
counts. Writers of math texts believe that extra words and repetition get in
the way of clarity, so there is little chance of picking up missed information
from reading on.
* Understand each
sentence before you go on. Expect to re-read, and then to re-read again. It may
take several passes through a section before you start to absorb the material.
* Study diagrams
and other kinds of illustrative material.
* Read when you are
relatively alert.
**DON'T GET DISCOURAGED. Even after you follow all the suggestions, you
probably will not completely understand everything in the section, but the
class meetings will be much more meaningful if you spend time to understand
while you read.
When you encounter a new topic that is frustrating
you, try to remember that previous topics were also difficult at first, but
that there is great satisfaction in learning and mastering a concept.
With hard work, you'll be able to gain that same sense of satisfaction with the
material in this course.
**GIVE IT A RE-RUN! After we have discussed a section in class, go back
and re-read the section -- Many points will be much clearer. Read the chapter over, soon after class. This
second reading will help you store the information you've learned in your
long-term memory.
**Print these suggestions and use them as
a bookmark. Reread them as needed.
If all of this seems like too
much work consider that it will take nearly as much work to fail. If it takes
only a little more work to succeed, then take the time to succeed!
Please send any comments to pmyers@sandiego.edu