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2 Chapter 0 Communicating Mathematics
0.1 LEARNING MATHEMATICS
One of the major goals of this book is to assist you as you progress from an individual
who uses mathematics to an individual who understands mathematics. Perhaps this will
mark the beginning of you becoming someone who actually develops mathematics of
your own. This is an attainable goal if you have the desire.
The fact that you’ve gone this far in your study of mathematics suggests that you
have ability in mathematics. This is a real opportunity for you. Much of the mathematics
that you will encounter in the future is based on what you are about to learn here. The
better you learn the material and the mathematical thought process now, the more you
will understand later. To be sure, any area of study is considerably more enjoyable when
you understand it. But getting to that point will require eort on your part.
There are probably as many excuses for doing poorly in mathematics as there are
strategies for doing well in mathematics. We have all heard students say (sometimes,
remarkably, even with pride) that they are not good at mathematics. That’s only an alibi.
Mathematics can be learned like any other subject. Even some students who have done
well in mathematics say that they are not good with proofs. This, too, is unacceptable.
What is required is determination and eort. To have done well on an exam with little or
no studying is nothing to be proud of. Confidence based on being well prepared is good,
however.
Here is some advice that has worked for several students. First, it is important to
understand what goes on in class each day. This means being present and being prepared
for every class. After each class, recopy any lecture notes. When recopying the notes,
express sentences in your own words and add details so that everything is as clear as
possible. If you run into snags (and you will), talk them over with a classmate or your
instructor. In fact, it’s a good idea (at least in our opinion) to have someone with whom
to discuss the material on a regular basis. Not only does it often clarify ideas, it gets you
into the habit of using correct terminology and notation.
In addition to learning mathematics from your instructor, solidifying your under-
standing by careful note-taking and talking with classmates, your textbook is (or at least
should be) an excellent source as well. Read your textbook carefully with pen (or pen-
cil) and paper in hand. Make a serious eort to do every homework problem assigned
and, eventually, be certain that you know how to solve them. If there are exercises in the
textbook that have not been assigned, you might even try to solve these as well. Another
good idea is to try to create your own problems. In fact, when studying for an exam, try
creating your own exam. If you start doing this for all of your classes, you might be sur-
prised at how good you become. Creativity is a major part of mathematics. Discovering
mathematics not only contributes to your understanding of the subject but has the poten-
tial to contribute to mathematics itself. Creativity can come in all forms. The following
quote is from the well-known writer J. K. Rowling (author of the Harry Potter novels).
Sometimes ideas just come to me. Other times I have to sweat and almost bleed
to make ideas come. It’s a mysterious process, but I hope I never find out exactly
how it works.
In her book Defying Gravity: The Creative Career of Stephen Schwartz from God-
spell to Wicked, Carol de Giere writes a biography of Stephen Schwartz, one of the most