A Guide to Writing Mathematics
Dr. Kevin P. Lee
Introduction
This is a math class! Why are we writing?
There is a good chance that you have never written a paper in a math class before. So you
might be wondering why writing is required in your math class now.
The Greek word
mathemas
, from which we derive the word mathematics, embodies the
notions of knowledge, cognition, understanding, and perception. In the end, mathematics is
about
ideas
. In math classes at the university level, the ideas and concepts encountered are
more complex and sophisticated. The mathematics learned in college will include concepts
which cannot be expressed using just equations and formulas. Putting
mathemas
on paper
will require writing sentences and paragraphs in addition to the equations and formulas.
Mathematicians actually spend a great deal of time writing. If a mathematician wants
to contribute to the greater body of mathematical knowledge, she must be able
communicate her ideas in a way which is comprehensible to others. Thus, being able to
write clearly is as important a mathematical skill as being able to solve equations.
Mastering the ability to write clear mathematical explanations is important for
nonmathematicians as well. As you continue taking math courses in college, you will come
to know more mathematics than most other people. When you use your mathematical
knowledge in the future, you may be required to explain your thinking process to another
person (like your boss, a coworker, or an elected o
ffi
cial), and it will be quite likely that
this other person will know less math than you do. Learning how to communicate
mathematical ideas clearly can help you advance in your career.
You will find that writing good mathematical explanations will improve your knowledge
and understanding of the mathematical ideas you encounter. Putting an idea on paper
requires careful thought and attention. Hence, mathematics which is written clearly and
carefully is more likely to be correct. The process of writing will help you learn and retain
the concepts which you will be exploring in your math class.
1
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What does good mathematical writing look like?
As you learn more math, being able to express mathematical ideas will become more
important. It will no longer be su
ffi
cient just to be able to write down some final “answer”.
There is a good reason why Herman Melville wrote
Moby Dick
as a novel and not as the
single sentence:
The whale wins.
For this same reason, just writing down your final conclusions in an assignment will not be
su
ffi
cient for a university math class.
You should not confuse writing mathematics with “showing your work”. You will not
be writing math papers to demonstrate that you have done the homework. Rather, you
will be writing to demonstrate how well you understand mathematical ideas and concepts.
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 Spring '09
 DANBERWICK
 Math, Division, MobyDick, Math Class, mathematical writing, intro duction

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