7. Explain how each formula is derived, or where it can be found.
Don't pull formulas out of a hat, and don't use variables which you don't define. Either
derive the formula yourself in the paper, or explain exactly where you found it, so other
people can find it, too.
Put important or long formulas on a line of their own, and then center them; it makes
them much easier to read:
|The total number of infected cells in a honeycomb
with n layers is
1+ 2 +K+ n = n(n +1)/ 2 .
Therefore, there are 100(101)/2=5,050 infected cells in a honeycomb with 100
|The total number of infected cells in a honeycomb
with n layers is 1+2+ . . . +n =n
(n +1)/2. Therefore, there are 100(101)/2=5,050 infected cells in a honeycomb with
Microsoft Word has an equation editor: pull down the
Insert menu, select Object, and
then Equation. If you don't have an equation editor, you may either try formulas with
tabs and fancy fooling, you may use Excel for matrices if you know how, or you may
wish to write the mathematics in by hand. All of these are fine options.
Caution: Mathematical formulas can be hard to do on a standard word processor. If
you've got something that's really complicated, feel free to leave space and then write it
out by hand later- but then don't forget to do so!
9. Provide the right level of mathematical detail
This is a difficult thing for many students, and takes practice. Reread the section above
on the difference between homework mathematics and more formal mathematics. The
audience for your papers should be someone who has taken the course. At a minimum
you should at least tell the person how you reached an answer. For example, when
solving a quadratic equation as before do not just state the equation and then the answer
as if from nowhere. If you used the quadratic formula then say you used the quadratic
10. Give acknowledgment where it is due.
I think Plagiarism is almost certainly the greatest sin in academia - some fiction writers
make plagiarism a motive for murder. It's extremely important to acknowledge where
your inspiration, your proofreading, and your support came from. (For example, I thank
Mark Stanton, a high school mathematics teacher in New York City, for catching a
spelling mistake in the previous sentence.) In particular, you should cite: any book you
look at, any computational or graphical software which helped you understand or solve
the problem, any student you talk to (whether in this class or not), any professor you talk
to (including and especially me, because I'll catch you if you leave me out). The more
specific you are, the better.
11. In this paper, are the spelling, grammar, and punctuation correct?
(a) It may surprise you that it is on spelling and grammar that people tend to lose most of
their points on their mathematics papers. Please spell-check and proofread your work for
grammar mistakes. Better yet, ask a friend to read your paper. Mathematicians are
generally not petty, but neither are we amused by sloppy or careless writing.
(b) Mathematical formulas are like clauses or sentences:
they need proper punctuation,
too. Put periods at the end of a computation if the computation ends the sentence; use
commas if it doesn't. An example follows.
|If Dr. Crannell's caffeine level varies
proportionally with time, we see that
Ct = kt
where Ct is her caffeine level t minutes after 7:35 a.m., and k is a constant of
proportionality. We can solve to show that k =202, and therefore her caffeine level
by 11:02 (t =207) is
In other words, she's mightily buzzed.
(c) Do not confuse mathematical symbols for English words
(= and # are especially
common examples of this). The symbol "=" is used only in mathematical formulas - not
|We let V stand for the volume of a single mug and
n represent the number of mugs.
Then the formula for the total amount of root beer we can pour, R, is R = nv .
|We let V = volume of a single mug and n = the #
of mugs. Then the formula for the
total amount of root beer R = nv .
|We let V stand for the volume of the mug and n
represent the number of mugs. Then
the formula for the total amount of root beer we can pour, R, is R is nV.
(d) Do, however, use equal signs when you state formulas
or equations, because
mathematical sentences need subjects and verbs, too.
|Then the formula for the total amount of root beer we can pour is R=nV.|
|Then the formula for the total amount of root beer we can pour is nV.|
12. In this paper, is the mathematics correct?
This is self-explanatory.
13. In this paper, did the writer solve the question that
was originally asked?
So is this.
IV. Good Phrases to Use in Math Papers:
• Therefore (also: so, hence, accordingly, thus, it follows that, we see that, from this
we get, then )
• I am assuming that (also: assuming, where, M stands for; in more formal
mathematics: let, given, M represents )
• show (also: demonstrate, prove, explain why, find )
• This formula can be found on page 9-743 of Discovering Calculus ©1999, Levine
• If you have any further questions, feel free to contact me or Sam Smart, who
helped me develop this formula for you.
• While I am very glad to help you this time, you should be advised that my usual
consultation fee is $85.
• (see the formula above ). (also: (see *), this tells us that . . . )
• if (also: whenever, provided that, when )
• notice that (also: note that, notice, recall )
• since (also: because )=
V. Helpful Hints for the Computer:
1. Underlining is the poor writer's italics. If you're on the computer, don't underline
without permission from the dean.
2. To find unusual symbols, go to the Insert menu and select Symbol.
If you look carefully enough, you can talk about name brands (Kleenex™, Toys R
Us®, Discovering Calculus©), and ask questions in Spanish: ¿Qué pasa?
3. I would encourage all of you to experiment with the equation editor in your word
processor. Even if you do not, please follow a few guidelines for mathematical
typesetting: variables should always be italics, numbers, symbols, and names of
mathematical functions should not. So sin x=0.45 is correct. The Microsoft
Word equation editor takes care of this detail for you.
4. Whether or not you use a computer, please proofread the final draft before you
give it to me. Please, please. No, really.
VI. Other Sources of Help:
You are always more than welcome to come see me during my office hours, or to make
an appointment to see me outside of office hours.
If you need help then please use the Writing Center, even though this is a math class. You
can call them at 240-567-7401 to make an appointment or stop by HU002. They know
how to help you organize a paper, as well as what to look for in a good essay. They want
to help you. I want them to help you. Get help.