Guide to Writing Mathematics Projects
(as adapted from Dr. Annalisa Crannell of Franklin & Marshall College)

When you turn in your writing assignment, you should use a paper clip to attach the checklist you have been provided to the front. Please use both the checklist and this outline as a guide while you write, because you will produce a much better report if you do. What follows here is a more detailed explanation of the criteria I will use for grading your papers.

Does this paper:

1. Clearly summarize the problem to be solved?

Do not assume that the reader knows what you're talking about. You don't have to restate every detail, but you should explain enough so that someone who's never seen the assignment can read your paper and understand what's going on, without any further explanation from you. Outline the problem carefully.

2. Provide a paragraph that explains how the problem will be approached?

If you can avoid variables in your answer, do so; otherwise, remind the reader what they stand for. If your answer is at the end of the paper and you've made any significant assumptions, restate them, too. Do not assume that the reader has actually read every word and remembers it all (do you?).

3. State the answer in a few complete sentences that stand on their own?

For example, what physical assumptions do you have to make? (No friction, no air resistance? That something is lying on its side, or far away from everything else?) Sometimes things are so straightforward that there are no assumptions, but not often.

4. Give a precise and well-organized explanation of how the answer was found, including:

• algebraic support
• graphical support
• numerical (tabular) support as appropriate?

It's a good idea not to plunge into mathematics without first warning your reader. Carefully outline the steps you're going to take, giving some explanation of why you're taking that approach. It's nice to refer back to this paragraph once you're deep in the thick of your calculations.

5. Clearly label diagrams, tables, graphs, or other visual representations of the math?

In math, even more than in literature, a picture is worth a thousand words, especially if it's well labeled. Label all axes, with words. Give diagrams a title describing what they represent. It should be clear from the picture what any variables in the diagram should represent. The whole idea is to make everything as clear and self-explanatory as possible.

6. Define all variables, terminology, and notation used?

Even after you label your diagram, you should still explain in words what your variables are. The more specific you are, the better. State the units of measurement. When you can use words like "of", "from", "above", etc., do so. For example:

We get the equation d =rt, where d is the distance, r is the rate, and t is the time.

We get the equation d =rt, where d is the distance from Sam's car to her home (in miles), r is the speed at which she's traveling (measured in miles per hour), and t is the number of hours she's been on the road.

Variables in text are italicized to tell them apart from regular letters.

7. Clearly state the assumptions which underlie the formulas and theorems, and explain how each formula or theorem is derived, or where it can be found?

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.

Sufficiently advanced copies of Microsoft Word have 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 if you know how, or you may wish to use MathCad. All of these are fine options.

8. Give acknowledgment where it is due?

Plagiarism is against school policy and is a crime. It's extremely important to acknowledge where your inspiration, your proofreading, and your support came from. 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).

9. Use correct spelling, grammar, and punctuation?

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. Mathematical formulas are like clauses or sentences: they need proper punctuation, too. Put periods at the end of a computation if you are ending the sentence; use commas if it doesn't.

Do not confuse mathematical symbols for English words (= and # are especially common examples of this). The symbol "=" is used only in mathematical formulas not in sentences:

Do, however, use equal signs when you state formulas or equations, because mathematical sentences need subjects and verbs, too.

10. Contain correct mathematics?

This is self-explanatory.

11. Solve the problem(s) that were originally asked?

This is self-explanatory.

Good Phrases to Use in Math Papers:

• Therefore, so, hence, accordingly, thus, it follows that, we see that, from this we get, then
• I am assuming that, assuming, where, M stands for; in more formal mathematics: let, given, M represents
• Show, demonstrate, gives evidence for, explain why, find
• This formula can be found on page 9-743 of Discovering Calculus ©1999, Levine and Rosenstein.
• 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 per hour.
• See the formula above, see *, this tells us that . . .
• If, whenever, provided that, when
• Notice that, note that, notice, recall, since, because

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. In addition, I have a collection of "excellent papers" from previous classes, so you can see the kinds of papers that I've enjoyed reading.

Even though this is a math class, please feel free to use the Writing Center here at the ASUE Center Building. You can visit their website at http://www.east.asu.edu/learningcenter/ ,call them at 480-727-1452, or reach them by email: learningcenter@asu.edu

You may also get help at the CGCC Learning Center. The contact information there is:

http://www.cgc.maricopa.edu/learning/center/ or 480-732-7231 or contact Caryl Terrell-Bamiro at caryl.terrell-bamiro@cgcmail.maricopa.edu to discuss the CGCC Writing Center.

The people in these deparments 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! J