Describing a model

In general, your paper can be of one of two sorts. It can be a description of
an original modeling project. Alternatively, it can be a review of some modeling
topic from the scientific literature. In either case, you should choose a topic that
you are interested in, find and reference appropriate background information, use
mathematical methods from this class, and write a clear, interesting, and carefully
edited paper.
Tw o or three students can work on a project together, but each student must
still write their own independent term paper. In addition, you should acknowledge
and credit any collaborators in your paper.
Review papers should summarize and synthesize a series of papers that focus on the same topic. You should describe how these papers formulate and analyze their models and how they improve on one another.
The responsibility for finding a course project is yours, but we will be happy
to give you feedback and to provide some help in locating resources. If you are
unsure if your topic is appropriate, please ask.
The exact format of each paper will differ, but a typical project paper may
well contain the following components or sections:
(1) Title and Author
(2) Abstract
Write a short 50–100 word summary of the entire paper that describes your
topic, the methods that you used, and what you discovered.
(3) Introduction
Describe your problem. Explain why it is interesting. Give some background and history. Motivate the approach that you will use. Then, use the
last paragraph as a road map for the rest of the paper. That is, use the last
paragraph of the introduction to describe what the reader will find in each of
the following sections.
(4) Mathematical model
Motivate, write down, and describe your model. Define your variables and
parameters. Explain your notation. Explain and justify your simplifications.
(5) Analysis
Describe the mathematical methods that you are using to solve or analyze
your model. Lead your reader through the analysis in a succinct and readable way.
(6) Example
Illustrate your analyses with an example, i.e., for a particular set of parameters or functions. Interpret your example in terms of the original problem.
(7) Conclusions
Summarize your results. Summarize what you did and what you learned.
Discuss limitations of your approach and how you might extend your analyses to overcome these limitations. Tie your results back to the original problem.
(8) Acknowledgements
Acknowledge your collaborators and credit them for their contributions.
Thank other people who helped you.
(9) References
Include a bibliography of the books, journal articles, and other sources that
you cited in your paper. (Yes, you should be citing relevant literature.) Format your references in a standard and consistent manner. See a style manual
or look at some published scientific papers if you don’t know how to correctly cite and format references.
Please type your paper. If you need to, type the text and write the mathematics in by hand. Better yet, use a mathematical typesetting system (such as LaTeX, Lout, or groff). Submit a hard copy of your paper.
You can earn writing or W credit for this class. To earning writing credit,
you must submit a first draft of your paper on Tuesday, February 26, 2019 and incorporate the comments that you receive into your final paper, due on Thursday,
March 14, 2019.
I will grade your term papers on a 100-point scale. In particular,Iwill
aw ard up to 20 points each for (1) mechanics (spelling, grammar, references, handling of equations); (2) clarity of thought, writing, and implications; (3) originality/novelty of project and/or thoroughness of review; (4) mathematics (appropriateness, depth, breadth, accuracy, explanations, exposition); and (5) application
area (depth, breadth, accuracy, exposition).
Pet Peeves
At the end of the quarter,Isuddenly have to read 70 term papers. As a result, I always appreciate interesting, well-written papers that keep to the spirit of
this class. I hav e, in turn, learned that there are certain items that annoy or irritate
me more than they should. Here is my list of pet peeves:
(1) Inappropriate topics
Be sure to write a paper that uses mathematical methods from this class.
(2) Passive voice
Please write in an active voice. Few things are as soporific as reading 70
term papers written in the passive voice.
(3) Spelling errors
Please run your manuscript through a spell checker.
(4) The wicked which
The words which and that are not interchangeable. Please see a style manual for the appropriate use of these two words.
(5) Unnumbered displayed equations
Please number all displayed (versus in-line) equations. Please see Mermin
(1989), referenced below, for reasons why. You can easily find Mermin’s
paper on the internet.
(6) Incorrectly punctuated equations
Mathematics is prose. So, if a sentence ends with a displayed equation, you
still need a period (or other punctuation mark) at the end of your sentence,
i.e., at the end of the displayed equation. Or, if your displayed equation precedes a where, you need a comma at the end of your displayed equation.
Also, don’t precede every displayed equation with a colon (especially if you
don’t use colons elsewhere). Rather, integrate your equation into the flow of
your sentence. (Try reading your sentence aloud.) See Mermin (1989) for
further discussion.
(7) Incomplete or inconsistently formatted references
Provide enough information so that I can track down your references. Follow standard formats and be consistent in your formatting. (See a style
manual or look at some published scientific papers for examples.) Don’t
cite a preprint or a url if you can cite a published source.
Mermin, N. D. 1989. What’s wrong with these equations ? Physics Today, 42
(10), 9–11.