CAPSTONE PAPER MATH 395
CRITERIA FOR WRITING
OBJECTIVES:
i) To improveyour writing of mathematical prose.
ii) To encourage you to pursue new mathematical topics of interest to you.
iii) To enable you to use the mathematics resources in the libraries.
Paper Topic approved byFeb. 3
Paper Draft dueFeb. 17
Paper DueFeb. 27
An expository paper seeks to explain a subject to its audience. Since mathematics topics are not generally controversial, you do not need to argue a thesis. But your paper should have a focused goal within your topic that you are trying to convey. The paper should not simply be a revision of another article of the same genre or length. I expect you to use sources for your paper, so be sure to give credit where it is due. All direct quotes must, of course, be credited, as must all paraphrases. You will likely include figures from another source. These are, in effect, direct quotes and must be cited. You might find a large part of your paper ending up as a paraphrase of one source. It is acceptable to say this at the start of such a segment rather than citing every sentence or paragraph. For example, you might say, "The material on page 3 is basically a digestion of Sibley [1, 278-283]." In all cases, do not take the risks of plagiarism.
AUDIENCE: The students of this class are the intended audience, even if I am the one grading the paper. Three to six minutes of dedicated reading per page by another student should yield a decent understanding. I will post the finished papers on our Moodle page so that you can read one another’s papers.
I expect you to pick a topic beyond what you have learned in classes. This can include an entirely new area, an application new to you or a connection between areas of mathematics.
FORMAT: Your paper should be 5 to 10 pages of text in 12 point font on a word processor. Typeset math symbols and digital figures are great, but hand lettered symbols and hand drawn figures are acceptable. I much prefer electronic submissions, but a hard copy is acceptable, provided you print on both sides.
The first page should start with the title, your name and an introductory paragraph. Then continue with the body of your paper. Number each page. Mathematics articles generally have no footnotes except to acknowledge grant monies, which is hardly relevant for you (yet!). When you refer to something in your bibliography, it is standard in mathematics to give the author's last name followed by the number of that item in your bibliography, enclosed in brackets. If the item is a book, you should provide page numbers as well inside the brackets. For example, Sibley [1,264268] gives a short introduction to the idea of a field in algebraic structures. While I encourage you to use web sites, you must also use print sources in essential ways. Some (immodestly chosen) examples will illustrate the standard bibliographic style in mathematics.
For a book: 1. Sibley, Thomas Q., The Foundations of Mathematics, Hoboken, NJ: Wiley, 2009.
For an article: 2. Sibley, Thomas Q., The possibility of impossible pyramids, Mathematics Magazine, 73 # 3 (June 2000), 185—193.
There is no standard citationfor web sites,so include the complete html code, the author (or sponsoring institution), title and any relevant subheadings to enable the reader to find the source. Also give the date you last visited the site.
DRAFT: To help you write a better paper, I will give feedback on drafts, focusing on suggestions for presenting the content. (I will make brief comments about the writing, but I will count on you polishing the exposition for Oct. 12.)
Use clear, concise, correct English. While I will base your grade primarily on your ability to digest and present mathematics clearly and correctly, I will also grade on your composition skills. Indeed, no one can present mathematics well without using language well. Strive for active verbs—mathematics too easily elicits the verb "to be" in its many forms, especially the passive voice. Without active verbs, technical writing tends to feel ponderous or worse. Develop concepts rather than grind through unenlightening details. If you include proofs, they should do more than validate results; they should explicate relationships.
TOPICS: You must get your topic approved by me. Here are a number of topics I think you will find interesting and appropriate. I expect you to consult with me about these topics, where to look for material on them and how to understand and present the material. The first student requesting a topic gets it.
1. Differential geometry—such as minimal surfaces and soap bubbles.
2. Knot theory—for example, knot coloring.
3. Bayesian statistics.
4. Computer graphics, computer aided design and geometry.
5. Wavelets.
6. Finite geometries and statistical design theory.
7. Voronoi Diagrams and Delaunay Triangulations.
8. Evolutionary game theory.
9. Music and mathematics—for example, change ringing or fugues.
10. Quasicrystals and Penrose tilings.
11. Voting theory—for example, power indices.
13. Chaos and dynamical systems.
14. Bioinformatics and mathematics.
15. The Traveling Salesman Problem and NP-completeness.
16. Historical topics, such as the solution of cubic equations.
17. Your choice.