Writing Project (Spring, 2005)
Mathematics 225 (Discrete Mathematical Structures, Spring 2005)
Mathematics and Computing Department
York College (CUNY)
Jamaica, New York 11451-0001
web page: www.york.cuny.edu/~malk
Select one or more counting problems and write a self-contained introduction concerning how to solve this problem (or problems). Your essay should include a specific version of the problem in some "real world" setting (e.g. What is the number of different ways to seat Alice, Barbara, and Cheryl and Dave, Ed, and Fred around a circular table so that no two men or women sit next to each other?). The essay should describe how to generalize the specific example to a general setting (e.g. How many ways can one seat n men and n women around a circular table so that no two men or women sit next to each other?). You should also discuss, if possible, other "real world" examples where your analysis would apply (e.g. if you originally discuss how to find the number of shirt/pants pairs a person can wear, you might give as a further example, the number of ice-cream flavors/toppings pairs that can be selected at a sundae bar).
You should write as if your intended audience is either students such as those in a high school or college class) who are not familiar with how to solve the counting problem(s) you treat, or a boss (supervisor) to whom you report. Your essay will serve as an introduction to the solution of the problem(s). Thus, your discussion should be as elementary and clear as possible.
You can use as part of your description and solution standard formulas (e.g. nCr or nPr) and can insert by hand any symbols that are not easy to type using your word processor or typewriter. (Hand written essays are also acceptable. In either case use reasonable margins and write only on one side of a page.)
You can use diagrams (which can be inserted hand-drawn into your text if you wish) to help make your explanations clearer. If you do use diagrams be sure to explain in the text what the diagrams illustrate or mean, and refer to the diagrams in the text.
Length: Minimum 1000 words; no maximum.
by April 4, 2005 (Monday)
a. Regard this as a first draft and we will work together towards improving the first draft.
b. Do not fail to attend on April 4 without having already handed the paper in or contacting me about its status. I would rather have it late than that you cut class to avoid turning it in.