MCS 236 Expository Paper

Write your paper for an audience of other MCS 236 students. In other words, assume that your audience has the same general knowledge and interests as you do, but is not necessarily well informed about your topic. Strive to capture the reader's interest and to hold it, and strive for clarity and a natural flow in your exposition of the technicalities of your topic.

Consult the handout given earlier on special guidelines for writing mathematics well.

Your paper should be about 5-10 pages long. It should be typed, but you may include handwritten formulas and hand-drawn diagrams.

Schedule

Possible topics

• The four-color theorem with proof that any planar graph can be five-colored
• Primality testing with proof of the Lucas-Lehmer test
• RSA encryption with a proof showing why RSA works
• Polya counting theorem
• Applications of modular arithmetic--large integer arithmetic, check digits (ISBN,UPC codes, etc.)
• Traveling salesman problem
• Fermat's last theorem
• Fascinating properties of Fibonacci numbers
• Generalizations of Fibonacci numbers: u_n = a u_n-1 + b u_n-2.
• More about Pascal's triangle/binomial coefficients
• Pascal's triangle modulo a prime and fractals
• Greedy algorithms
• Topic of your choosing--approved by me

Grading guidelines

• The F paper is rare. This grade is usually reserved for cases of plagiarism and excessive lateness. However, exceptional failure to comply with the terms of an assignment may also result in an F.

• The D paper, in some significant way, doesn't answer the question that was asked. It lacks a thesis or an argument, or it has a thesis which is inappropriate to the assignment. A D paper which does answer the question is filled with mechanical faults (errors in grammar and/or spelling). Paragraphs do not hold together; ideas do not develop from sentence to sentence. This paper usually repeats the same thoughts over and over, perhaps in slightly different language but often in the same words. It is usually rambling and directionless.

• The C paper has a thesis which is vague and broad, or which answers only part of the question(s) asked; or it may make a good argument without first offering a thesis statement (usually in the introduction). The C paper rarely uses evidence well; sometimes it uses no evidence at all and relies entirely on unsupported personal opinion. Even with a clear and interesting thesis, a paper with insufficient supporting evidence is a C paper. Sometimes a C paper has a good deal of evidence, but it is not part of a coherent argument and the reader can only make sense of it with great difficulty (if at all); thus, the evidence is ineffective. This paper may not effectively address [the mathematical issue].

• The B paper makes sense throughout. It has a thesis that is appropriate, complete and worth arguing. It does not digress, and it ends by keeping the promise it made to the reader in the beginning. The reader always knows where the paper is going and what the author wants to say. The paper presents interesting ideas, supported with sound evidence which is both to the point and well documented. This paper effectively addresses ... the particular topic.

  The paper is well organized and although some sentences may not be elegant, the ideas in them flow well and thought naturally follows on thought. The paragraphs may be unwieldy now and then, but they are organized around one main idea. The reader does not have to read a paragraph two or three times to figure out what the writer is trying to convey.

  The B paper is, for the most part, mechanically correct. There will be occasional spelling and grammar errors, but these are few in number and do not prevent the reader from following the ideas in the paper.

• The A paper is rare. It has all the qualities of a B paper, but in addition it is lively, well paced, interesting, even exciting. Everything in it seems to fit the thesis exactly. The paper has style. Reading this paper, the reader feels a mind at work. The sure mark of an A paper is that the reader continues to think about it after reading it, even wanting to tell others about it.

  This paper may have a proofreading error or two, even occasional misspelled words or a minor error in grammar, but these errors are the consequence of the normal accidents all good writers encounter.

Citations and bibliography

Your paper should not rely on just once source unless it is a book report.

In your bibliography, in addition to Hacker's guidelines, add one sentence to each reference which explains to the reader why the source is (or is not) reputable.