Each week, I will give you a research project that is due one week later. Each week's project is really a choice of several options; you may choose any one of them.


Please write these up as coherent essays with full sentences. The only exceptions are diagrams, graphs, or examples of programming code; even these should serve to illustrate your written prose. Typing and proofreading your text would probably be a very good idea! I don't grade on the basis of handwriting or grammar, but if I can't read your project (either because it's illegible or because the English makes no sense), then that will be bad for your grade.

Some of the project specifications include a list of questions. Please don't just write your paper as a list of questions and answers. Instead, these questions are intended to suggest what you might want to write about. Your essay should make sense on its own, even to somebody that never read the project description.

Typically, a good project will be about two or three pages. So you don't need to write a lot of words; the important thing is to make it clear that you've thought about the ideas.

Types of projects

Some options involve Programming; these may or may not require you to write actual code, but they will all require some programming familiarity or knowledge. But you can't do a Programming project by only writing a program! Like other projects, Programming projects are essays, asking you to write your own thoughts about a topic; your programming code (if any) only illustrates your essay. (You will never have to do a Programming project.)

In later weeks, some options will involve Proofs; I will ask you to write a rigorous mathematical proof for these. But even these projects are really essays, since a written proof in mathematics (as practised by human beings) is simply an essay explaining why something must be true. So don't just give a string of logical symbols with no words. (You may eventually have to do a Proofs project.)

Most projects are neither Programming nor Proofs; these are the most straightforward.


You may want to do outside research for your project. In fact, I would recommend it! Some material on the topics that I will ask about can be found on the Internet by a simple web search. You can also look at the Resources listed at the bottom of the first day's handout (and linked from the course web page). But don't hesitate to look in the old-fashioned library if you find a reference that you think might be helpful. The textbook by Rosen also has a lot of extra material that's not central to the course but could help you with your projects.

You must cite your sources!: Any idea that didn't come from class, one of the two textbooks, or your own mind should be attributed; any words that didn't come from your own mind should be quoted and cited. In the first two years that I taught this course (as MATH 112), there were several students that failed to cite sources; this is plagiarism, a form of cheating (one that's easy to catch, too). But there's really no reason to cheat in this way, because it's perfectly OK to use other people's ideas and words as long as you don't claim credit for them. (I was pleased to see last year that nobody committed any serious plagiarism.) However, the point of the essay is to say what you think; so, after copying somebody else's words with quotation marks and a complete citation, be sure to write your own words explaining your reaction to it.

June 28

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