Extra Credit assignments for Math 118
Fall 2007

If you choose to do one of the following extra credit projects, you can improve your grade by up to 5%. Note that this isn't enough to change an F to a passing grade, but is enough to move a C- to a C or a B+ to an A-.

Each of these assignments should take a fair amount of effort, about equivalent to writing a paper in another class. The amount of extra credit given will depend on how well you do the project. Projects are due by the time of the final (you can give them to me before final, or at the final, but not after.)

• Investigate and explain the Johnston power index and compare it with the two we studied in the class (Banzhaf and Shapely-Shubik). Explain the method, give some examples. See p. 79-80 in the text.
• Investigate and explain the Nearest Insertion Algorithm for solving traveling salesman problems. Include a detailed description of the algorithm, at least two carefully worked out and explained examples, and a comparison between this algorithm and the Nearest-Neighbor algorithm that we covered in class.
• Make a functional slide rule (there are lots of instructions around on the web). Write a page or two explaining how the slide rule works (that is, its relation to logarithms, etc.). Include several worked out examples of how to use the slide rule to multiply and divide both large and small numbers. You can optionally include more advanced uses if you like. (You can keep the slide rule you make, but you must show it to me.)
• Do the Kruskal-Steiner Fiber-Optic Cable Network Project described on page 268-270 of the text.
• Investigate Penrose Tilings, which are an aperiodic tiling, sort of like a wallpaper pattern which never repeats. Explain how Penrose tilings are made, and include a discussion between them, the golden ratio, and quasicrystals.
• Find real-world examples of all seven of the border symmetry types of pattern we discussed, and all 17 of the wallpaper symmetry types. You can use the flowchart on p.406-7 to help you classify them. Make sure you explain why each of your 24 examples corresponds to the selected symmetry types. (Note that some of these patterns will be very hard to find.)
• Investigate and explain Envy-Free division algorithms (see p. 126 of your text). Include a detailed description and several worked out examples.

A reminder:
Plagiarism is simply the use of others' words and/or ideas without clearly acknowledging their source. As students, you are learning about other people's ideas in your course texts, your instructors' lectures, in-class discussions, and when doing your own research. When you incorporate those words and ideas into your own work, it is of the utmost importance that you give credit where it is due. Plagiarism, intentional or unintentional, is considered academic dishonesty and all instances will be reported to the Academic Judiciary. To avoid plagiarism, you must give the original author credit whenever you use another person's ideas, opinions, drawings, or theories as well as any facts or any other pieces of information that are not common knowledge. Additionally quotations of another person's actual spoken or written words; or a close paraphrasing of another person's spoken or written words must also be referenced. Accurately citing all sources and putting direct quotations of even a few key words in quotation marks are required. For further information on plagiarism and the policies regarding academic dishonesty go to the Academic Judiciary website.