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.