Math 110 - Fall 2004
Discovering in Mathematics

Class Schedule: TR 10:20-11:45 am - Emerson 001

Final Project. For your final project, you should submit results of your research on a mathematics-related topic of your choice. The project should be in the form of a poster, a paper, or a product. In all cases, your project should include a written page properly crediting all sources used in your research. All forms of projects should also include original text, written by yourself. I don't want to know what someone else learned, I want to know what you learned from your research.

The final project is worth 40 points and is due before the final exam on December 14. Three bonus points will be awarded to your project if it is submitted before midnight on the last day of class, December 10.

Ideas for possible topics were discussed in class last Tuesday. If you didn't make it to class that day, you should come and see me, or talk to classmates. If you are having trouble thinking of a topic, come see me. I have lots of ideas.

Tessellation Project. For your first large project this semester, you will create a full poster-size, Escher-style tessellation. Your tesselation should be your original creation and exhibit precision, careful attention to detail, and at least a little bit of color. Your poster should measure between 22" X 14" and 22" X 28". On the back of your poster you should include a small sample tiling of the underlying geometric figure that your tessellation is based on. The Tessellation Project is worth 40 project points and is due in class on Tuesday, November 2 (election day). Late projects will be accepted but will be penalized 10 points for each day late. No projects will be accepted after Friday, Novermber 5.

If you are stumped, you might work thru some of the Escher examples at the Totally Tessellated site. For each example there is a link to printout a worksheet to practice the indicated technique.

We will discuss some of the details each day in class before the due date, but you should take a look at the references on the Totally Tessellated Website. To get an idea what I am thinking about in terms of "Eshcer-style", look particularly at this, this, and this. If you want to get started, go ahead an look in detail at the refences on this site, and check back here for addition links and project information regularly.

Another excellent resource for ideas (and Howtos) on tessellations is Tessellations.org. Particularly take a look at the "Do It Yourself" section. Thanks to Rebecca Novalis for the reference!

For the following problems, reference the links below:
Voting-age population in 2000
The US Population Clock

Work the following problems as hand-in homework. Show the math and explain your solution.

1. Suppose I have started a chain-letter containing a list of 5 names (all my own) and have sent it to you and 4 other people asking each of you to send $5 to the name at the top of the list, remove that name, add your name to the bottom of the list, and send it on to 5 more people. Suppose that no one "breaks the chain" and also that every one in the US eventually receives a copy of the letter before anyone receives a second copy of the letter. (And that no one will ever pay a second time.)
   • How much money will I receive?
   • How much money will you receive?
   • At what level will senders no longer be eligible to receive money?
2. Suppose the current voting-age population is the same as in 2000. If on one day, each student in our class (24) contacted 2 other people to verify their voter registration, and had each of them contact 2 more people on the following day, etc; AND if no eligible voter was contacted twice, how many days would it take for the entire voting-age population of the US to be contacted?

The Chisenbop (Chisanbop) tutorial handed out in class on 9-14 can be found by clicking Basic Computing: Chisenbop. Another tutorial by the same author is The Chisenbop Tutorial. This second tutorial has interactive graphics to help you practice your chisenbop.

Journal Guidelines

1. Record a date and approximate time spent on each journal session.
2. Attempt uncollected problems.
   • Briefly describe problem and/or draw sketch if helpful/required.
   • Record thoughts.
   • Show work on all attempts and show solution (if possible).
   • Classify as easy, not too bad, challenging, or difficult.
   • Record ideas, questions, and thoughts, especially for challenging, and difficult problems.
   • Note who you worked with (if anyone).
3. Attempt extra unassigned problems.
   • Choose problems that interest you.
   • Follow same guidelines as in 2. above.
   • Extra, even-numbered Level 3 and Problem Solving problems which you solve correctly (or address thoroughly) without assistance will earn bonus.
4. Record resources used outside of the book.
   • Internet (include URL).
   • Other books/magazines/films (include title, etc.).
5. Record anything else related to the course that you want.