Revised report due Friday, February 25.

Your **main goal** is to address Question 5 (you may want
to, but do not have to, organize your answer along the lines suggested
by Question 6).

Also address **one** of the following three:

- Questions 7
**and**8;**or** - Question 9 (be sure to read "Visualizing Iteration" after Question 9);
**or** - Question 10 [note that "Question 10" on page 11 has a typographical error, and is printed as "Question 1: 0"].

Revised report due Friday, March 4.

Your **main goal** is to answer the question "For which m
does the set of non-zero squares (mod m) form a cyclic difference set
with (m-1)/2 elements?". Questions 1-3 help you discover this
experimentally. Theoretically, Questions 4-8 help you answer for
which m are there (m-1)/2 distinct non-zero squares, and Questions
9-10 help you answer for which of **those** do we get
cyclic difference sets.

Revised report due Friday, April 1.

Your **main goal** is to answer the question "Which
properties of the parameters*p, q, r, s* determine the symmetry
of the parametric curves

Revised report due Friday, April 8.

Your **main goals** are to:

- Address the issues of primes (mod 4) in Exercises 15 and 16.
(Exercises 13 and 14 are good warmups for this.
You may not be able to prove everything you observe in Exericse 15.)
**AND** - One of the following:
- Address the issues of Euler's simple method for finding primes in Exercises 9, 11, and 12.
(Again, you may not be able to prove everything you observe,
though you can prove at least a few simple observations.)
**OR** - Address the issues of the density of primes in Exercises 19 and 20. (Again, you may not be able to prove everything you observe, for instance a formula for the density of primes, but you can check your answer for reasonableness.)

- Address the issues of Euler's simple method for finding primes in Exercises 9, 11, and 12.
(Again, you may not be able to prove everything you observe,
though you can prove at least a few simple observations.)

Revised report due Wednesday, April 27 (with an automatic extension until Friday, April 29, which is Dead Day) .

Your **main goal** is to answer the question: "What
should the survey-taker do with the results?" In other words, what is
your estimate of the proportion of True Yesses as a function of the
proportion of reported yesses? Answer this in the most general
setting, where the probabilities of answering the real question (dime
lands heads) and the answer to the decoy question being yes (penny
lands heads) are variables.

This is some mixture of Questions 1-3, 8, and 11.

Revised report due Friday, May 6 (last day of finals).

Your **main goal** is to find the chromatic polynomial
of the following three kinds of graphs:

- The complete graph on
*n*vertices; - The path on
*n*vertices; and - The cycle on
*n*vertices.

Structure for these investigations is provided by Questions 1-3, parts of Question 5, and Questions 6-9.

No official revisions, but I encourage you to consult with me as you write your report.

Talk to me in advance so that we can set up a reasonable main goal for you to pursue.

Also note that, **instead** of an optional 7th lab, you
may turn in a re-revision of any of the first six reports, or you may
turn in nothing at all. (See syllabus for how all this
affects your grades.)