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:
Your main goal is to investigate the following:
In particular, address Questions 2 and 3, and either of the following:
Questions 4 and 5 guide you in further analyzing one interesting feature of the distribution of the GCD's, while Question 6 guides you in looking at how the Euclidean algorithm works on Fibonacci numbers.
Note that there is not much to say, theoretically, in Questions 2 and 3; here, you will simply need to analyze data very carefully. You can still make somewhat precise statements about what you can expect. Questions 4-6, however, guide you to proving some interesting things about the Euclidean algorithm.
Your main goal is to answer the question "Which properties of the parametersp, q, r, s determine the symmetry of the parametric curves
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.
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.
Your main goal is to find the chromatic polynomial of the following two kinds of graphs:
This is Questions 7 and 9 (and just a very few parts of Question 5 as warmups). Exercises 4-10 are also good practice with some of the tools you'll need, though these exercises do not directly answer our main questions.
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.)