You may consider any of the questions, but be sure to at least address Questions 6-8, and at least one of Questions 9 and 10 [note that "Question 10" on page 11 has a typographical error, and is printed as "Question 1: 0"].
Consider Questions 1-3 (in short, "For which m does the set of non-zero squares (mod m) form a cyclic difference set with (m-1)/2 elements?"). 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.
Consider Questions 1,2, and 6; and either Questions 3,4, and 5, or Question 7.
Consider Questions 3, and 4; also consider either Questions 6, first part of 7 (ignore "area"), and 9, OR Questions 5, 7 (all of it), and 8. [The 6-7-9 option is more combinatorial; the 5-7-8 option is more geometric.]
Consider Exercise 3 and Questions 3 and 4. Also consider either Exercises 12 and 13, OR Questions 7,8, and 9. [The 12-13 option is more number theoretic; the 7-8-9 option is more geometric.]
Consider Exercises 10 and 11 and Questions 1, 2, 3abc. Also consider Question 4, which is pretty tough (if you answer it completely, it will be worth extra credit). Also, series numbers 2, 5, 7, and 10 from section 11.6; for each one, first conjecture whether or not it converges, and if it does, to what value, and try to prove your conjecture (some will be very hard to prove, others are pretty straightforward, so do what you can, you don't need proofs for all of them for full credit).