Math 2325 Intro to Higher Math -- Assignments

Spring 2003

Dr. Duval

Chapter 1, Linear Iteration

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"].

Chapter 2, Cyclic Difference Sets

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.

Chapter 3, Euclidean Algorithm

Consider Questions 1,2, and 6; and either Questions 3,4, and 5, or Question 7.

Chapter 7, Polyhedra

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.]

Chapter 8, p-adic numbers

Report due Thursday, April 17.
Revised report due Tuesday, April 29.

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.]

Chapter 11, Sequences and series

Report due Thursday, May 1.
Revised report due Friday, May 9

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).

Optional lab of your choosing

You may turn in the first draft at any time until Friday, May 9. If you want to have a chance to revise your report, you must turn it in with sufficient time for me to grade it, and return it to you, and for you to then submit the revision by Friday, May 9. Allow a minimum of two days for me to grade your initial report.