# Math 2325 Intro to Higher Math -- Assignments

## Spring 2003

### 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.