MA-351 Homework 2

Due at 4:59pm in my mailbox in SAS 3151, Tuesday, October 16, 2018

All solutions must be submitted in hardcopy either to me in class or placed in my mailbox. Note my office hours on my schedule.

1. DMM, §2.3, Problem 13 on page 50 (for digraph (a) of Fig. 2.17 only).

2. DMM, §2.4, Problem 10 on page 59. Note that R' is the transposed of R and × is entry-wise multiplication.

3. DMM §3.6, Problem 13, page 168. Note that your coloring also needs to include the country "11" surrounding countries 1-10.

4. For Problem 1(b) on the first exam (3 states, populations 500, 500, 100 and representatives n = 4, 5, 6, ...), an Alabama Paradox is observed at n = 6. Does there exist a second n for which a paradox is observed? Please explain.

5. Please draw the binary tree (with left-right children distinguished) corresponding to the parenthesis expression (()()())()(())()