Homework, MATH 475, Spring 2005

Homework is from our text (Tucker) unless indicated.
Homework is due at the beginning of class on the day listed.
You are welcome and encouraged to help each other in solving the problems, but for homework which is turned in, you must write your own solutions.
You will usually learn the most if you work on the homework alone before consulting solutions or a classmate.

Homework #1 (Thurs. Feb. 3)
1.1:   4,9,25(iii)ab
1.2:   6ab
1.3:   1b,2,6,12
1.4:   8,24,27a

When you must decide if two graphs are isomorphic (as in 1.2.6ab above), do one of two things. (i) If the graphs are isomorphic, give the one-one correspondence between vertices of the two graphs which defines the isomorphism. (ii) If the graphs are not isomorphic, then prove this. Usually this will require describing a property which is invariant under isomorphism (such as the number of edges, or the number of vertices of degree 2) on which the two graphs do not agree.

Homework Assignment #2 (Thurs. Feb. 10)
Ch. 1 Suppl. Ex: 20, 25a
2.1:   10, 18a (you can assume the result of prob. 12), 19ac
2.2:   16 [there is a quick proof -- don't do a lot of cases], 22
2.3:   12
2.4:   2

Homework Assignment #3 (Thurs. Feb. 17)
3.1:   1ab, 2, 10, 16, 30 (read 5, 14)
3.2:   4, 6 [you may use Ex. 3.1.5], 16a [at the beginning the 8 quart pitcher is full and the others are empty], 24, 26, 27
3.3:   5, 7ac (show logic! answer is in the back)

Homework Assignment #4 (Thurs. Feb. 24)
3.4: 1,2,10a
4.1: 2a
4.2: 3, 6, 14c, 15b

Homework Assignment #5 (Thursday March 10)
4.3: 2abc, 8
4.4: 1,2,6,9,10,13

Homework Assignment #6 (Tuesday March 15)
5.1: 2,6,8a,10,15,20,30,34,40, 42(just 8x8)

Homework Assignment #7 (Tuesday April 5)
5.2: 1,2,4,5,8,12,16cd,17,28,34,56,64,66
5.3: 2,3,4,10,12,20

Homework Assignment #8 (Thursday April 14)
(Briefly explain solutions, especially if the answer is in the back of the book. For problems with answers in the book, you'll do best to find your own solution before you check in the back of the book.)
5.4: 3, 7, 10, 14, 34, 54, 58, 61
5.5: 7, 13, 14ae, 19
5.6: 1

Homework Assignment #9 (Thursday April 21)
6.1: 2a, 4, 14a, 16, 18a, 26a
6.2: 2, 4, 14, 18, 22
6.3: 1a, 2, 5, 18
6.4: 1,2,10
6.5: 6

Homework Assignment #10 (Tuesday April 26)
NOTE! Justify your solutions, especially if the final answer is given in the back of the book.
7.1: 2ab, 5, 20, 26, 27c, 31

Homework Assignment #11 (Tuesday May 3)
NOTE! Justify your solutions, especially if the final answer is given in the back of the book.
7.2: 1ac, 7
7.3: 3a, 10, 11
7.4: 6
7.5: 1b

Homework Assignment #12 (Tuesday May 10 )
NOTE! Justify your solutions, especially if the final answer is given in the back of the book.
8.1: 8, 12, 25
8.2: 1, 4, 5, 7, 25, 30