Homework #1, due Friday, April 11
Section 5.1, problems 18,22,26 (don't bother commenting on the answers given, just find the correct answer),35,36,46
Section 5.2, problems 4,7,9,24,30,36 (again,for 30, just find the right answer)
Section 5.3, problems 2,10,14,16,28,3120,24,30
Solutions
Homework #2, due Friday, April 18
Section 5.3, problems 9,16,23
Section 5.4, problems 2,10,12,16,22,37
Section 5.5, problems 1,3c,3d,14abc,19,
Section 6.1, problems 2ace,4bc,14ab,19,23 (hint for 19: instead of counting increasing sequences of integers c1 <= c2 <= c3 <= c4 <= c5, think about counting sequences of integers d1,d2,d3,d4,d5,d6 where d1 = c1, d2 = c2 - c1, ..., d5 = c5 - c4, d6 = 20 - c5.)
Solutions (small typo in 5.4.12 corrected)
Homework #3, due Friday, April 25
Section 6.2, problems 6,8,18,22,24
Section 6.3, problems 2,6,11,12,16
(Hints for 6.3: for #6, a distribution of r balls into 3 identical boxes is the same as a partition of r into at most 3 parts. Given such a partition of r, consider the conjugate partition. For #11, consider all partitions of r into k parts, and separate them into those that have a 1 in them, and those that have parts all of size at least 2. For #16, consider a partition of 2r+k into r+k parts and think about what happens when you subtract 1 from each integer in the partition.)
Section 6.4, problems 4,8,13,17,20 (clarification on 20: n is fixed. Suppose we have r distinct objects; we want to count the number of ways of choosing any possible subset of the r objects and then stacking them into n distinct boxes -- stacking them in the boxes implies that the order in which they are placed matters.)
Solutions (typo in solution to 6.2.18b and solution to 6.3.6 fixed)
Homework #4, not to be turned in, but recommended as preparation for the midterm
Section 7.1, problems 2,4,6,16,18,20
Section 7.3, problems 1,2,3,6,7
Section 7.4, problems 1,2,5,10,12
Solutions
Midterm #1 from Winter 2008 (warning: does not include material from chapter 7)
Solutions
Actual midterm
Solutions
Homework #5, due Friday, May 9, 2008
Section 7.5, problems 3,8,13,15
Section 8.1, problem 30
Section 8.2, problems 4,6,18,34,40
Solutions
Homework #6, due Friday, May 16, 2008
Section 1.1, problems 2,3,16,22
Section 1.2, problems 2 (remember a directed graph can have an edge going from A to B and an edge going from B to A), 6bce, 8, 10
Section 1.3, problems 3,7,8,13,15 (hint: if G is connected, obviously the graph obtained by adding the edge (x,y) is still connected. For the converse, it is easier to assume that G is disconnected and show that the graph obtained from adding the edge (x,y) is still disconnected.)
Solutions
Homework #7, due Friday, May 23, 2008
Section 1.4, problems 5,6,7aceg,8,10abcd,15a,16,18a,27
Solutions
Homework #8, due Friday, May 30, 2008
Section 2.1, problems 1,2,3,10,16
Section 2.2, problems 3,4bdgp,9a,16
Section 2.3, problems 1abefn,2,4,6ab
Solutions
Homework #9, due Friday, June 6, 2008
Section 2.4, problems 4,5,14ace
Section 4.3, problems 2bc,7,8,14,15
Solutions