Monday, August 31. 2.1, 2.2. “and C” in Problem 9 on p. 46 is a misprint.
Wednesday, September 2. 2.3. In #3, determine also for “antisymmetric”
Wednesday, September 9. 2.4. Misprints in homework exercises: in #7(a) “…defines an equivalence relation on R”; in #11(a) “…relation on Z\{0}”
Monday, September 14. 2.5
Wednesday, September 16. 5.1.
Monday, September 21. Lecture, and office hours were canceled.
Wednesday, September 23. 5.2
Monday, September 28. Exam 1. No new homework.
Wednesday, September 30. 5.3
Monday, October 5. 6.1
Wednesday, October 7. 6.2
Reminder: next time we meet on Tuesday instead of Monday. Same time, same place.
Tuesday, October 13. 6.3 (n>m in 6.3.2 is not important) Extra credit problem: prove that for every positive integer n, in any sequence of n^2+1 pairwise distinct numbers, one can pick either a strictly decreasing subsequence of length n+1 or a strictly decreasing subsequence of length n+1 (a susbsequence may consist not necessarily of consequent elements, there may be gaps, for example 1,2,5 in 1,13,9,2,5)
Wednesday, October 14. 7.1
Monday, October 19. 7.2. Additional homework problem: you have to move in a city from the intersection A to the intersection B which is 5 blocks North and 8 blocks East. How many different ways are there if you can only drive N or W, and one of the roads is closed? (The answer depends on which road is closed; choose one, and solve for it.)
Wednesday, October 21. Exam 2. No new homework. If you read the book in advance, note that there is a big mistake in Table 7.3 on p. 233 (Find it!)
Monday, October 26. 7.5 . In Table 7.3 in the book, in the intersection of “at most one to a box” and “same”, should stand (n choose r)
Wednesday, October 28. 7.6
Monday, November 2. 7.7
Wednesday, November 4. More examples on 7.7, 9.1 (One of homework problems contains a misprint: vertices must be edges. Additional homework problems: IntroductionToGraphs
Monday, November 9. 9.2
Wednesday, November 11. 9.3. Examine the last pair of graphs in the handout we used in class for isomorphism.
Monday, November 16. 10.1, started 10.2. Homework: 10.1
Wednesday, November 18. 10.2 Additional homework exercise: prove that the graph of the n-dimensional cube is Hamiltonian.
Monday, November 23. 10.3 (When reading this section, you may skip the discussion of matrix multiplication, transforms, etc.; exercises 5 and 7 are optional. Additional exercise: add the missing line in the matrix A in Example 6.) , 11.2 (problems 8(b), (c) are optional.)
Monday, November 30. 12.1
Wednesday, December 2. Exam 2. Homework for the next Monday: 12.1
Monday, December 7. Finished 12.1. Quiz 9. Homework for the next time: read in advance 12.2 (may skip the proof of Theorem 12.2.3)
Wednesday, December 9. Discussion of quiz, 12.2, discussion of the Final
