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Secret code: § = section, ¶ = paragraph.
Doubling the symbol means plural.
Boldface problem numbers on hand-in homeworks are the ones that were graded.
Asterisked* problems are bonus problems that were graded but not required.
## 8-10(a) means part (a) of each of 8, 9, and 10. ## 8, 10(a) means all of # 8 and part (a) of # 10.
| Date | Reading & Study | Topics | Homework exercises for discussion on |
Hand in on | Notes |
|---|---|---|---|---|---|
| #1 W 8/24 – M 8/29 |
Ch. 1 except §§1.3, 1.5 |
Samples of combinatorics |
W 8/24: The points-lines problem.
F 8/26: Ch. 1, ## 1, 4(a), 10. M 8/29: Ch. 1, ## 13, 15, 22. |
HW 1, W 8/31: Ch. 1, ## 2, 3, 4(b), 7, 11, 14, 24, 25, 29, (37 optional). |
|
| #2 W 8/31 – "M" 9/6 (Tu is "M"!) |
Ch. 2: §1 (for 8/31), §§2–3 (9/2), §§4–6 (9/6) |
Counting principles; Permutations & combinations; Multisets |
"M" 9/6: Ch. 2, ## 1–3, 4(a), 7, 11, 12, 17 (work on these problems before 9/6 and bring questions and answers to the class). W 9/7: ## 21, 28(a), 34. |
HW 2, F 9/9: Ch. 2, ## 4(b,c), 8, 9, 16, 20, 22, 39(a-c), 41, 56. |
|
| #3 F 9/9 – W 9/14 |
Ch. 3, §§1–2 (9/9), §3 (9/12) | Pigeonhole Principle; Ramsey theory |
W 9/14: Ch. 3, ## 1, 2, 7, 9, 14, 19(a). | HW 3, F 9/16:
Ch. 2, ## 28(b), 32, 40; Ch. 3, ## 1, 5, 6, 10, 19(b,c). |
|
| #4 F 9/16 – W 9/21 |
Ch. 4, §§1–2, 5 | More about permutations; Partially ordered sets |
W 9/21:
Ch. 3, # 26;
Ch. 4, ## 1, 2, 6-8(a), 36, 37, 38, 42, 48. |
HW 4, F 9/23:
Ch. 3, # 27; III #3; Ch. 4, ## 6-8(b), 8(c), 10, 39, 43, 45, 47. |
Problems "III": see announcements page. Note correction to #39. We'll discuss 39, 47, et al. in class. |
| #5 F 9/23 – M 10/3 |
Ch. 5, all (§6 for 9/30); permutation patterns |
Binomial coefficients; Partially ordered sets |
M 10/3: Ch. 5, ## 3, 7, 10, 19, 30, 35, 39, III #4, III #6 (work on these problems before 10/3 and bring questions and answers to the class). | HW 5, F 10/7: Ch. 5, ## 6, 8, 11, 13, 16, 20, 23, 25, 32*, 33, III #5, III #7*. | Click to hear what change ringing sounds like. Postpone the proofs of Theorems 5.6.1 and 5.6.2 until later. |
| F 10/7 | Homework review | HW ##1–5 | Any problems you have questions about, including Newton's binomial theorem. | ||
| #6 M 10/10 – M 10/17 |
Ch. 6, §§1-5 10/10: §§1-2 10/12: §§3-5 |
Principle of Inclusion and Exclusion | F 10/14: Ch. 6, ## 1, 3, 4, 7, 11, 17, 21, 24(a). | HW 6, M 10/17:
Ch. 6, ## 5, 9, 10, 13, 14, 16, 26, 33. |
Warning about Thm. 5.5.1 and hints for Ch. 6, #40 (on the announcements page). |
| W 10/19 | Review class | Everything we've done up to §6.4 | Omit § 5.6. | ||
| M 10/24 | Midterm Test I | Everything we've done up to §6.4 | Omit §5.6. | ||
| #7 W 10/26 – F 10/28 |
§6.5 | Permutations with restricted relations | F 10/26: Ch. 6, ## 27, 30, 32. | HW 7, M 10/31: Ch. 6, ## 28, 29, 31. | |
| #8 F 10/28 – M 11/7 |
§§4.5, 5.6, 6.6 (omit pp. 195-198) | Partially ordered sets; Möbius inversion |
Before M 10/31, practice computing Möbius functions: # III.10.
W 11/2, DO IT: # III.10.
M 11/7: Ch. 4, # 47; Ch. 6, ## 34, 36, 37. Hint for # 34: Use the matrix interpretation. |
HW 8, W 11/9:
Ch. 4, ## 48, 50; Ch. 6, ## 35, 38(Π3,Π4), 40. |
Tests will only have simple questions about the Möbius function and Möbius inversion. Read notes on matrices for Möbius function and inversion. Note correction to Ch. 4, #50. |
| #9 W 11/9 – M 11/14 |
§§7.1–7.2 | Number sequences; Generating functions |
M 11/14: Ch. 7, ## 1(a,c), 2, 3(b), 4, 8. | HW 9, W 11/16: Ch. 7, ## 1(d), 2, 3(c), 5, 6, 9, 10, 11. |
|
| #10 W 11/16 – M 11/21 |
§§7.4–5 | Linear recurrence relations | M 11/21: Ch. 7, ## 13(a-c), 14(b,d), 15, 17, 19, 22, 31, 33, 42. | HW 10, M 11/28: Ch. 7, ## 13(e), 14(a,c,e), 18, 20, 34, 35, 44, 45. |
Linear r.r. have two solution methods. One uses g.f., the other does not. Learn both! See "Supplements" to Section 7.5, for non-homogeneous recurrence relations of the kind in §7.5. Corrections for p. 245 and p. 246. |
| M 11/28 | Review class | Everything we've done since Midterm I; and everything on posets. | |||
| W 11/30 | Midterm Test II | Everything we've done since Midterm I; and everything on posets. | |||
| #11 F 12/2 – W 12/7 |
§§10.1, 10.4 | Latin squares | M 12/5: Ch. 10, ## 10, 12, 17(a,c), 41, 42. | HW 11 (or "12"), W 12/7: Ch. 10, ## 11, 13, 17(d,f), 43. | §10.1: Omit GCD's, except easy ones like gcd(4,10).
Omit the block designs on pp. 381–384. |
| #12 W 12/7 – F 12/9 |
§10.4 | Affine planes | F 12/9: Ch. 10, ## 44, 52, 54, 61. | — | |
| M 12/12 | — | 5:40–7:40 p.m. in CW 107 | Comprehensive; but no Latin rectangles. (Expect P.I.E.) | ||
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