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Secret code: § = section, ¶ = paragraph.
Doubling the symbol means plural.
Date | Reading & Study | Topics | Homework exercises for discussion on |
Hand in on | Notes |
---|---|---|---|---|---|
M 8/29 – W 8/31 | Ch. 1 except §§1.3, 1.5 |
Samples of combinatorics |
M 8/29: The points-lines problem.
Tu 8/30: Ch. 1, ## 1, 4(a), 10, 13, 15, 22. |
HW 1, F 9/2: Ch. 1, ## 2, 3, 4(b), 7, 11, 14, 24, 25, 29, 37. |
See the Day 1 points-lines problem, III #1 in the announcements page. |
Th 9/1 – W 9/7 | Ch. 2, §§1–6 (§§1–3 for Fri) |
The 2 (or 4) counting principles; Permutations & combinations; Multisets |
W 9/7: Ch. 2, ## 1–3, 4(a), 7, 11, 12, 17, 21, 28(a), 34. |
HW 2, F 9/9: Ch. 2, ## 4(b,c), 8, 9, 16, 20, 22, 39, 41, 56. |
|
Th 9/8 – Tu 9/13 | Ch. 3, §§1–2 | Pigeonhole Principle |
Tu 9/13: 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). |
|
W 9/14 – Tu 9/20 | Ch. 4, all M 9/19: §5 |
More about permutations & combinations; Partially ordered sets |
Tu 9/20:
Ch. 3, # 26;
Ch. 4, ## 1, 2, 6-7(a), 11-12(a), 23-24(a), 26, 36, 37, 38. |
HW 4, Ch. 3, # 27; III #2; Ch. 4, ## 6-7(b), 9, 19, 21, 30, 35, 39, 47. |
Problems "III" are on the announcements page. Note correction to #39. |
W 9/21 – W 9/28 |
Ch. 5, all; W 9/28: §6 |
Binomial coefficients; Partially ordered sets |
F9/30: Ch. 5, ## 3, 7, 10, 19, 30, 35, 39, III #3. |
HW 5, W 10/5: Ch. 5, ## 6, 8, 11, 13, 16, 20, 23, 25, 32, 33. | Schedule changes because of cancelled classes on F 9/23 and Tu 9/27. |
W 10/5 – Tu 10/11 |
Ch. 6, §§1-5 F: §§1-3 |
Principle of Inclusion and Exclusion | Tu 10/11: Ch. 6, ## 1, 3, 4, 7, 11, 17, 21, 24(a), 27, 29, 30. | HW 6, F 10/14: Ch. 6, ## 5, 9, 10, 13, 14, 16, 26, 33. | |
F 10/14 – Tu 10/18 | §§4.5, 5.6 | P.o.sets | F 10/14: Ch. 4, ## 42, 47; Ch. 5, ## 35, 48, 50. M 10/17: Test review. |
HW 7, F 10/21: Ch. 4, ## 48, 50; Ch. 5, ## 29, III #4. |
Test 1 is on T 10/18, covering Ch. 1-6 except §6.6. Note correction to Ch. 4, #50. |
F 10/21 – W 10/26 | §§6.6, 7.1 | Möbius inversion; Number sequences |
Ch. 7, ## 1(a,c), 3(b), 8, 9. |
HW 8, Ch. 7, ## 1(d), 2, 3(c), 7, 10, 11(b). |
On tests I will only ask the simplest questions about the Möbius function and Möbius inversion. Notes on matrices for Möbius function and inversion. Warning about Thm. 5.5.1 and hints for Ch. 6, #40: see the announcements page. |
F 10/28 – Tu 11/1 | §§7.2–3 | Generating functions | HW 9, F 11/4: Ch. 7, ## 13(e), 14(c,e), 18, 19, 23, 24(c), 26. | ||
W 11/2 – Tu 11/8 | §§7.4–5 | Linear recurrence relations | Tu 11/8: Ch. 4, ## 38(2 sets), 39(n=2); Ch. 7, ## 21, 33, 37, 38(b,c), 43. |
HW 10, F 11/11: Ch. 4, ## 38, 39; Ch. 7, ## 14(c,e)(now find hn by g.f.), 27, 30, 38(d,e), 40, 41, 42, III.5. |
There are two solution methods. One uses g.f., the other does not. Learn both! See the announcements page, "Supplements" to Section 7.5, for the complete system for solving non-homogeneous recurrence relations of the kind in §7.5. |
W 11/9 – Tu 11/15 | §§7.6, 8.1–2 | Counting sequences: Catalan, Stirling |
Tu 11/15: Ch. 4, ## 40, 51; Ch.7, ## 43, 45, 48(a,c,e); Ch. 8, ## 1-3, 6, 7, 12(a,b), 17, 18(k=5), 19(a). |
See the next line. | |
W 11/16 – M 11/21 | §8.3 |
Counting sequences: integer partitions |
F 11/18: Ch. 8, ## 21(n=1,2,3,4), 26(a). |
HW 11, F 11/18: Ch.7, ## 44, 46; Ch. 8, ## 4, 8, 10, 11, 12(c), 13, 19(b), 22(a), 26(b), 27. |
Test 2 is on T 11/22, covering partially ordered sets, Ch. 7 and §§8.1–3. No questions on §8.4. In §8.3, none on g.f. or the p.o.set of integer partitions. There probably will be a computation of a Möbius function (not hard) and Möbius inversion. |
M 11/28 – Tu 11/29 | §8.4 & circle geometry problem | Cutting up space | Tu 11/29: Ch. 8, ## 28, 31, III.6. |
— | |
W 11/30 – Tu 12/6 | §§8.5, 10.1, 10.4 | Schroeder numbers; Latin squares |
Tu 12/6: Ch. 8, ## 32, 33; Ch. 10, ## 1-2, 10, 14-15(a), 17(a,c). |
HW 12, W 12/7:
Ch. 8, ## 34, 35; Ch. 10, ## 3-4, 11, 12, 13, 14-15(b), 17(d,f), and 41, 42. |
Don't study the proofs of g.f.'s for Schroeder numbers. Don't memorize the g.f.'s. Do read about dissections (end of §8.5). |
W 12/7 – Th 12/8 |
§10.4 | Latin squares; Affine planes |
Th 12/8: Ch. 10, ## 44, 50, 52, 54, 61. |
— | Omit the block designs on pp. 381–384. |
M 12/12 | — | REVIEW SESSION | 12:00–2:00 in WH-329 | Bring your questions and comments.
WH-329 is in the East Wing of the building. Don't go upstairs in the West Wing; you'll be lost. | |
Tu 12/13 | — | 12:50–2:50 in SW-102 | Comprehensive |
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