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All written homework assignments must be handed in at the beginning of class.
Discussion problems are for class discussion, or for a student to present a complete or partial solution at the board, followed by class discussion.
Everyone should be prepared to discuss at least one of these problems, preferably more than one. Discussion can be about where you had trouble with the problem, or a part of the problem that you have any idea about, not necessarily a solution.
Not-so-secret code: § = section, ¶ = paragraph.
Doubling the symbol means plural.
Boldface problem numbers on hand-in homeworks are the ones that were graded.
MW means separate grades for math (M) and writing (W).
"A" problem numbers are in the Additional Problems.
Asterisked* problems are bonus problems that were graded but not required.
"Br" means readings and problems in the Brualdi book Introductory Combinatorics (see the PDF).
Cameron is marked C when ambiguous.
| Dates | Reading & Study | Topics | For discussion | Hand in | Notes | |
|---|---|---|---|---|---|---|
| 8/21-30 | §§3.1-3 | Basic combinatorial counting methods, with examples | F 8/30: §3.13 # 1, 2, 3(a,c). | HW 1, W 9/4: §3.13 # 3(b,d). |
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| 9/4-6 | Ch. 1; some of Ch. 2 | Interesting counting and other problems | F 9/6: Ch. 1 # 1. Ch. 2 # 7. | HW 2, F 9/6: Ch. 3 # 3(e). |
In Ch. 1, look at the "Sample Problems". In Ch. 2, read only the parts you understand. Some other parts will become understandable as we advance in the book. | |
| 9/9-13 | §§3.5-8 | More combinatorial counting methods | F 9/13: Ch. 3 ## 7, A1, A4, A5. | HW 3, M 9/16: Ch. 3 ## 8-11, A2, A3, A6, and A4, A5. |
We're omitting §§3.4, 3.9, 3.10. (Not 3.8, my error.) Omit Ch. 3 #4 for discussion. | |
| 9/16-20 | §§3.8, 5.1-2 | Ordering; PIE and other inversions | F 9/20: Ch. 3 ## 14(note), A7(N=5), A8(a), A10(a), A12(a). | HW 4, 9/23: Ch. 3 ## 16, A7(N=6,7), A8(b), A9, A10(b), A11, A12(b). | W 9/18: Quiz on recent work (Ch. 3). I've posted the union version of PIE on the announcements page. | |
| 9/23-27 | §§5.3, 5.5 | Stirling numbers! & permutations | F 9/27: Ch. 5 ## 1, 11(a), A14(n=5), A15, A17(a,c). | HW 5, 9/30: Ch. 5 ## 3(a-c)(d), 4, 8, A13, A14, A16, A17(b)(d: optional). | Omit statement of (5.2.1) and all of (5.2.2), (5.2.3). A14 grading: I looked only for correct Stirling number or recurrence. | |
| 9/30 | §§4.0-1, Br§§7.0-1 | Recurrences & Fibonaccis | M 9/30: Quiz on Ch. 5. Warning! Notation for Fibonacci numbers is different in our two books; the announcements page explains this. | |||
| 10/7,8,9 (Note Tues. 10/8) |
§§4.2-3, Br§§7.2,4 Both cover the same topics. |
Generating functions & recurrences | M 10/7: Ch. 4 ## 1, 9(a i) | HW 6, W 10/9: Ch. 4 ## 2(a)MW, 2(b)MW, 9(a iii), Br§7.7 ## 1(a,b), 8, 13(a-c). | Note the infinite binomial theorem (4.2.1) (also see Brualdi page 234). I will discuss these readings. Brualdi's many examples are helpful. Bring questions. | |
| 10/14 | Review | |||||
| 10/16 | TEST 1 | Everything so far. Sorry about the exam date change. I didn't account for the weird schedule 10/7-11. (It's confusing to professors, too.) | ||||
| 10/18 | §4.5, Br§8.1 | Catalan numbers | No office hours today. Omit Bell numbers in §4.5. | |||
| 10/21-25 | Br§1.4, C§§6.1-3, 6.6 | Latin squares | F 10/25: Br§1.8 # 23. Br§8.6 # 1. | HW 7, M 10/28: Ch. 6 # 1(a: n<4)(b,c). Br§1.8 ## 22, 24. Br§8.6 ## 2, *5. A18(ab,cd,ef). | Br§1.4 is a friendly introduction to Latin squares. Then read Cameron. | |
| 10/28-11/1 | Br§§10.1, 10.4 | Finite fields & orthogonal Latin squares |
HW 8, F 11/8: Br§10.5 ## 37, 39, 42, 55, 60 (read 58-59). | In Br§10.4, omit anything about BIBD's. | ||
| 11/4-8 | C§§9.1-3 | Finite fields, vector spaces, affine & projective planes | W 11/13: A19(i-iii)(a), A21. | HW 9, F 11/15: A19(i-iii)(b), A20, A22. | F 11/8: In §9.2 omit matrices except the reduced echelon forms. Omit proofs of (9.2.3)-(9.2.5). In §9.3, focus on planes, not higher dimensions. Post-test for Test 1 (optional), about 2/3 hour at end of class. | |
| 11/11-15 | C§9.5, §§8.1-2 | Projective and affine planes; Steiner triple systems | HW 10, W 11/20: Ch. 8, ## 3(n=7), 7, 8, 9. | We've gone over much of §9.5 last week and §8.4 this week. | ||
| 11/18-22 | §8.4; Ch. 7 to §7.2, Br§5.3 | Packing vs. covering; Sperner theory |
W 11/20: Br§5.7 ## 19, 30. | HW 11, F 11/22: Br§5.7 ## 13, 31, 35. | ||
| 11/25 | Review | |||||
| 11/26 | TEST 2 | It covers everything we've done since Test 1 (except the problem of likes and dislikes in class Friday). | ||||
| 12/2-4 | Br§§3.1, 3.3(to top of p. 80) | Pigeonhole Principle; Ramsey's Theorem | W 12/4: Br§3.4 ## 4, 5, 16. General review. | Omit Applications 3-6 in Br§3.1. Quiz 12/4 on Ramsey's Theorem. | ||
| W 12/11 | — | REVIEW SESSION | 2:00–4:00 in WH-309 | Bring your questions and comments. That's what a review session is for! | ||
| F 12/13 | — | 8-10 a.m. in FA 241 | Comprehensive. | |||
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