Math 386: Combinatorics: Schedule

Fall 2016
Tom Zaslavsky


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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, F 9/23 M 9/26:
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 –
  Tu 9/27
  W 9/28
Ch. 5, all;
M 9/26 Tu 9/27
W 9/28: §6
Binomial coefficients;
Partially ordered sets
Tu 9/27 W 9/28
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
Tu 10/25 W 10/26: Ch. 6, ## 35, 36, 37;
Ch. 7, ## 1(a,c), 3(b), 8, 9.
HW 8, F 10/28 M 10/31: Ch. 6, ## 37, 40;
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.
NEW: 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 Tu 11/1 W 11/2: Ch. 7, ## 13(a-c), 14(b,d), 15, 17, 22, 24(b,d), 25. 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 §8.4 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     —  
FINAL EXAM
    12:50–2:50 in SW-102       Comprehensive


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