Math 386: Combinatorics Homework Assignments

Fall 2005


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General Advice
on homework problems

Besides finding the answer, always try to explain, as well as you can, how you know you have the correct answer.

When solving problems, a systematic solution is better than guesswork. You often may find a solution by intelligent guessing, but then you should look for a way of showing that your solution is correct. This part needs to be systematic if it is to be completely convincing. (This will be clearer after a few days of class!)

Allow 15 minutes per problem (minimum) before you give up, even if you feel you're getting nowhere. These problems need time for thought. If you're still stuck, go on to another problem. Return to the sticky problem later (say, the next day). Often, it then looks easier because you tried hard the first time and then gave your mind time to grind it up – I mean, to come up with ideas. To get the advantage of this method, you have to start the problems well ahead of time. Last-minute effort will not work well in this class.

Rules for hand-in homework.

  1. Hand in a final draft: neat work that is well organized and not cramped. Use as much space as you need. Please also leave some extra space between problems for my comments.
  2. You may discuss hand-in HW with other people, but you must write it up in your own words.
  3. No little stubbies from tearing a page out of your binder. Remove them neatly, please!
  4. Fasten the pages securely. Staples are best. Folding the paper over and/or tearing it is no good (not secure); paper clips don't hold well.


HOMEWORK I (8/29)

Due Wed., 8/31:
Read Ch. 1 intro and Sect. 1.1.
Do (for class discussion) Ch. 1, ## 1-3.

Due Thurs., 9/1:
Read Sect. 1.2.
Do Ch. 1, ## 5, 8.

Due Fri., 9/2:
Read Sect. (especially about fault lines), 1.3.
Do Ch. 1, ## 12, 22, 26.

Hand in Fri. 9/2: Ch. 1, ## 4(a), 9, 10, 11.


HOMEWORK II (8/29)

Due Wed. 9/7:
Read Sect. 3.1.

Due Thurs. 9/8:
Do Ch. 1, ## 16, 19.
Do Ch. 3, ## 1-3, 4(a,b), 5(a).

Hand in Fri., 9/9:
Ch. 1, ## 7, 15, 27.
Ch. 3, ## 4(c), 6.


HOMEWORK III (8/29)

Read Sects. 3.2-3.3.

Do for discussion on
Wed. 9/14: Ch. 3, ## 8-10, 13.
Thurs. 9/15: Ch. 3, ## 11, 12, 16.

Hand in Fri. 9/16: Ch. 3, ## 5(b), 14, 15.


HOMEWORK IV (9/16)

Read for Mon., 9/19: Sects. 3.4-3.5.

Do for discussion on
Wed., 9/21: Ch. 3, ## 17, 18, 20, 27, 31, 32, 39(a,b), 45(a).
Thurs., 9/22: Ch. 3, ## 29, 30, 36, 38, 43, 45(b,c).

Hand in Thurs., 9/22: Ch. 3, ## 26, 39(c).

Hand in Fri., 9/23: Ch. 3, ## 19, 33, 42, 44).


HOMEWORK V (9/28)

Read for Thurs., 9/29: Sects. 5.1, 5.2.

Read for Fri., 9/30: Sect. 5.3 to the middle of p. 136.

Do for discussion on
Fri., 9/30: Ch. 5, ## 1-4, 7, 15, 16, 19.
Thurs., 10/6: Ch. 5, ## 5, 8, 17, 21, 23, and A1.

Hand in Mon., 10/10: Ch. 5, ## 6, 9, 10, 11, 14. (In #14, assume that k ≥ 0, but don't assume k ≤ r.)


Problem Set A


HOMEWORK VI (Corrected) (10/10)

Read for Wed., 10/12: Read Sect. 5.4 to p. 140; Sect. 5.5.

Do for discussion on
Wed., 10/12: Ch. 5, ## 13, 22, 40, and B1.
Fri., 10/14: Ch. 5, ## 42, B3.

Hand in Mon., 10/17: Ch. 5, ## 20, 24, 41, and B2, B4.


Problem Set B


HOMEWORK VII (10/14)

For Mon., 10/17: Read Sect. 5.4.

Do for discussion on
Wed., 10/19:
Ch. 5, ## 17, 25, 31, 35 (for n = 2,3,4), 36, 38.
Thurs., 10/20:
Ch. 5, ## 23, 32, 34, 35 (for n = 5).

Hand in Fri., 10/21:
Ch. 5, ## 33, 35 (for all n), and C1.


Problem Set C


HOMEWORK VIII (10/14)

For Mon., 10/24: Read Sections 6.1-6.2.

Do for discussion on
Wed., 10/26: Ch. 6, ## 1, 3, 4, 7, and # D1.
Thurs., 10/27: Ch. 6, ## 8, 9, and # D2(a).

Hand in Fri., 10/28: Ch. 6, ## 2, 5, and ## D2(b), D3.


Problem Set D


HOMEWORK IX (11/2)

For Thurs., 11/3: Read Sections 6.3-6.4.
Do for discussion on
Fri. 11/4: Ch. 6, ## 10, 11, 16, 21, 24(a).
Mon. 11/5: Ch. 6, ## 12, 15, 17, 19, 24(b), 26.


HOMEWORK SET X (11/2)

For Wed. 11/9: Read Section 2.1 (omit Application 6).

Do for discussion on
Fri. 11/11: Ch. 2, ## 1, 4, 5, 7.

Hand in Mon. 11/14:
Ch. 6, ## 13, 14, 24(c), 30.
Ch. 2, ## 1 (for k = 23), 10.


HOMEWORK SET XI (11/2)

For Mon., 11/14: Read Section 2.2.

Do for discussion on:
Wed. 11/16: Ch. 2, ## 2, 3, 8, 14.
Thurs. 11/17: ## 9, 11, 13, 16 (see
correction), 18.

Hand in Mon. 11/21: Ch. 2, ## 1 (for k = 24), 6, 15, 17, 19.


HOMEWORK SET XII (11/21)

Read Section 10.1 to page 373 and Section 10.4 to page 396.

Hand in Mon. 11/28: Ch. 10, ## 1, 3, 5, 9, 10, 37.

Do for discussion on:
Wed. 11/30: Ch. 10, ## 2, 7, 11, 12, 14(i), 15(i), 38, 39.


HOMEWORK SET XIII (11/28)

Read Section 10.4 to the middle of page 403 (but skip page 400 and the top of page 401).

Do for discussion on:
Wed., 11/30: Ch. 10, ## 13, 14-15(ii,iii), 42, and E1(a,b), E2(a), E3(a).
Thurs., 12/1: Ch. 10, ## 40, 41, 47, and E1(c), E2(b), E3(b).

Hand in Fri., 12/2: Ch. 10, ## 16, 43, and E2(c), E3(c).


Problem Set E


HOMEWORK SET XIV (12/7)

Reading: Finish Section 10.1.

Do for discussion on Fri. 12/9:
Ch. 10, ## 17, 48, and F1, F2, F3 (or F4), F5.


Problem Set F


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