Homework assignments
- Doing the assigned homework regularly, seriously, and carefully is
vital to your success in this course. Although your homework is lightly
weighted, you should keep in mind that you can only learn mathematics
by doing problems. This will be crucial for your exam
performance.
- Homework will be
assigned on Thursday and usually be due on
Thursday two weeks later.
- No late homeworks will be accepted.
- IMPORTANT: If you use ANY outside help on an
assignment, then you must acknowledge this. For example
if you talk to anybody but me about the assignment write
down the name and problem number. Similarly if you used
the internet, computer programs or books other than the
textbook.
Failure to acknowledge using the work of somebody else
is plagiarism and will not be tolerated.
- If you use a theorem that was not proven in class
in the solution of a problem, then you must include the
proper statement of the theorem, source where you found
it as well as a complete proof of the theorem and proofs of
any auxiliary results needed in its proof. Should you ever
find yourself in this situation, then you may be on the
wrong path and should consult me.
- Let me know if you have problems with the downloading.
- On the screen pdf files may show poorly,
but if you print them out, it should be quite legible.
- Every assignment will consist of 6 problems.
You need to do any 5 problems to receive full credit.
If you do all 6 problems then only the first 5 problems will
be counted.
- Every problem is worth 4 points, so that the max number of points
per assignment is 20 (without extra credit).
- Please STAPLE your homework and write NEATLY.
If one of the pages of your assignment gets lost, or
I can't read something it's YOUR problem.
The following due dates are tentative. For the
exact due dates always check out the assignments
themselves.
Assignment 1,
due Thursday, September 16.
- 9/14:
Hint on 2: first try this problem on some of the posets you constructed
for problem 1 before attacking it in generality.
- 9/12:
Hint on 3a: first find a poset in which some maximum chain misses
some maximum antichain.
- 9/10:
Problem 6a: investigate the proof of Sperner's theorem closely.
At one stage you should suppose that there are sets A,B in level
(n+1)/2 such that A is in the maximum antichain, but B
isn't. Choose such A,B whose intersection is as large as possible.
- 9/5:
Assignment 1 posted.
-
Assignment 2,
due Tuesday, October 5.
- 10/12:
Solutions to Assignment 2 now on eres.
- 10/12:
everybody got 2 bonus points, since the hint on problem 6a) was wrong.
- 10/7:
The displayed expression in problem 5(a) on assignment 2 was way off
and has been corrected. Nobody attempted this problem.
- 9/27:
the second half of Assignment 2 has now been posted.
- 9/27:
the due date for Assignment 2 has been moved from 9/30 to 10/5.
- 9/21:
#1 on Assignment 2:
You may assume A is a subset of [n] and we are talking
about the colex order of k-subsets of [n]. (Thanks, Hector)
- 9/16:
The first half of Assignment 2 has been posted.
-
Assignment 3,
due Thursday, October 21.
- 10/10:
Assignment 3 has been slightly changed.
- 10/8:
Assignment 3 has now been posted.