Homework assignments

Homework will be assigned on Thursday and be due on Thursday of the following week IN CLASS (unless announced otherwise).
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 Brualdi. Failure to acknowledge using the work of somebody else is plagiarism and will be dealt with harshly.
If you use a BIG 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 are probably on the wrong path and should consult me via email.
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 7 problems. You need to do any 6 problems to receive full credit. If you do all 7 problems then you will not receive credit for problem #7, UNLESS you tell me which one to skip. So please indicate which of the 7 problems you want me not to grade.
Every problem is worth 5 points, so that the max number of points per assignment is 30.
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. I may decide to deduct points for sloppy work on future assignments.
Try all problems, you never know which one is easy -- this is especially true for Combinatorial Arguments.

Assignment 1 is due on Thursday, 1/29.

Remember: Do only 6 out of the 7 problems.
Sorry for the delay in posting assignment 1, but my system was down Thursday night.
#1: Break the board into smaller pieces.
Typo in #2: It should be 30 (instead of 40) and 5x6 (instead of 5x8). This mistake has been fixed above.
#3: This may involve some amount of case analysis. Try to keep it as simple as possible.

Assignment 2 is due on Thursday, 2/05.

Remember to write down who you worked with! I will take of 1pt from now on if you do not specify.
Last reminder: Do only 6 out of the 7 problems.
Advice on PHP questions: first decide what your objects are, then what n is (there should be n+1 objects), and finally explain what the n boxes are and how the PHP leads to the conclusion.

Assignment 3 is due on Thursday, 2/12.

Alternative solution to #2 (by Serena): There are {15 choose 11}=1365 teams altogether.
Of those the ones with 8 line players, {8 choose 8}{7 choose 3}=35 ways,
and the ones with 5 backfield players, {5 choose 5}{10 choose 6}=210 ways, are bad,
leaving 1365-35-210=1120 good teams.
You may assume in 1.a) that r takes values between 0 and n.
#2 through #7a (except 4d): There are several ways of doing many of these, so please give an actual number as an answer AS WELL AS an expression involving factorials and such.
#2: count the number of teams, not the number of formations these teams can make on the field.
#3: It should have been southWESTERN corner, and let's refer to this corner as C.
#3: Just touching a corner of the block under water is OK, but you can't walk along the block.

Assignment 4 is due on Thursday, 2/26.

#1: The approach to e) is quite different to that of a) or b)-d).

Assignment 5 is due on Thursday, 3/04.

#2 is mandatory, but the last part will be graded leniently.
Some of you may have to review some Calculus (like how to multiply power series), so start early!
Some students turn in work that looks more like scratch work than homework. Please use scratch paper while working out a problem and then put it on paper. (Even good students typically do not get the correct solution to most problems on the first attempt.)

Assignment 6 is due on Thursday, 3/11.

#3e) is extra credit.
#6: the notation is different from that used in the book, but it is more standard in the literature.
#7, as it appeared on Friday, will be on next weeks assignment. It has been replaced with the current #7.

Assignment 7 is due on Thursday, 3/18.

The solutions contained some errors, most notably in the displayed equations of 3b) and 5b), as well as the equation of 7a). The fixed solutions are on electronic reserve.
#1: A closed form answer is not needed in b) and d), but in the other two parts your answer should be a number as usual.

Assignment 8 is due on Thursday, 4/8.

If you use any (Fibonacci) identities which we have not proved yet, then YOU must prove it. Of course the identity from the exam counts as proved.
#7: The old #7 has been moved to the next assignment. It has been replaced with a simple, but useful, theoretical question.
1d): The RHS was incorrect (and has been fixed on Wednesday, 3/24).
4b): do that one by applying the recursion repeatedly rather than guessing an answer, and then proving it by induction.

Assignment 9 is due on Thursday, 4/15.

#6a: You can't just divide by A(x) or B(x), since both of them may have constant coefficient 0. Instead argue by contradiction, and focus on the smallest nonzero coefficients.

Assignment 10 is due on Thursday, 4/22.

#7b had a typo which made the problem impossible. The typo has been fixed on the assignment, and this part will be graded VERY leniently.

Assignment 11 is due on TUESday, 5/04, 5:15PM.

If you turn the assignment in at the due date you will get it back graded by 5/6.
If you don't turn the assignment in on the due date, then you may not get it back before the final. You HAVE to turn it in at the beginning of class on 5/6 to receive credit for this assignment.
Questions 1-3 are relevant for Exam 3.