#ATTENDANCE QUIZ FOR LECTURE 14 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p24
#with an attachment called
#p24FirstLast.txt
#(e.g. p24DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Dec. 8, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 10

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER

1. Write down (manually) all the integer partitions of 7.
[7],
[6,1],
[5,2],[5,1,1],
[4,3],[4,2,1],[4,1,1,1],
[3,3,1],[3,2,2],[3,2,1,1],[3,1,1,1,1],
[2,2,2,1],[2,2,1,1,1],[2,1,1,1,1,1],
[1,1,1,1,1,1,1]

2. Write down the set of partitions of 7 into odd distinct parts (again) and set of partitions of 7 into odd parts
[7],
[6,1],
[5,2],[5,1,1],
[4,3],[4,2,1],[4,1,1,1],
[3,3,1],[3,2,2],[3,2,1,1],[3,1,1,1,1],
[2,2,2,1],[2,2,1,1,1],[2,1,1,1,1,1],
[1,1,1,1,1,1,1]

[7],[5,1,1],[3,3,1],[3,1,1,1,1],[1,1,1,1,1,1,1]

3. What is the A number of this sequence?
Sequence: [1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297,385,490,627]
The A number is A000041.

4. Who wrote the classic book on the theory of partitions? What is his birth date?
George Andrews wrote the classic book on the theory of partitions. His birth date is December 4, 1938.

5. What is the A number of this sequence?
Sequence: [1,1,2,2,3,4,5,6,8,10,12,15,18,22,27,32,38,46,54,64]
The A number is A000009.

6. What is the A number of this sequence?
Sequence:[1,1,1,2,2,3,3,4,5,6,7,9,10,12,14,17,19,23,26,31]
The A number is A000607.

7. Whose theorem is it that these above two sequences are the same?
seq(nops(PnD(i,2)),i=1..20);
seq(nops(PnC(i,{1,4},5)),i=1..20);
Euler's theorem.

8. Is this sequence in the OEIS? What is the A number of this sequence if it is?
Sequence: [6,27,98,315,913,2462,6237,15035,34705,77231,166364,348326,710869,1417900,2769730,5308732,9999185,18533944,33845975,60960273]
Yes, the sequence is in the OEIS, the A number is A071734.

9. 
i. Does there exist a k between 0 and 6 such that seq(pn(7*n+k)/7,n=1..60) is an integer sequence?
Yes, for k=5. However, this sequence is not in the OEIS.
ii. Does there exist a k between 0 and 10 such that seq(pn(11*n+k)/11,n=1..60) is an integer sequence? Does it exist in the OEIS? What is the A number if it exists?
Yes, for k=6. This sequences is not in the OEIS.

10. Why (How?) should Dr. Z from now on make you watch the lectures before the recitation?

The class is technically asynchronous so many people choose to watch the lectures when they have the time,
so long as they complete and submit the homework assignments on time.

I think that in order to get students to do the homework before recitations, recitations should be a one-time
weekly 2 hour session held one or two days before the homeworks are due so that students can have enough time
to both watch the lectures and start the assignments. I think some students (including myself) sometimes struggle
to watch the lectures on time because of conflicting class schedules/weekly assignment due dates.

For example, the due date for the previous week's hw is due Sunday night, and the recitation for the current
week's first lecture is held on Monday night, which I don't think is enough time for most people to both watch
the lecture and start the homework, in addition to Monday classes.