#ATTENDANCE QUIZ FOR LECTURE 24 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

# Question 1: State the integer partitions of 7

# Answer: 
# {[7],[6,1],[5,2],[4,3],[5,1,1],[4,2,1],[3,3,1],[3,2,2],[4,1,1,1],[3,2,1,1],[2,2,2,1],
# [3,1,1,1,1],[2,2,1,1,1],[2,1,1,1,1,1],[1,1,1,1,1,1,1]}

# Question 2: Write down the set of partitions of 7 into distinct parts and the number of
# integer partitions that are odd. 

# Answer:
# Distinct Parts: {[7],[6,1],[5,2],[4,3],[4,2,1]}
# Odd Parts: {[7], [5,1,1], [3,3,1], [3,1,1,1,1], [1,1,1,1,1,1,1]}
# The number of partitions with only distinct values and the number of partitions with
# only odd values are equal. 

# Question 3: What is the A-Number of this sequence [1,2,3,5,7,11,15,22,30...]?

# Answer: A000041

# Question 4: Who wrote the classic book on the theory of partitions? What is his birth date?

# Answer: The Theory of Partitions was written by George E. Andrews. He was born
# on December 4th, 1938. 

# Question 5: What is the A-Number of this sequence? [1,1,2,2,3,4,5,6,8,10,12,15,18,22..]

# Answer: A000009

# Question 6: What is the A-Number of this sequence? [1,1,1,2,2,3,3,4,5,6,7,9,10,12,14,17...]

# Answer: A003114
# Question 7: Whose theorem is it that these two above sequences are the same? 

# Answer: Rogers-Ramanujan Identity

# Question 8: What is the A-Number of this sequence? [6,27,98, 315, 913, 2462...]

# Answer: A071734

# Question 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? What is the A-Number? 
# (ii) Does there exist a k between 0 and 9 such that seq(pn(10*n+k)/10,n=1..60); is an
# integer sequence? What is the A-Number? 

# Big Open Problem: Can you find other A and B such that pn(A*n+B)/A is always an integer
# sequence. 

# Answer:
# (i) k = 5 yields an integer sequence. It is A071746 in the OEIS. 
# (ii) There exist no k between 0 and 9 such that the command yields an integer sequence.

# Question 10: 
# Why should Dr. Z. from now on make you watch the lectures before the recitation? 

# Answer: Students can come in with questions from watching the lectures, so it 
# makes the recitations more helpful. Dr. Z. is also able to elaborate and explain 
# concepts that students are confused about from the lectures.