It has been a long week since last Tuesday. Starting with an analysis exam on Wednesday, then some crazy combinatorics homework assigned on Wednesday and due on Friday, and of course algebra homework that was due on Friday. Then to make things interesting we got more combinatorics homework assigned on Friday to be due today!
The analysis exam went pretty well. I got a 93 and the median score was a 78. I probably should have received a perfect score, since the only comment on the problem I missed points on was that I needed to justify a statement that followed pretty trivially from the assumption that I made, there wasn’t much space to write the solution in so things were pretty squeezed in there so he probably missed my assumption, but it isn’t really worth arguing over.
The crazy combinatorics homework was a pretty strange assignment. Some of the problems required about 1 line for a complete solution. And then there was the two problems that a lot of people didn’t bother to do. The first one wasn’t very difficult conceptually, but my proof took a whole page to write up. The second one was to find the number of k-length chains in the symmetric chain partition of the power set of a set with cardinality N. It was as simple as counting the number of chains longer than k-1 and subtracting the number of chains longer than k, but the method of counting the number of k+1 chains wasn’t intuitive to me at all.
I am still really enjoying the algebra class. It seems like that is the only class were I really feel like I am playing by a defined set of rules. A lot of times in analysis I find myself using informal arguments to try and figure out where I need to be heading in the proofs. And combinatorics a lot of times just seems like a big bunch of hand waving. At least with algebra the definitions are all set out and you just have to manipulate things according to the rules.