On Monday, we started on Set Theory in our Proofs class. As a short primer, here goes:
A set is a collection of objects. It can be defined by a list, like {1, 2, 3}, or by a rule, like "numbers between 1 and 3, inclusive."The basic set operations are union, intersection, and complement. The complement of a set is everything not in that set. The union of two sets is anything in either set. The intersection of two sets is anything that is in both sets. Easy-peasy.
There are properties that define various things about these operations. For instance, if A is a subset of B, every element in A is also in B (just like it sounds), and if A = B, that means that A is a subset of B and B is a subset of A (again, just like it sounds).
So on Monday, we were introduced to these concepts. We did one small proof, and then we were told we'd have a quiz Wednesday. I didn't really have time to study for this quiz or anything, so I didn't.
Quizzes in our class are designed to take about 35 minutes. They typically consist of some questions (including a "short essay" where you write a few sentences about something) and some proofs. This quiz was no different. In addition to a short essay and a definition question, it had 3 proofs for us to write.
When I saw what we had to prove, I probably literally paled, because I thought there was just no way I could do them. They were actually pretty simple relative to the realm of set theory proofs, but having never done a single one of those on my own (in recent years, at least), I was nonplussed.
Nevertheless, I started working on them. After I had finished one of the three, Dr. Johnson noted that only I and one other person were still working. I started the second one and the other guy turned in his paper.
"I can go out in the hall," I said.
"No, it's OK, we'll wait," said Dr. Johnson. Then, "Wait, how much more do you have to do?"
"At least a proof and a half!" I said, perhaps somewhat obstreperously.
So he had me go into the hall. With my second proof done, I had completely filled up the back of the paper the quiz was printed on, and had only the tiny spaces between questions on the front side to write my third proof in. I contemplated interrupting the class for more paper, but decided against it. So I ended up writing the third proof in the space under where it was written. I used it as two columns and, instead of writing statements and reasons separately, I put the reasons in brackets after the statements. And I wrote really small. And I barely fit it into the space.
When I turned in my quiz, I noticed that the backs of all the other quizzes that I could see were...blank.
So either the other people in my class have some amazing proof-writing mojo that lets them write a 20-line proof in 4 or 5 lines, or the majority didn't really try the proofs at all. I will find out on Monday. I suspect he's going to have to make this quiz extra credit or something; I doubt he will actually flunk the entire class.
3 comments:
It's kind of strange that Dr. Johnson didn't appear to see anything weird in the quick return of quizzes from people with blank papers... (Is it just me or is anyone else reading this picturing Dr. Johnson as the famous dictionary writer and kicker-of-stones Samuel Johnson, frequently referred to as Dr Johnson? I am now imagining Samuel Johnson watching a Broncos game. This is too much.)
(The Broncos game reference is because Dr. Johnson told us he had graded our tests during the Broncos game, hence why he didn't do such a great job with it.)
I kind of mentioned it to him after class, the "why was I so slow" question, at least. He obviously didn't want to talk about it, and kind of put me off with like, "well we'll see about that on Monday" mumbling. But I pressed on and said, "Did other people not do the proofs?" and he admitted the same thought had crossed his mind.
I am very interested in hearing more about this story. It's creepy.
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