anfin’s Blog

. . . we prefer to have perfect square scores in all frames numbered with the square of an even prime.

Proof: The other day, one of the techniques students asked me what classes I was taking. I of course replied that I was taking Spanish and Number Theory. “What’s number theory?” they asked. A completely reasonable question, I thought, and so I said, “It’s basically the theory of integers…for instance we do a lot of stuff with primes.” And then the bright young chemist said something that I couldn’t quite comprehend. He asked, “What are prime numbers anyway?”

I did anyway. Yes that’s right. I started the Putnam this morning and with only one 2 hour break for lunch finished after dark. For those of you who are wondering what in the world the Putnam is, I’ll tell you. The Putnam is a math test given nation wide on the first Saturday of December. It is designed for undergrads and consists of 12 outstandingly difficult questions. How difficult you ask? Well if it’s any indication, the mode score is generally a 0 (in a good year it might be 1). In other words, over half the people that take it get a 0, and what’s worse, the test is out of 120 points instead of 100. Anyway, my goal for the day was to get a 1. It’s possible that I might have assuming the graders are feeling generous, but honestly, I highly doubt it. That’s right I spent my entire day trying to score 1 point on a math test and it probably didn’t happen. In conclusion, don’t you just hate those people who, in the face of the other test-takers saying, “I think I might have started to have the right idea on 1 or 2 of the problems,” walk out of the Putnam telling the professor, “Yeah, well, I really didn’t have time to refine my proof…”

So the appendices of math books normally contain a list of answers to some of the problems in the book, right? Well our discrete math book contains a section entitled, “Lots of Hints and Comments; Some Answers.” Entries include, “The answer is not 20,” “This one is not so simple,” and a picture of a guinea pig. Lovely.

I have now learned that, assuming I ever go to a three hour party during which I drink at a steady rate of one 12 oz. bottle of beer every 30 minutes, I will be seriously imparied after 0.739 hour and I will be legally intoxicated after 1.24 hour. It will then be 6.6 hours after the start of the party before I will legally be able to drive and 8.94 hours before I will no longer be seriously impaired. Finally, my maximum blood alcohol content will be 0.164 g alchohol per 100 mL blood. So now you know what I have learned in my mathematical models class. Now imagine you are a lowly freshman in an introductory Calculus class who has come Math Resource Center to dive into homework, and you hear the upperclassmen in the room deriving such a model. I don’t know about you, but this strikes me as a funny image. The end.

Prove by use of truth tables as many parts of Theorem 6.2 as you can tolerate.