USAMO and other such stuff

So today Sam, Turcza, Alexey, Gavin, Andy and I had a little party after school to talk about inequalities. I seriously hope there is an inequality on the USAMO next week. I might actually walk away with a point total x x e {s} where s is the set of positive real numbers. Hey look! Set notation!

Honestly, though, I think I might actually get partway through an inequality if one should grace me with its presence. In the last week I’ve learned how to use (effectively) AM-GM, Cauchy-Schwartz, Cauchy-Schwartz II (return of the squares), Nesbit, Jensen, and the Rearrangement Inequality, plus (!) x + 1/x ³ 2. I still have a couple to get to, and then there is the added pain of having to find out how to use them effectively, but anyway, hopefully I’ll get lucky and one will come.

ARML Practice II (return of the mathletes) is also tomorrow. I have all my Homework done, including the evil #10, which is the worst problem in the history of mankind. Also, Math Team State is in a couple of weeks. Our sophomores are looking really strong. We might take top 5 this year.

No track today, and a free day in swimming! Thank goodness! Also, thank goodness for late arrival tomorrow! Happy day!

JB

PS I have another challenge for you all. Complete the following statement:

If you live in a glass house, you shouldn’t _______.

Have fun with it. Don’t give anything boring, like, oh, say, throw stones.

JB