Saturday, January 29, 2011

Harvard MIT Math Tournament travel teams

Our Albany Area Math Circle HMMT travel team names celebrate the contributions of three distinguished researchers from our area:

Charles Proteus Steinmetz 1865-1923

Frank Albert Benford 1883-1948

Katharine Burr Blodgett 1898-1979

Albany Area Math Circle-Steinmetz team

Matthew Babbitt
Ashley Cho
Gurtej Kanwar
Paul Rapoport
Schuyler Smith
Wyatt Smith
Felix Sun
Jay White

Albany Area Math Circle-Benford team

George Gelashvili
Cecilia Holodak
Preston Law
Zubin Mukerjee
Elizabeth Parizh
Gili Rusak
Aniket Tolpadi
Jason Xu

Albany Area Math Circle-Blodgett team

Ryan Cheu
Matt Gu
Satjiv Kanwar
Justina Liu
Isaac Malsky
Luxi Peng
Philip Sun
Laura Tang

Sunday, January 2, 2011

Happy Prime New Year!

Jim Tanton tweets:

If you start to look for other primes that are also average primes, you may stumble into some fascinating conjectures related to various forms of the Goldbach conjecture.

Pat Ballew also blogs about fascinating properties of 2011:

Well, it's the first prime day (the 2nd day of the year 2011) of a prime year that is the sum of a prime number of consecutive primes. In fact, it can be written as the sum of a prime number of consecutive prime numbers in at least two ways. The easy one is 2011 = 661+673+677, the other one that I know takes eleven consecutive primes...find it..I have been told there is not a year that can be expressed as a sum of successive primes in more than two ways for over a thousand more years That, my mathematical readers, is a lot of primes.

2003 was the last prime year, and it had the special property that the sum of its digits was also prime... not true for 2011.

Both 2017 and 2027 will be prime, but only 2027 is expressible as the sum of consecutive primes, but not a prime number of them.2081 is the next year that will be, like 2011, a prime that is the sum of a prime number of consecutive primes. If you forget, I'll remind you on Jan 2nd of that year... guess I better start working on a healthier diet... let's see, that will make me .... WOW, that IS a big number....
So what is the next year that can be expressed as a sum of consecutive primes starting with two... 2 + 3 + 5 + 7 ...... ????

Saturday, January 1, 2011

Albany Area Math Circle honors last year!

As we look forward to a new year ahead, it is fun to look back on the exciting accomplishments for our Albany Area Math Circle in 2010, and to compare those numbers to a decade ago, right before our math circle started up.

In 2010, Albany Area Math Circle students represented 17% of the Distinguished AMC12 Honor Roll students in the state, all the more impressive since the Capital Region only has about 4% of the state's population. As a measure of the impact of our math circle, it is interesting to compare our 2010 results to the results from the AMC12 contests given in 2000 and 2001, right before our math circle started up. Only 4% of the AMC12 Distinguished Honor Roll students in New York State came from our area back then!

Looking at the 2010 USAMO qualifier list paints a similarly impressive picture. Five of New York's 28 USA Math Olympiad (USAMO) qualifiers (18%) were Albany Area Math Circle students in 2010. By contrast, back in 2000 and 2001, before our math circle started up, there was only one USAMO qualifier from our area, 5% of the total number in those years. For almost two decades prior to 2000, there had been zero USAMO qualifiers in our area.

The annual AMC Honor Roll book has just become available here. Screenshots of a few especially noteworthy pages from the book are below:

The excerpt above comes from pages 50-51, which lists the top 5 teams in each of the ten regions in the US and Canada. AAMC was tied for second place team in our region (New York/NJ) in 2010! Back in 2000 and 2001, a composite AMC12 team based on the strongest three students in the Capital District would have been 50 to 60 points behind first place Stuyvesant. This year, our math circle team was only 3 points behind Stuyvesant (and looking only at the AMC12B date contest, our math circle team actually beat Stuyvesant's team by 9 points!)

Pages 57-59 list the top 10 individuals in each of the ten regions in the US and Canada, as well as the top-scoring 9th grader in each region. As you can see from the screenshot above, Albany Area Math Circle had two of the top 10 individuals in our NY-NJ region, and we also had the highest scoring 9th grader in the region!

"But wait, there's more!" (as they say on those late night TV infomercials.) Albany Area Math Circle students placing on the AMC12 Distinguished Honor Roll are highlighted in yellow below (note that some of our members are listed under their schools where they took the tests):

Congratulations as well to all math circle students listed on the AMC12 Honor Roll on pages 91 to 94: Paul Rapaport (Albany Academy), Heidi Chen (Emma Willard), Zubin Mukerjee (Guilderland), Aniket Tolpadi and Jason Xu (Niskayuna), Adam Parower and Gili Rusak (Shaker), Felix Sun (Shendandehoah), and Jay White (homeschooler).

And shout-outs as well to our Upstate New York friends in the Ithaca Math Circle! They are off to an awesome running start! A search on "Ithaca" in the AMC Honor Roll book reveals 18 instances of their students listed on the honor lists. We will have a post highlighting their math circle coming soon.