Albany Area Math Circle

Winter holiday mathematics

2011-12-28T13:04:00.000-08:00

Albany Area Math Circle is taking a brief break from our regular Friday evening meetings, but that doesn't mean we aren't surrounded by wonderful mathematics, so here are some treasures to share with your friends and family members. I would love to hear from other math circle members about interesting mathematical aspects of their cultures. I am sure there are many that I do not know about.

Last night was the last of the eight nights of Hanukkah. There is all sorts of fun math in Hanukkah, such as figuring out how many candles you need in a box to cover all eight nights of Hanukkah, which will be one less than a triangular number. There are many fun combinatorics problems to construct and explore as well. How many different color combinations can be constructed if you have n different colors of candles available?

Today's Albany Times Union had a great mathematics of Hanukkah story, A one-in-trillions dreidel game, about a remarkable string of luck by a first-time dreidel player, who managed to spin the four-sided top 68 consecutive times without ever seeing the losing side come up and winning the entire pot 56 of those spins. This inspired his great-nephew, a Princeton sophomore studying operations research and financial engineering, to pull out his calculator to compute the astronomically large odds against such a long streak of good luck.

There are several ways to model this probability calculation and it would be interesting to discuss the pros and cons of each approach. One simple possibility is to compute the likelihood of never losing in 68 spins, which would be 1 - (3/4)⁶⁸, which works out to 1 in 22.5 trillion. You can make the odds even more astronomical if you also consider the likelihood that he actually wins the pot on 56 of those 68 non-losing spins, because the remaining three sides are equally likely to come up, and only one of those spins yields the entire pot to the spinner.

Of course, this kind of analysis gives rise to interesting philosophical discussions of the sort that physicist Richard Feynman raised in his book, The Meaning of It All: Reflections of a Citizen Scientist, when he talked about the probability of seeing a particular license plate in a parking lot as well as the work of Stanford mathematician Persi Diaconis on the mathematics of coincidences.

Moving onto Christmas, we are currently in the midst of the fabled "Twelve Days of Christmas," as memorialized in the song that starts with one gift given on the first day (December 25, "a partridge in a pear tree"), three gifts given on the second day (December 26, "two turtle doves" plus another "partridge in a pear tree"), and so on through the twelfth day (January 6, which happens to be our next math circle meeting date!)

John Cook at the Endeavor blog has a great post on the mathematics of the Twelve Days of Christmas. He observes that the total number of gifts received each day is a triangular number and also notes that the cumulative number of gifts received through the end of each day is a tetrahedral number. He has written up several nice proofs demonstrating that this is true in general, and he also includes a wonderful link and illustration from the Math is Fun blog.

The Math is Fun blog's illustration at right is a great way to illustrate the triangular/tetrahedral nature of the 12 Days of Christmas song for your younger friends and relatives. The image shows the situation for the first five days of Christmas, with the top layer representing the number of presents given on the first day (1), the next layer representing the number of presents given on the second day (3), the next layer the presents given on the third day (6), the next layer the presents given on the fourth day (10), the next layer the presents given on the fifth day (15). The cumulative number of presents given on the first through fifth day is the number in the entire five layer tetrahedron, or 1+3+6+10+15 = 35. You can extend this indefinitely, of course. If you stop after 12 days, you will have a 12-layer tetrahedron with a cumulative total of 1+3+6+10+15+21+28+36+45+55+66+78 presents, which turns out to be 364, a very nice number, since it is one less than the number of days in a typical year!

Another fun fact to share with your younger friends and relatives: take the number of cumulative gifts received during the 12 days and multiply it by the number of days in 2012 and you get a nice opportunity to discuss factoring differences of squares since 365² - 1² = (365-1)(365+1).

There are wonderful mathematical possibilities to explore in every religion and culture--including the modular arithmetic of the various calendar systems generally designed to reconcile discrepancies between lunar and solar numbering systems, which move many holiday observations around relative to one another. It's also interesting to note the frequency with which calendars in so many widely divergent calendars use a 7-day week. This is mathematically very convenient, since the number nearest to 365.24 with a conveniently large number of factors is 364, which is divisible by 7.

The Hebrew calendar has a 19-year cycle with a leap month in seven of those years. The Islamic calendar has a 30-year cycle with a leap day added to the final month in 11 out of those 30 years. The Gregorian calendar commonly used in the west appears to have a four year cycle with a leap day every four years, but it's actually more complicated than that.

New years festivals are observed at many different times in different calendars, starting with the Jewish new year, Rosh Hashanah, which arrives in early fall. The Hindu new year celebration happens on their festival of lights, Divali, in mid-fall. The Chinese New Year generally comes later in winter than the Gregorian new year on January 1. The early Roman calendar (before Caesar came along and reformed it) began its new year in March, had only ten lunar months, and then had a mysterious unlabeled winter period of 61 day that were apparently not considered to belong to any month. Caesar changed the New Year to January 1, but later Christian rulers moved it to March, before Gregory moved it back to January.

AMC8 honors

2011-12-14T16:00:00.000-08:00

Congratulations to the following students from Albany area schools who achieved national recognition on the very challenging AMC8 contest given last month. Congratulations as well to all the math circle student coaches who have supported and encouraged the students, particularly Zubin Mukerjee, whose satellite middle school math circle had many high scorers again this year.

William Wang, eighth grader at Farnsworth Middle School, was one of four students in the state to manage a rare perfect score. In many years, there are no perfect scores in the entire state of New York. William joins a long list of AAMC students with high scorer in the state plaques on the AMC8, starting with Raju Krishnamoorthy (1998), Drew Besse (2001), Dave Bieber (2004), Andrew Ardito (2004, 2005), Schuyler Smith (2006), Matt Babbitt (2007), and Ziqing (Bill) Dong (2010).

Joining William on the Distinguished Honor Roll are Bill Dong (Farnsworth, 23 points), Alex Wei (Van Antwerp/Niskayuna CSD, 23 points), and Eric Pasquini (Farnsworth, 22 points.)

William, Bill, and Eric had a school team score of 70 points, which ranked Farnsworth third place in the state and earned the school national school honor roll standing. Jeremy Collison from Farnsworth also achieved national Honor Roll recognition with a score of 18 points.

Niskayuna middle school students from Iroquois and Van Antwerp joined forces to rack up a team score of 65 points, ranking 7th place team in the state and earning a spot on the national school Merit Roll list. In addition to Alex Wei, other Niskayuna CSD students earning national Honor Roll status were: Patrick Chi and Liam McGrinder with 21 points, Andrey Ahkmetov, Gideon Schmidt, and Jason Tang with 20 points each, Matthew (Rocket) Ruona with 19 points, Alice Hollocher, Darius Irani, and Vladimir Malcevic with 18 points.

Other teams that made the national Merit Roll list included Bethlehem Middle School with a team score that ranked top 30 in the state. Four of their students also earned individual Honor Roll standing as well: Wenyuan Hou (21 points) Eliot Shekhtman and Iris Zhou (18 points), and Bowen Chen (17 points).

Alex Cao (21 points) and Jeff Shen (19 points), both from Shaker Junior HS and competing on the Albany Area Math Circle team, earned individual national Honor Roll Recognition. Along with the score contributed by tying school bronze winners Gwenda Law (O'Rourke) and Helen Yuan (Shaker), the Albany Area Math Circle team landed on the school Merit Roll as well.

Albany Academies also landed on the national school Merit Roll with a team score of 51 points. Zoe Shannon (18 points) and Joseph Aiello (17 points) earned individual Honor Roll recognition as well.

The following students in sixth grade or below received individual recognition for their scores on the Achievement Roll: Bethlehem MS: Michael Klisiwecz, Isabella Ruud, and Eliot Shekhtman; HACD: Max Benson; Niskayuna CSD: Gregory George and Gabriel Kammer.

All national honor lists are available at this link.

Sign up for our December Math Meet

2011-11-29T11:16:00.001-08:00

Albany Area Math Circle continues our very well-received monthly middle school math meets program again this year. We will be using the Math Meets contest problems written by the always awesome George Reuter, the world famous coach of the Upstate NY Math team.

Congratulations to all the brave students who participated in our October and November math meets! Every question solved added to the team's totals due to the fact that we had less than 10 students in each division!

Shout-outs to our high scorers of the meets: Gwenda and Gabriel (Nov-middle school division); Jeffrrey (Oct-middle school division); Matt B, Matt G, David, and Philip (Nov-hs-no calc division); David, Gideon, and Luxi (Nov-hs calculator division); Alex and Alice (Oct hs-no calc division), Cecilia, Gili, and Matt B (Oct hs calc division).

Congratulations as well to the following perfect scorers: Gili, Matt B, and Zubin (Oct hs-no calc); Matt B, Philip, and Zubin (Nov hs calc); Jerry and Patrick (Oct ms.) (Note: due to a no-duplicate award tradition, perfect scorers are NOT elgible for high scorer of the meet recognition.)

Thanks to all our high school students who have participated as mentors--you DO make a difference in helping "scary math problems" look less scary to the next generation of problem solvers! And your courageous example in tackling tough problems of your own alongside our middle schoolers is inspiring also!

The biggest value of this type of activity comes from the collaborative discussions and reflections afterwards. You can find last year's problems (and solutions!) here. The December math meets problems focus on geometry, so I recommend looking at last year's December math meet problems to prepare for this month's meet.

There are also playbooks with tips and even videos made by Coach Reuter to explain the solutions to last year's problems available here.

Space is limited and advanced signup on the form below is required.

<p>&amp;amp;amp;lt;p&amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;Loading...&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;amp;amp;amp;amp;lt;/p&amp;amp;amp;amp;amp;amp;amp;gt;&amp;amp;amp;lt;/p&amp;amp;amp;gt;</p>

Congratulations to Ms. Schmidt!

2011-11-23T13:33:00.001-08:00

Albany Area Math Circle is beaming with pride to announce that our co-advisor, Alexandra Schmidt, has been recognized as a National Board Certified Teacher.

Alexandra, who teaches at Hebrew Academy of the Capital District, is one of only 50 middle school math teachers in New York to achieve this rigorous professional recognition. She has also been a major contributor to the success of our middle school math outreach program, as well as a supporter and facilitator of many opportunities for our high school students. She was our lead proctor when Albany Area Math Circle hosted the statewide high school math tournament, NYSML, in 2010.

Alexandra Schmidt, NBCT, in her classroom--with her Tough Traveler Albany Area Math Circle advisor bag!

Although her school is a small one, I do not know of any other school in the Capital District that includes more students as fully in their MATHCOUNTS program as Alexandra's MATHCOUNTS program does. She shares my philosophy that the excitement, deep challenges, and collaborative shared Aha! moments of those problems ought to reach as many students as possible, not just a handful of the "top n" students eligible for official competition. I wish all students in the country had teachers as willing to share such engaging challenges with their students.

All students involved in her MATHCOUNTS program (not just the students on the official competition team) get invited to her home for ice cream sundaes with her special homemade fudge to celebrate afterwards. That reflects a belief--which I share as well--that every member of the greater MATHCOUNTS community has a role to play in encouraging and supporting the mathematical and problem solving development of other members of the community.

A graduate of Stanford University, with training and experience as an engineer before she decided to teach mathematics, Alexandra brings a strong awareness of the role that mathematical problem solving and teamwork play in the "real world" to her classroom. She also embodies all that is best about the spirit of generosity of math coaches, helping students everywhere, not just students in her own school. (For more on this spirit, see here and here.) She has also composed her own original problems and contributed them to the greater national problem solving community. MATHCOUNTS chose to highlight those problems as the "Coaches' Problems of the Month" in January 2010. You can find her problems and annotated solutions here. (MATHCOUNTS is happy to accept original problems from students as well as coaches--if you have problems to contribute, check out this link.)

"There are no foolish questions and ...

2011-10-27T10:59:00.000-07:00

no man becomes a fool until he has stopped asking questions" Charles Proteus Steinmetz

Hat tip to the always awesome Pat Ballew for reminding me of this wonderful quote from Charles Steinmetz, the mathematical and electrical "Wizard of Schenectady."

Our PUMaC team "Albany Area Math Circle Steinmetz" fittingly bears his name.

Charles Steinmetz founded the GE research labs (originally in a stable behind his home in the Stockade neighborhood of Schenectady) and also founded the electrical engineering department at Union College, where taught for many years. He also served as President of the Schenectady City School Board (campaigning with a motto of "a seat for every bottom" at a time when the schools were bursting at the seams, requiring double shifts) as well as President of the Schenectady City Council.

His story is a fascinating one--this Smithsonian blog post is a great source. An excerpt:

a brilliant student of mathematics and chemistry at the University of Breslau, but he was forced to flee the country after the authorities became interested in his involvement with the Socialist Party. He arrived at Ellis Island in 1888 and was nearly turned away because he was a dwarf, but an American friend whom Steinmetz was traveling with convinced immigration officials that the young German Ph.D. was a genius whose presence would someday benefit all of America. In just a few years, Steinmetz would prove his American friend right.

Read the Smithsonian article for some of the many great Steinmetz stories. I especially liked the anecdote about the time he went off to trouble-shoot an electrical generator at the nascent Ford Motor Company, and asked for "only a notebook, pencil, and a cot" and then proceeded to spend two straight days "scribbling computations on a notepad" before figuring out a simple solution to Ford's problem. You can also read more about Steinmetz on our blog here.

A willingness to be like Steinmetz--to persevere and think very hard, to try outlandish ideas, to make mistakes, and--above all--to ask questions is the key way that new students can contribute to our math circle. Please be brave about asking questions.

PUMaC team

2011-10-26T21:18:00.000-07:00

I am pleased to announce the eight outstanding students who will represent Albany Area Math Circle at the Princeton University Math Contest (PUMaC) this year:

Matthew Babbitt, heeg
Zubin Mukerjee, Guilderland High School
Wanwan Fei, Emma Willard School
Matt Gu, Guilderland High School
Cecilia Holodak, Niskayuna High School
Preston Law, heeg
Gili Rusak, Shaker High School
Aniket Tolpadi, Niskayuna High School

PUMaC is the most challenging team math competition in which our math circle participates, especially since we compete in the A division, against powerhouse teams from all over the country as well as international teams. We are glad to have a terrific team of very energetic, experienced, and enthusiastic students. Collectively, they have a great deal of experience in other challenging math competitions, including AIME, ARML, HMMT, and Math Prize for Girls.

For past PUMaC adventures see these past blog posts:

Albany Area Math Circle at 2010 PUMaC

Albany Area Math Circle at 2009 PUMaC

Albany Area Math Circle at 2008 PUMaC

The official name of our A-division PUMaC team is Albany Area Math Circle-Steinmetz, in honor of Charles Proteus Steinmetz. You can read more about him in my next post.

Albany Area Math Circle helpers with Math Prize for Girls

2011-09-26T22:11:00.000-07:00

It started with a "stuffing party" at the Union College Kenney Community Center. Thanks to math circle volunteers Sue Bieber, Rita Biswas, Elena Dolginova, Cecilia Holodak, Catherine Miller, Zubin Mukerjee, Elizabeth Parizh; Gili, Michal, and Zvi Rusak, and Alexandra Schmidt as well as Advantage Testing administrator Tina Lesem, hundreds of Math Prize for Girls tote bags got stuffed with pencils, bluebooks, blank answer forms, hats and flowers, copies of the rules and other handouts of Math Prize information.

Gili and Catherine got to be experts at "artisanly fluffing" the fabric flowers.

Of course, hugs and giggles are inevitable when you confront stacks of hundreds of hats.

Alexandra's awesome shirt made the event even more awesome, of course. (If you are wondering how YOU can get a shirt as awesome as hers, you need to know they are not for sale! You have to earn one--by composing and submitting a set of your own cool original problems to MATHCOUNTS. Both coaches and students can submit problems. If yours are selected for their Problems of the Month feature, then you too can have a shirt like Alexandra's. Details are here. And bear in mind that writing your own original problems is a great way to develop your problem solving skills too!)

But I digress ...

A week later Math Prize for Girls happened at MIT--and it was also completely awesome! The expertly and artisanly stuffed bags made the start of the day much smoother this year. The photo at right shows lei-clad proctor Elisse Ghitelman greeting students and handing them bags with everything they would need (except, of course, for the test itself, which she distributed later.)

Later that day, Albany Area Math Circle alumni Gurtej Kanwar, Zagreb Mukerjee, Liz Simon, and Felix Sun, all college students in Cambridge now, helped out in the grading room. The picture below shows Felix with some of the other MIT student volunteers wearing some of those artisanly fluffed flowers clipped to their hats, adding a very cheerful note to the festivities.

Albany Area Math Circle was proud to have four participants in Math Prize for Girls this year--Cecilia Holodak and Elizabeth Parizh from Niskayuna High School, Gili Rusak from Shaker, and Wanwan Fei from Emma Willard. It was a bit crowded and chaotic after the ceremony, so we did not manage to get a photo with all our contestants and volunteers, but we did manage to get Felix, Elizabeth, Cecilia, Wanwan, and myself (with my own artisanly fluffed flower!) into a photo here:

A special note of thanks to Albany Area Math Circle advisor, Rita Biswas, who drove all the stuffed tote bags to Cambridge, and then spent three days with us making sure that countless details of Math Prize 2011 went smoothly!

Math Circle alum wins Harvard Social Studies essay prize

2011-09-03T11:24:00.000-07:00

In yet another demonstration of the "Do math and you can do anything!" motto, a shout-out of congratulations goes to Albany Area Math Circle alumnus Zagreb Mukerjee.

Zagreb (shown above with a middle school math circle he led during his high school years) is now a junior at Harvard concentrating in Social Studies, a unique all-honors program which requires a great deal of independent research and analytical writing.

Last week, the Harvard Social Studies department announced that Zagreb was a winner of the Mill-Taylor prize for his epistemological essay titled Utilitarianism and its Discontents.

MILL-TAYLOR PRIZE The Mill-Taylor Prize is awarded for the two best Social Studies 10 essays written by any sophomore concentrating in Social Studies. The prize is given out at the beginning of the junior year.

The apparent moral of the story: if you can explain advanced mathematics clearly enough to excite eager and enthusiastic young students, then writing an expository analytical essay on epistemology is a piece of cake.

Albany Area Math Circle student off to Russia

2011-09-03T11:10:00.000-07:00

Congratulations to Wyatt Smith, an Albany Area Math Circle rising senior, who has demonstrated once again that our math circle students excel in a broad variety of domains.

Eleventh-grader Wyatt Smith of Clifton Park was the winner of the second annual Albany-Tula Alliance Student Essay Contest.

Smith will be traveling to Russia in September 2011 with a chaperone from the Albany-Tula Alliance for a two week stay in Tula. There he and two other contest winners will meet with other students and have an opportunity to attend classes at Lev Tolstoy Tula State Pedagogical Institute.

In this year's competition, which took place in February, students ages 16 to 18 submitted 1,500 word essays on the role that the space race might play in maintaining world peace and technological cooperation.

Albany Area Math Circle in Ghana!

2011-07-21T10:37:00.000-07:00

Albany Area Math Circle advisor Bill Babbitt has just returned from a trip to Ghana where he was part of a team headed up by RPI Professor Ron Eglash. There, they worked with students at Ayeduasi School, using software they had developed to introduce the mathematical concepts of rotation, translation, dilation, reflection, and iteration in contexts of cornrow and kente cloth design. Here are two of the students displaying the design they had created:

There is a detailed account of Mr. Babbitt's mathematical adventures in Ghana on his blog here.

Albany Area Math Circle student speaks at national math circle conference

2011-06-22T08:12:00.000-07:00

The National Association of Math Circles recently posted selected videos from their annual national meeting this spring in Houston.

One of their videos features a presentation given by Albany Area Math Circle member Elizabeth Parizh on the social aspects of math circles:

Math Clubs and Their Social Aspect:
A View Inside and Out
Elizabeth Parizh

Many children today are put off from participating in math activities because it is not popular among school kids. I will describe my own experiences as both a coach and a student in such math clubs, and explains what it is like for kids, and especially girls. I find that this is a very important problem that needs to be solved, because these students are America’s future and need to be prepared to help their country prosper. And yes, this does require math.

Elizabeth's talk was very well received, though unfortunately the videographer's microphone was placed to pick up more of the crowd reaction than of Elizabeth's voice (which came through quite clearly in person.) Her slides are available here.

The other talks and activities at the meeting were also excellent and several of the other featured videos are available here.

Elizabeth also assisted Bard College Professor Japheth Wood in leading sessions on the theory of impartial games designed for middle school and high school teachers. They used the game of Nim to illustrate the ideas of game trees, strategy, and concepts such as the addition of games. More details of that activity, including handouts, are available here. Professor Wood leads the Kingston Math Circle to our south--you may also want to check out his blog, News from the Math Wizard.

Albany Area Math Circle representatives at Math Prize for Girls

2011-06-20T16:11:00.000-07:00

Congratulations to the four Albany Area Math Circle students who have qualified for invitations to the Math Prize for Girls to be held at MIT in Cambridge, Massachusetts on September 17. They are all four outstanding representatives of all that is best in our math circle: massive enthusiasm for tackling mathematical challenges and eagerness to share their mathematical knowledge with others in our community.

From left to right above are:

Elizabeth Parizh, a rising junior at Niskayuna High School

Gili Rusak, a rising freshman at Shaker High School

Cecilia Holodak, a rising sophomore at Niskayuna High School.

At lower right is Zhixin (Wanwan) Fei, a rising senior at Emma Willard School.

They are a remarkably talented and experienced group. All four are veterans who also participated in the Math Prize for Girls last year. Elizabeth, Gili, and Cecilia have all participated in MATHCOUNTS, NYSML, ARML, and the Harvard-MIT Math Tournament.

Elizabeth has been student coaching at Iroquois Middle School. She was one of only a few high school students across the country invited to join adult math circle leaders at the annual national meeting of the National Association of Math Circles which took place at the University of Houston this March, where she gave an excellent and very well-received presentation on her experiences both as a student in a math circle and also as a coach of younger students. The audience for her presentation were mostly adult leaders of math circles, many of whom remarked to me afterwards how helpful her perspective was to them. At the Julia Robinson Mathematics Festival associated with that meeting, Elizabeth also participated as an apprentice to Bard College Professor Japheth Wood, helping him lead a session on game theory based on the Game of Nim. Elizabeth was an AIME qualifier this year.

Gili was the second highest scoring 8th grader from anywhere in the US or Canada at Math Prize 2010, was among the top 10 in the state at the state MATHCOUNTS championship this year, and was already among our top high school students in 7th and 8th grade on contests such as AIME and HMMT. She plans to student coach younger students next year.

Cecilia also plans to student coach younger students next year. Her many honors include being the first girl in a decade to win the CountDown Round at the Chapter MATHCOUNTS contest and being part of a four person Science Bowl team that placed 7th in the country at the National Science Bowl event in Washington, DC last year.

Wanwan qualified for AIME this year on the AMC12. Last year, she was the highest scorer on the AMC10 of anyone in this area, male or female, and she was also among the five highest scoring girls anywhere in the state on that contest. She is among a group of Emma Willard students who have been discussing launching a math mentoring program for younger girls in the future, an exciting initiative for our area.

Upstate NY ARML team

2011-06-05T17:40:00.000-07:00

Congratulations to the Albany Area Math Circle students who represented Upstate New York on the all-star teams at ARML, the national high school math championships held at Penn State this weekend: Matthew Babbitt, Cecilia Holodak, Preston Law, Zubin Mukerjee, Jien Ogawa, Elizabeth Parizh, Paul Rapaport, Schuyler Smith, Felix Sun, and Jay White joined a stellar group of math students from other parts of Upstate New York to do our region proud.

As usual, the problems were extremely challenging--indeed, the veteran members of the problem writing committee cheerfully admit that some of them get zeroes on the contests when taking them for practice as part of the development process!

Special congratulations to Allen Liu, a seventh grader from the Rochester area, who got 9 out of 10 correct on the individual round and ranked 10th in the country after tiebreaks!

Congrats as well to team high scorers Schuyler Smith and Felix Sun, veteran seniors who managed to get 7 out of 10 correct for team high scorer honors.

Congratulations again, Matthew!

2011-05-26T16:22:00.000-07:00

Albany Area Math Circle student Matthew Babbitt, a tenth grader from Fort Edward, New York, was among the top 10 American students on the Asia Pacific Math Olympiad (APMO), earning an Honorable Mention and helping the US team take second place among the 34 participating countries.

The other students on the United States APMO team along with Matthew were quite a distinguished group: Xiaoyu He, Wenyu Cao, Evan O'Dorney, Albert Gu, Calvin Deng, David Yang, Benjamin Gunby, and Mitchell Lee. (In fact, all the other APMO top ten students have won the USA Math Olympiad at least once. Several have won it multiple times and have made the International Math Olympiad team, where they have won gold and/or silver medals.)

XXIII Asia Pacific Math Olympiad

2011 Summary of Results
Top 20 countries:

1 KOREA 289
2 USA 269
3 THAILAND 228
4 PERU 223
5 TAIWAN 220
6 JAPAN 208
7 RUSSIA 205
8 SINGAPORE 205
9 BRAZIL 190
10 HONG KONG 173
11 CANADA 164
12 AUSTRALIA 156
13 KAZAKHSTAN 154
14 MEXICO 141
15 INDONESIA 135
16 NEW ZEALAND 128
17 ARGENTINA 121
18 MALAYSIA 108
19 AZERBAIJAN 101
20 TAJIKISTAN 82

Math Circle stalwarts challenge Watson @Jeopardy!

2011-05-07T16:34:00.000-07:00

Yesterday, two pillars of the Albany Area Math Circle, advisor Bill Babbitt and veteran student leader Matthew Babbitt, traveled to IBM Watson Research Laboratories along with members of RPI's Human Media Interaction class. As part of their field trip, they got to play as a team head to head against Watson (or perhaps we should say, "two heads to no head" against Watson). The photo above came early in the game. Watson pulled ahead--by a large margin--after this shot was taken.

Congratulations to Professor Rita Biswas!

2011-05-04T10:09:00.000-07:00

Earlier today, Albany Area Math Circle advisor Rita Biswas won the John S. Levato Endowment Award for Teaching in recognition of her outstanding teaching at the University at Albany (SUNY) School of Business.

In addition to the great work she does at UAlbany, she has also served as an outstanding advisor to our math circle, most notably in the excellent work she did in organizing arrangements for the University at Albany to host the high school state championship math meet, NYSML, last year. She has also served on the coaching staff of the Upstate New York Math Team, traveling with them to the national math championship meet, ARML, at Penn State on the weekend after Memorial Day. She has also organized weekend expeditions to the Princeton University Math Contest (PUMaC) and the Harvard-MIT Math Tournament as well as helping with proctoring the USA Math Olympiad and supporting our middle school outreach initiatives. Our math circle is very fortunate to have her as an advisor.

Congratulations Schuyler!

2011-05-02T15:54:00.000-07:00

Albany Area Math Circle member Schuyler Smith has been named by US Secretary of Education Arne Duncan as one of the 141 US Presidential Scholars this year. Congratulations as well to Union College Astrophysics Professor Rebecca Koopman, whom Schuyler has nominated for the US Presidential Scholar Teacher Recognition Award. They will be honored in a ceremony in Washington, DC in June.

Schuyler's official US Presidential Scholar biography appears below:

Schuyler has always been curious about the world around him. He grew up in Upstate New York, and feels more at home exploring mountains than navigating cities. Today he's a National AP Scholar, and the state champion and nationally ranked in many math and science competitions. He's completed most of the math and computer science majors at Union College. In 2008 he started an open source project that has been used to teach physics to high school and college students, and currently works as a teaching assistant for Art of Problem Solving. Each week he volunteers to teach math to middle schoolers. Schuyler has observed on the world's largest telescope, and his research papers on galaxy clusters and evolutionary robotics have been published nationally and internationally. In his free time he enjoys tennis, sailing, clarinet, computers, photography, flashlights, and penguins.

ADDENDUM: It is worth noting that Schuyler is only the second student from this part of the state to be honored as a US Presidential Scholar in recent years. The last Presidential Scholar from our region, Beth Schaffer, selected in 2007, was also a member of Albany Area Math Circle throughout her four years at Guilderland High School, and served as our math circle's co-captain during her junior and senior years. Beth was also a mentor and coach to Schuyler's state championship winning homeschool MATHCOUNTS team back when he was an eighth grader. Beth is now a senior at MIT, where she has been a lead organizer of the Harvard-MIT Math Tournament. She has also been a coach for the Upstate New York AllStar Math Team, which will represent Upstate New York at the national high school math tournament at Penn State next month. Schuyler is a senior veteran member of that team.

Math Circle student runs for school board

2011-05-01T11:18:00.000-07:00

Math Circle member Rich Reitz is running for a seat on the Niskayuna Board of Education in the upcoming school district election on May 17.

His biography on the school district website illustrates that our math circle students have interests that span many dimensions beyond mathematics:

Richard Reitz is seeking a first term on the Board of Education. Currently a senior at Niskayuna High School and a lifelong district resident, Reitz, who will be graduating in June, has attended Niskayuna schools for the past 13 years.

Reitz plans to attend Schenectady County Community College beginning in the fall. He also plans to cross-register in math courses through Union College. Reitz achieved AP Scholar with Honor status while at the high school. He has received the President’s Volunteer Service Award for community service each of the last four years (2007-2010) and anticipates receiving the award in 2011.

Reitz currently serves as co-president of Nisky S.T.A.R.T. (Students Today are Recycling Together), the recycling club at Niskayuna High School. An accomplished musician, he is also a cellist in the Empire State Youth Orchestra.

Reitz is also active in community clubs and organizations. As of April 15, he has achieved Eagle Scout status. He also participates as a member of Cap City Bang Bang, a local ultimate Frisbee team.

The other two candidates are incumbent board members John Buhrmaster and Deb Oriola. Their biographies are available here.

Interested voters can meet all three candidates tomorrow evening (May 2) at 7 p.m. at the annual "Meet the Candidates Night" at Van Antwerp Middle School Auditorium.

UPDATE 5/18/11: The election had a record turnout of 3,305 voters, the highest total in over a decade. Although Rich did not win a seat on the School Board, over 38% of the voters cast ballots for him.

Upstate New York mathematical uprising in Central NY

2011-04-25T11:33:00.000-07:00

Check out the story on the Math Prize for Girls Community Blog.

And, Albany Area Math Circle students, if you haven't yet sent in your application to the Upstate New York ARML team, do it now! This year's Upstate NY teams are going to be especially great, thanks in part to the great resurgence in Ithaca as well as awesome students all over Upstate New York.

NYSML 2011

2011-04-03T15:59:00.001-07:00

Congratulations to the hardy, energetic, intrepid, and enthusiastic band of Albany Area Math Circle students who made the long trek to the far reaches of Suffolk County on the eastern end of Long Island to represent our math circle at the annual state high school math tournament, NYSML. We are proud of all of you: Shreya Arora, Matthew Babbitt, Ryan Cheu, George Gelashvili, Cecilia Holodak, Gurtej Kanwar, Preston Law, Zubin Mukerjee, Jien Ogawa, Elizabeth Parizh, Paul Rapaport, Simran Rastogi, Gili Rusak, Schuyler, Wyatt, and Isaac Smith; Aniket Tolpadi, Jay and Philip White. We'd also like to recognize Gideon Schmidt, who eagerly and enthusiastically embraced the invitation to join in the NYSML challenge and prepared with us, but was held back at the last minute by a bout of strep throat.

Our hats are off to salute the New York City, Nassau County, and Monroe County (yay! Upstate solidarity shout-out!) teams for bringing home first, second, and third place team honors in the A-division this year. Congratulations to you!

Our hats are off as well to salute the awesome members of the Ithaca Math Circle who won first place in the B-division this year! What a year your--relatively young--math circle has had: taking home B-division honors at PUMaC, HMMT, and now NYSML. We are thrilled that our Albany Area Math Circle students will be able to join forces with you and the many other awesome Upstate New York students at ARML in June.

Congratulations as well to the individual "high scorers of the meet" who got 9 out of 10 of the individual problems correct--they were definitely tougher this year! There were no perfect scorers this year, largely due to the extreme challenge of problem #8, solved by only seven students in the state. We were pleased that two of those seven "higher scorer of the meet" students came from our Upstate NY neighbors on the Ithaca and Monroe County teams. Monroe's ever-awesome Allen Liu stayed in the tiebreaks to the very end, finishing second place in the state.

Our team high scorers this year were Matthew Babbitt, Gurtej Kanwar, and Schuyler Smith, each with 8 correct solutions. Other especially high scores included Preston Law, Zubin Mukerjee, and Jay White, who solved 7 problems; Cecilia Holodak and Paul Rapaport, who solved 6 problems; Elizabeth Parizh and Aniket Tolpadi, who solved 5 problems.

Other high points of the NYSML 2011 experience: relays went better than they did at our practices and our relay teams racked up an impressive number of points. Most impressively, there was great collaboration by Albany Area Math Circle students on the Power Round, resulting in 47 out of a possible 50 points on that round!

~~And, for the second year in a row, Albany Area Math Circle ranked first in New York State on the NYSML Seasonal competition!~~ [CORRECTION May 8 NYSML Executive Director Curry informed us today that he just realized that he made an error in collating results. Bronx Science was actually first place. Albany Area Math Circle was second place.]

Shown below are Matthew Babbitt, Jay White, and Schuyler Smith accepting the plaque on behalf of Albany Area Math Circle from NYSML officials, Mrs. Susan Schneider, Ms. Toni Lynn Swinson, and Mr. George Reuter. It was a special honor and pleasure to have the award presented by Mrs. Schneider, the widow of Dr. Leo J. Schneider, a long-time NYSML official who composed countless great math contest problems that have challenged and inspired our students.

Thanks to all the NYSML officials who made the event a great experience, especially the inimitably awesome emcee and President George Reuter, the ever-organized and always helpful Vice President Anchala Sobrin. Many thanks as well to Executive Director Mike Curry, to the host committee (we now appreciate how much work is involved in preparing for an event like this one!), and to all the volunteer coaches, proctors, and scorers who made this event possible and successful.

Special thanks to all the parents who drove carpools and/or organized travel details to make it possible for our math circle students to participate. Particular thanks to Katherine Scheib and Rita Biswas, who proctored other teams, and to Dwight Cheu, who worked in the scoring room.

Extreme thanks to Bill Babbitt and Rita Biswas for organizing and coordinating countless details to make this happen.

And finally, once again, thanks to the students of the Albany Area Math Circle--your enthusiastic embrace of mathematical challenges inspires us all!

Further adventures of math circle alumni: David Rolnick

2011-03-29T06:30:00.000-07:00

Albany Area Math Circle alum David Rolnick is profiled in this excerpt from an MIT admissions blog post about French House, where he lives:

Let's start with that kid over there - the one at the dining table closest to you, with the brown hair. That's Davie.

Davie is a junior from southwest Vermont, double-majoring in Math and Music. At MIT, he is involved in the Gilbert & Sullivan society - which performs comic operas by Gilbert and Sullivan - and the chamber chorus, which is a class that runs for three hours per week.

Non-MIT-related hobbies include "birding", which consists of "watching birds, looking at birds, and studying birds", and doing the same for insects. Davie has written about a hundred and fifty nature articles, most for a local paper, but also a few in the Vermont Entomological Society Journal and local nature newsletters. At his house in Vermont, he has found about 540 species of moth, seven of which had not previously been found in Vermont.

If you’re feeling brave, go ahead and challenge him to a game of bananagrams.

Afterwards, ask him why he likes MIT. He'll tell you that in all his time here, he has met “maybe one person” who wasn't "really nice."

Now ask him to tell you about French House. He’ll list some nouns: "quirkiness, silliness, friendliness, cooking, intellectualism, humanities, incidentally French, games."

Check out the engaging video Dave and his housemates created to encourage prefrosh to consider living in French House--sounds like a lot of fun to me! (Dave is the one in the orange shirt.)

David has appeared in several MIT operatic productions--the photo below by MIT Tech photographer Elijah Meniah shows Dave (center) starring as KoKo in an MIT Gilbert & Sullivan Players production of Mikado last year:

Dave also participated in the Duluth Research Experiences for Undergraduates (REU) program. The first photo below shows him presenting his work in progress to his fellow students:

The second photo below shows David and other Duluth REUers getting to ready to set out on one of that program's legendary weekly excursions (as a break from their research)--white water rafting:

Congratulations to David on his many accomplishments--including yet another Honorable Mention in this year's Putnam College Math Contest. And congratulations as well to our other AAMC alums who made the national top scorer lists this year: Yipu Wang, a sophomore at Cornell, who made the Putnam top 188, and to Andrew Ardito, a freshman at Princeton, who made the national top 500 list.

Congratulations to Evan O'Dorney

2011-03-16T06:19:00.000-07:00

17-Year-Old Wins Intel's $100K Science Prize

SiliconValley.com reports:

Danville's Evan O'Dorney wins Intel Science Talent Search

At 17, Danville's Evan O'Dorney already has won the National Spelling Bee and a gold medal at an international math Olympiad, meeting two presidents along the way. On Tuesday, he claimed the triple-crown: the coveted Intel Science Talent Search's $100,000 top prize.

Evan became California's first budding scientist to take home what's known as the Nobel Prize for high school students.

"I'm excited and shocked," Evan said after his win Tuesday. "This has been exciting, especially the judging interviews. All the science questions and working with scientists who are in very different fields than me, I'm very grateful."

...

Perhaps it's no surprise that this scholastic ninja -- did we mention he's a black belt in tae kwon do? -- once again has found himself taking down his overachieving competition: In 2007, he correctly spelled "schuhplattler," "laquear" and "serrefine" to win the Scripps National Spelling Bee. That's when he met his first president: George W. Bush.

At the Intel competition, something about approximating square roots won him the top prize and a chance to meet President Barack Obama, who had called to congratulate him the year before.

That's when Evan won gold at the 51st International Mathematical Olympiad, and the top prize in "Who Wants to be a Mathematician?" Well, Evan does. He hopes to one day be a professor of mathematics -- and continue singing and playing the piano.

Yes, in addition to claiming academic prizes, Evan also studies piano performance and composition at the San Francisco Conservatory of Music, and has written, among other things, a musical representation of the number pi, an opera and a piano concerto.

...

Evan says the person who's had the most influence on his scientific career is his mother, Jennifer, who home-schools him. His dad, Michael, is a BART operator.

His Intel prize is the result of research he did after Stanford University professor Brian Conrad invited him to tackle a problem regarding the approximation of square roots.

"After mulling the problem over in my head for nearly a year," he wrote in his Intel application, "I began generating and studying large amounts of computer data." He then describes manipulating formulas and observing patterns in the computer's calculations, and in the end, he came up with "an unexpectedly simple" formula. Well, maybe for him.

"A deep, lifelong fascination with the patterns of numbers," Evan wrote, "was my main source of inspiration throughout."

What the SiliconValley.com article unfortunately doesn't say is that Evan is a long-time and very active member, contributor, and leader in the Berkeley Math Circle. He is second from right in this picture, next to the circle's leader and founder, Zvezda Stankova. (Those are Klein bottles drawn on the blackboard in the rear, by the way.)

He is not a solitary mathematician who works alone. That's an invalid stereotype to begin with, and Evan certainly does not exemplify it.

Two years ago, at the Great Circles conference at Mathematical Sciences Research Institute (MSRI), I watched him captain the Berkeley Math Circle as his team of six challenged the Stanford Math Circle in a "Math Battle". (No, it's not a contact sport! He didn't need to use his tae kwon do skills. It's an oral battle of mathematical wits in which teams work together to develop and present solutions to tough mathematical problems in front of a panel of judges. It takes teamwork, good mathematical skills, good poise and thinking on your feet, and good communication skills. Check out the streaming video here.)

After winning many local Bay Area math contests, Evan took over the job of running the Bay Area monthly math contests himself. He is a great example of an important principle in practice--the more you give of your own mathematical understanding to others, the more you yourself will grow mathematically.

And he coaches MATHCOUNTS too!

2011-03-10T20:59:00.000-08:00

Wrong: an original composition performed by the multi-talented Hilly Adler, with passions for math and music.

Hilly is a sophomore at Albany High School, who helped Hackett Middle School math teacher Tamara Moffett to coach the school's first-ever MATHCOUNTS team.

I like the title of Hilly's work: "Wrong."

Young aspiring mathematicians need to embrace and celebrate the wrong more....no great math gets done without stumbling and working through a lot of wrong answers along the way.

AMC B-date AIME Qualifiers and Young Student Honors

2011-03-07T13:25:00.000-08:00

AMC 12B STUDENT TEAM MEMBERS

Schuyler Smith 123.0
Felix Sun 121.5
Jay White 120.0

AMC 12B School team score is: 364.5

AMC 10B STUDENT WINNER

ZUBIN MUKERJEE 127.5

AIME Qualifiers:

Based on AMC12B:

SCHUYLER M SMITH 123.0
FELIX W SUN 121.5
JAY T WHITE 120.0
MATTHEW W BABBITT 109.5
GURTEJ S KANWAR 105.0
WYATT C SMITH 103.5
JASON Y XU 99.0
MATTHEW Z GU 97.5

Based on AMC10B:

ZUBIN MUKERJEE 127.5
ERIC WU 123.0
GREGORY P HICKEY 120.0
WILLIAM WANG 120.0
ALEXANDER WEI 117.0

Young student honors:

AMC12B scores of 90 or above for students in tenth grade or below:

Cecilia Holodak, grade 9 Niskayuna HS 96.0
Preston Law, grade 10, heeg 91.5

AMC10B scores of 90 or above for students in eighth grade or below:

William Wang, Farnsworth MS, grade 7, 120.0
Alex Wei, Van Antwerp MS, grade 7, 117.0
Patrick Chi, Iroquois MS, grade 7, 114.0
Gili Rusak, Shaker JHS, grade 8, 114.0
Philip Sun, Acadia MS, grade 8, 111.0
Ziqing Dong, Farnsworth MS, grade 7 106.5
Martin Shreiner, Van Antwerp MS, grade 8, 103.5
Isaac Smith, heeg, grade 8, 102.0
Gideon Schmidt, Iroquois MS, grade 7, 97.5
Qu Chen, Shaker JHS, grade 7 97.5
Alex Cao, Shaker JHS grade 8, 90.0
Philip White, heeg, grade 7, 90.0

Divisibility rules explained

2011-03-06T09:26:00.000-08:00

As James Tanton points out, many students (and teachers!) use the divisibility rules, but can't explain why they work. That is unfortunate, because the explanations are a great stepping stone to modular arithmetic. The video above explains the divisibility rules for 3 and 9. (Double-click on it to see it full screen!)

Here's his explanation for the divisibility rule for 11.

And here's his explanation for the divisibility rule for 7. After viewing this one, you should have ideas about how to create your own divisibility rules for numbers like 13, 17, 47, etc.

Math Circles make a difference:

2011-03-05T12:09:00.000-08:00

OAKLAND, Calif. (KGO) -- A Mills College professor has won the nation's highest award for teaching math. Zvezdelina Stankova, Ph.D., has made it her mission to inspire Bay Area students to follow a path in mathematics.

Stankova probably wouldn't be here had it not been for her math teacher in her native Bulgaria. In class one day she was given a second chance to solve a math problem.

"I was very puzzled how my classmates could do it and I couldn't. I couldn't believe it, that that was the case. So I went to the math circle and three months later I won the local math Olympiads with a perfect score," said Stankova.

That day her teacher told her, "What comes from within you, can take you very far." Stankova now gives that advice to all her students.

That happened a quarter century ago. Zvezda has had many adventures and accomplishments since then--check out the video above for more. Or, if you prefer text to video, see here. (Hat tip: David Cordeiro of the Metroplex Math Circle.)

In 1998, after getting her PhD in mathematics from Harvard University, Zvezda drew on her childhood experiences with Bulgarian math circles to found the Berkeley Math Circle. You can read more about the Berkeley Math Circle in this remarkable book. Here is a sample chapter on combinatorics from Paul Zeitz, one of the Berkeley math circle's many contributors.

Anagha and the Persistent Chickens

2011-02-26T07:38:00.001-08:00

Sounds like the name of a rock group, right?

But it's not...the picture above shows Anagha Tolpadi last year working with a group of four wonderful sixth and seventh graders who decided to call themselves "The Persistent Chickens." Persistence and perseverence is the key--and encouragement by mentors like Anagha helps!

All four of the "Persistent Chickens" did very well on the fall middle school math contests and received invitations to join our high school math circle in taking the challenging AMC10 high school contest with us on Wednesday. Congratulations to all of you!

Anagha is now off studying math at Cornell. To the persistent chickens: keep on keeping on....encourage each other and younger students in the way that Anagha encouraged you. The more you help others, the more you will learn yourself.

Congratulations to our AIME Qualifiers

2011-02-24T12:14:00.000-08:00

Albany Area Math Circle is pleased to congratulate the following students who qualified for the American Invitational Math Exam based on AMC12A or AMC10A taken with Albany Area Math Circle on February 8:

AMC12A AIME Qualifiers

SCHUYLER M SMITH 124.5
FELIX SUN 123.0
MATTHEW W BABBITT 120.0
JAY T WHITE 114.0
RYAN CHEU 99.0
ELIZABETH PARIZH 99.0
WYATT C SMITH 99.0
ANIKET TOLPADI 97.5
PRESTON T LAW 94.5
ASHLEY CHO
WANWAN FEI
PAUL RAPAPORT
MATT WALSH
JASON XU

AMC10A AIME Qualifiers

Zubin Mukerjee 144
Alex Wei 127.5
William Wang 123.0
Ziqing (Bill) Dong 121.5
Philip Sun, 120

AMC10A Young Student Honors
(for students in 8th grade or below who scored above 90 on AMC10A):

Alex Wei, grade 7 Van Antwerp, 127.5
William Wang, grade 7 Farnsworth, 123
Ziqing (Bill) Dong, grade 7 Farnsworth, 121.5
Philip Sun, grade 8, Acadia, 120
Isaac Smith, grade 8 heeg, 115.5
Gili Rusak, grade 8 Shaker, 111
Nathan Soedjak, grade 7 heeg/Colorado Math Circle, 97.5
Ryan Soedjak, grade 7 heeg/Colorado Math Circle, 97.5
Gideon Schmidt, grade 7 Iroquois, 93
Philip White, grade 7 heeg, 93
Zachary Benson, grade 8 Hebrew Academy of the Capital District, 91.5

AMC12A Young Student Honors
(for students in 10th grade or below who scored above 90 on AMC12A)

Matthew Babbitt, grade 10 heeg 120
Elizabeth Parizh, grade 10 Niskayuna HS 99
Aniket Tolpadi, grade 9 Niskayuna HS 97.5
Preston Law, grade 10 heeg 94.5

We will update this list as we get reports from students who took the A-date at other AMC A-date contest locations in the Capital District. AMC B-date qualifers will also be added when we get those reports.

Albany Academy update:
Congratulations to AIME qualifier Paul Rapoport on the 12A.

Emma Willard School update:
Congratulations to AIME Qualifiers Soyeun (Ashley) Cho and Wanwan Fei on the 12A.

Colorado Math Circle update:
Congratulations to Nathan and Ryan Soedjak, who both received Young Student Honors for scores of 97.5 on the AMC10A. Nathan and Ryan were active in our math circle before their family moved to Colorado, where they now attend the Colorado Math Circle. The photo below shows Nathan, Troy Wang, and Ryan working together at an Albany Area Math Circle middle school meeting last year.

Niskayuna update: Congratulation to AIME qualifier Alex Wei from Van Antwerp MS and to Gideon Schmidt from Iroquois MS for young student honors on AMC10A. Congratulations also to AIME qualifiers Elizabeth Parizh, Aniket Tolpadi, and Jason Xu on the 12A.

Guilderland HS update: Congratulations to AIME qualifier Zubin Mukerjee, a tenth grader at Guilderland High School, who scored 144 on the AMC10A. Congratulations also to Matt Walsh, who qualified for AIME on AMC12A.

Bethlehem HS update: Congratulations to AIME qualifier Ryan Cheu on the 12A.

Shenendahowa update: Congratulations to AIME qualifier Felix Sun on the 12A and Philip Sun on the 10A.

Harvard MIT Math Tournament congratulations!

2011-02-20T07:39:00.001-08:00

Full HMMT public results are now available here. There were 100 teams and over 700 individuals participating, including many of the strongest math teams from all over the country, as well as teams from Beijing, Shanghai, Korea, and Nairobi.

Congratulations to our A-team (Albany Area Math Circle Steinmetz) for finishing 13th place on the A-division team round, amidst some very distinguished competition. Congratulations as well to AAMC B2 for placing 19th on the B-division team round and AAMC B1 for placing 28th.

Congratulations as well to the following students who ranked high in individual subject tests:

Matthew Babbitt
6th place individual Combinatorics/Geometry
25th overall individual sweepstakes

Ashley Cho
37th place individual Algebra/Geometry

Gurtej Kanwar
13th place individual Algebra/Calculus

Felix Sun
8th place individual Calculus/Combinatorics

More Chapter Congratulations!

2011-02-15T13:08:00.001-08:00

Congratulations as well to Thomas Glozman of Maple Avenue Middle School, a member of our middle school math circle who won first place in the TriCounty MATHCOUNTS Chapter! Thomas is at right in the photo above working with Gideon Schmidt from Iroquois Middle School at one of last year's middle school math circle meetings. We are all about the building of bridges...solving problems together since 2001!

Chapter MATHCOUNTS Congratulations!

2011-02-06T11:00:00.000-08:00

Congratulations to all the awesome high school student coaches who have helped to coach the middle school students who did such an outstanding job at today's chapter.

The top seven teams all included students who have participated in our middle school math programs and/or have been coached by Albany Area Math Circle student coaches and/or advisors. Out of the top 20 individuals, 17 students have also participated in our middle school math circle programs and/or had AAMC student coaches.

First place team: Farnsworth Middle School

Three of the four students on Farnsworth's team have participated in our middle school math programs, as have several of their individual members. Student coach Zubin Mukerjee has done a particularly awesome job of working with William Wang and Bill Dong in his satellite middle school math circle. Bill Dong was 5th place individual; William Wang ranked 3rd on individual writtens, and won the Countdown Round. Alicia Chen, a member of the "persistent chickens" team from our middle school math circle made the Countdown Round also, ranking 11th.

Second place team: Shaker Junior High School

Gili Rusak, who ranked 2nd on writtens and made the semifinals in Countdown, led the Shaker team to a 2nd place team finish. Gili is already a member of our high school math circle, due to qualifying for AIME last year. She also participated in Zubin Mukerjee's satellite math circle before joining our high school group. Prior to that, she was a member of satellite math circle mentored by Matthew Babbitt and Zubin's older brother Zagreb. Her teammate Alex Cao, who ranked in the top 20, has been an active member in our middle school math circle meets for the past two years.

Third place team: Van Antwerp Middle School

Student coach Jason Xu and his assistant Suman Padhi coached the successful VA team, which had two students participating in Countdown: Alexander Wei (4th place individual) and Andrei Akhmetov (13th place individual.) Their teammate Jason Tang also made the top 20.

Fourth place team: Home Educators Enrichment Group

Student coach Matthew Babbitt and his assistant Jien Ogawa coached this team, which did a superb job on the team round. Team captain Isaac Smith made the Countdown Round in 12th place and his teammate Philip White also made the top 20.

Fifth place team: Acadia Middle School

Student coach Felix Sun coached the Acadia team, as well as Koda Middle School. Three of the team members made the Countdown Round: Jerry Qu (8th place writtens), Joe Lou (7th place writtens), and Phillip Sun, first place writtens.

Sixth place team: Iroquois Middle School

Iroquois student coaches were Aniket Tolpadi and Elizabeth Parizh. Team member Gideon Schmidt made the Countdown Round, while his teammates Rocket Ruona and Patrick Chi also made the top 20. Gideon, Rocket, and Patrick have all been members of our middle school math circle. Patrick has also been a regular at Zubin Mukerjee's satellite math circle in Guilderland.

Seventh place team: Hebrew Academy of the Capital District (HACD)

The HACD team is coached by Albany Area Math Circle advisor Alexandra Schmidt. Many of the HACD students have been participating in our math circle's fall math meets. Team member Zachary Benson qualified for the Countdown Round with a 9th place rank on individuals. For reasons of Sabbath observance, HACD students took the contest earlier in the week. HACD deserves special recognition for the awesome participation rates: their school is very small, with only 50 students in combined enrollment in all three eligible grades (6/7/8) but fully one-third of Hebrew Academy students in those grades are active and enthusiastic participants in their school MATHCOUNTS program! HACD mathletes celebrated afterwards with a party at their MATHCOUNTS coach's home. Her prodigious talents include the ability to make hot fudge and caramel sauce from scratch! (Click on the photo below for a clearer image of the mathletes' delighted expressions!)

A special shout-out to the newest team, Hackett Middle School from Albany City School District, which placed a very respectable 12th out of 21 teams, an awesome performance for a first outing for a brand new team that only started up in January.

The team's student coach was Hilly Adler, a student at Albany High School who is a former mathlete from Hebrew Academy. Hilly worked in concert with Hackett Middle School teacher coach Tamara Moffett. There were many bureaucratic obstacles to getting a team off the ground in a large urban school district. Kudos to Albany Area Math Circle advisor Alexandra Schmidt for supporting Hilly in being tenacious to make this team happen, and in providing advice about team coaching.

Shout-outs as well to Doyle Middle School coach Nancy Smith, whose team placed 10th. Nancy is a dedicated and experienced veteran coach whose students have recently begun participating in our middle school math meets. There are many challenges in coaching an inner city school team, and Nancy meets them all energetically. Several of her teams have gone to state and two of her mathletes have made it all the way to nationals. Nancy has recently started up an exciting and creative new outreach initiative to elementary schools in her district, bringing enthusiastic young mathletes to solve problems together even before they reach middle school.

Top 20 individuals

1. Phillip Sun Acadia
2. Gili Rusak Shaker
3. William Wang Farnsworth
4. Alex Wei Van Antwerp
5. Bill Dong Farnsworth
6. Noah Rudnick Shaker
7. Joe Lou Acadia
8. Jerry Qu Acadia
9. Zachary Benson Hebrew Academy of the Capital District
10. Gideon Schmidt Iroquois
11. Alicia Chen Farnsworth
12. Isaac Smith heeg
13. Andrei Akhmetov Van Antwerp
14. Jason Tang Van Antwerp
15. Jeremy Collison Farnsworth
16. Patrick Chi Iroquois
17. Rocket Ruona Iroquois
18. Billy Schmitt Schalmont
19. Phillip White heeg
20. Alex Cao Shaker

Thanks again to GE Global Research for general awesomeness in hosting our Chapter Competition and to all the volunteers who made it possible.

I'd also like to recognize the awesome math circle affiliated adult community volunteers who have helped to organize and coach teams: Bill Babbitt (heeg), Anil Tolpadi and Steve Schmidt (Iroquois), Hong Chen (Van Antwerp). Kudos as well to all the professional math teachers in the Capital District who sponsor teams at their schools. Without the support and leadership of adult sponsoring coaches, none of the 21 teams could have existed, let alone been as successful as they were!

Don't lose ALL your marbles!

2011-02-04T20:32:00.001-08:00

Tonight our math circle worked on the 50th anniversary American High School Math Exams (AHSME) problems, which contained one problem from each of the first five decades of the AHSME. (For those who don't know, the AHSME was the predecessor of today's AMC12 contest. And it all started in New York State in 1950--yay for New York pride!)

Here is one of the problems a number of tonight's students especially enjoyed from the 1991 AHSME contest given 20 years ago, before any of the students eligible to take this year's AMC contests were born.

To clarify these instructions, let's be clear that you can use the four allowed procedures as many times as you like, in any order that you like.

It looks very daunting at first--there are so many possibilities to consider.

If you want a hint, check the comments.

Harvard MIT Math Tournament travel teams

2011-01-29T08:18:00.000-08:00

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

Happy Prime New Year!

2011-01-02T07:09:00.000-08:00

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 ...... ????

Albany Area Math Circle honors last year!

2011-01-01T22:23:00.001-08:00

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.

Happy Holidays!

2010-12-21T16:04:00.001-08:00

I have received a few holiday gifts I'd like to share with you:

1) A beautiful video from Ken Fan at Girls Angle

The program Ken used to make the video above is a free open source 3D creation suite you can use too. Available at www.blender.org

2) A pointer from Melissa Smith of the Ithaca Math Circle to a great article by Nate and Sam Cornell. Nate is a psychologist at Williams College and Sam is a writer in San Francisco. Their article really accorded with decades of experience for me as a lifelong educator who continues to love her own learning challenges.

Here is a link to the article:
A Really Hard Test Really Helps Learning: Challenging tests and falling short may be hard on the ego, but they can do more than mere studying for eventually getting it right

Here's an excerpt that especially struck Melissa and resonated well with me also:

Both studies independently indicate a striking fact. We tend to assume that the best way to consume and remember information is through the application of rigorous, extended study. What we fail to see, however, is that the process of trying to work through a problem to which we don’t know the answer focuses our attention on it in a way that simply studying it does not. The desire to get the answer right, and the frustration of failure, is partly to account.

But there’s another element as well. When we struggle to learn something, and fail, the moment we finally get the answer it imprints itself more deeply on our mind than it would have had struggle and failure not preceded it.

3) Excellent advice from mathematician Lillian Pierce, currently at the Institute for Advanced Study: Try again! Fail again! Fail better!

4) A random factaroony from Number Gossip: 2011 is the first odious prime number we've had since 1999. For more about "odious" and "evil" numbers, see here.

5) And one last present (especially nice during those bleak and gloomy times when it feels like winter may never end ... or when it feels that a problem may never get solved.) A hat tip to the Metroplex Math Circle for calling my attention to this enchanting video. Double-click on the video for a bigger view to see the whole picture.

For more about the mathematics behind this video, see this website.

And remember ... just as sometimes the most unpromising-looking larvae can turn into the most exquisite and magical dragonflies, so too can the most hopeless looking math problems turn into the most awesome aha! experiences.

May 2011 be filled with many wonderful problems and discoveries! And many wonderful mathematical friends with whom to share them!

AMC8 Congratulations!

2010-12-14T22:18:00.000-08:00

Congratulations to all the Albany Area middle school students who embraced the challenge of the AMC8 with such enthusiasm this year! Congratulations as well to our high school students who have mentored many of them.

Honor Roll (scores of 18 to 21)

18 Alex Cao Shaker JHS
18 Alex Wei Van Antwerp MS
20 Patrick Chi Iroquois MS
20 Gideon Schmidt Iroquois MS
21 Shreya Arora Iroquois MS
21 Andrei Akhmetov Van Antwerp MS
21 Alicia Chen Farnsworth MS
21 Zach Benson Hebrew Academy of the Capital District
21 Sean Setzen Hebrew Academy of the Capital District

Honor Roll of Distinction (scores of 22 to 25)

23 Gili Rusak Shaker JHS
24 Philip Sun Acadia MS
24 William Wang Farnsworth MS
25 Ziqing (Bill) Dong Farnsworth MS

We will post additional honor scores here as we receive information about them.

Bill Dong's perfect paper of 25 is extremely unusual--there have been many years when there are no 25's anywhere in the entire state. It is all too easy for even the strongest students to make mistakes on a test like the AMC8, as many of our veteran high school students and alumni can tell you!

Bill joins a very rarefied group of students--Albany Area Math Circle's only previous perfect scorers on the AMC8 have been Raju Krishnamoorthy (1999), Drew Besse (2001), Schuyler Smith (2006), and Matthew Babbitt (2007).

Bill will also receive the AMC8 high scorer in the state award, as did Raju, Drew, Schuyler, and Matthew, as well as Andrew Ardito and Dave Bieber.

Students who would like to prepare for next year can find lots of old AMC8, AMC10, and AMC12 test problems, along with hints and solutions free and online at this webpage.

Fall Middle School Math Meets

2010-12-14T13:03:00.000-08:00

Thanks to everyone who contributed to the success of our inaugural season of Fall Math Meets! Watching you smile and make new mathematical friends and share cool math as you talked over the problems together after the contest is what makes it all worthwhile for us volunteer advisors.

There are many ways to measure success--we recognize a few of them here, but the ultimate measure of success is whether you continued thinking about and talking over the new ideas you learned afterwards.

October High Scorers:

8 points:
Zachary Benson, Sophie Rich, Helen Yuan

9 points:
Emily Honen, Jeffrey Shen, Cathy Shi, Max Thomas

10 points:
Bill Dong, Thomas Glozman, Ben Salem, Gideon Schmidt, Philip Sun, William Wang

"Whole is more than the sum of the parts" team award:
Adam, Emily, Jerry, Max

November High Scorers:

6 points:
Zachary Benson, Gwenda Law, Michelle Yu

9 points:
Alex Cao, Patrick Chi, Jerry Qu, Gideon Schmidt, William Wang

10 points:
Alicia Chen, Bill Dong, Philip Sun, Alex Wei

High scoring newcomer award:
Samuel Enriquez, Rafi Nizam, Jason Tang, Michael Zhu

"Whole is more than the sum of the parts" team award:
Jason, Mike, Zach

December High Scorers:

7 points:
Alex Cao, Thomas Glozman, Michelle Yu

8 points:
Bill Dong, Jerry Qu, Gideon Schmidt

10 points:
Alicia Chen, Philip Sun, William Wang, Alex Wei

High scoring newcomer award:
Sean Dory

"Whole is more than the sum of the parts" team award:
Daniel, Nabihah, Swetha, Thomas, Yang

In memoriam: Joel Brainard

2010-12-13T19:43:00.000-08:00

Our thoughts and hearts go out to Joel's daughter, Katherine Brainard, a founding member of our math circle, and to Joel's wife, JC Glendinning, an important driving force behind the beginnings of our math circle in 2001, and to their entire family.

Joel Pennington Brainard, 71, died peacefully on December 11, 2010, at NY Presbyterian Hospital in New York, NY. He is survived by his wife Jane Carol Glendinning; their children, Junior, 29, Katherine, 25, and Scott, 23; and his brothers Charles and William. A graduate of Oberlin College, Joel served in the Peace Corp in the Ivory Coast and later taught mathematics at Talladega College in Alabama. With advanced degrees from MIT and Cornell University, Joel was an engineer on energy conservation projects at Brookhaven National Laboratories on Long Island and was a consultant on public utility issues for the Vermont Low-Income Advocacy Council through Vermont Legal Aid in Burlington. His many colleagues remember him fondly for his more than 22 years of service as an economist and manager in the Office of Research at the NYS Public Service Commission. Joel was an extraordinary man whose thought, wit and kindness touched the lives of all who knew him. Family and friends remember his joy for life with deep affection. His energy and enthusiasm permeated his life, particularly his ingenious solutions of problems, both large and small. From reducing distortions in the pricing of the electrical grid to his unique approaches to car repairs, home construction, and even ski boot insulation and golf cart-to-ATV modification, Joel provided an inspiring example and will be greatly missed. In lieu of flowers, the family requests that gifts be made in Joel's memory to the Robert C. Parker School, which Joel helped found 20 years ago, or the Scleroderma Foundation, an institution which works to find treatments for an autoimmune condition that Joel fought creatively for many years. A Memorial Service will be held on Saturday, December 18th at 11:00 am at the Robert C. Parker School, 4254 West Sand Lake Rd, Wynantskill, NY.

The biggest Evil Abundant Number submitted at today's Middle School Math Meet?

2010-12-12T17:31:00.000-08:00

The teams at our middle school math meet today submitted the following numbers as candidates for the "biggest evil abundant number you can find."

24
720
111100
and

drumroll please....

And the winner is.....well, that's not so clear. We'll discuss it below. We'll also tell you what evil numbers and abundant numbers are.

But, first, a few important words of thanks!

We had a GREAT Middle School Math Meet today! Thanks very much to Felix Sun, Qun Lu, and the Principal of the CCC Chinese School Jianzhong Tang for making arrangements to host our December Middle School Math Meet at Shaker Junior High this afternoon. Thanks as well to Felix's mother, Le Xu, for organizing refreshments!

Thanks to UAlbany Professor Rita Biswas, Hebrew Academy math teacher Alexandra Schmidt, and Doyle Middle School math teacher Nancy Smith for helping to run the Math Meet. Thanks as well to our outstanding high school student coaches: Felix Sun (Shenendahoah High School), Zubin Mukerjee (Guilderland HS), Cecilia Holodak and Flora Mao (Niskayuna HS), Simran Rastogi and Gili Rusak (Shaker).

Thanks to all the students who came and worked enthusiastically on the problems.

Thanks to George Reuter of mathmeets.com, who did a great job of writing more great contest problems for the December math meet. We can't discuss those questions yet, since other teams may still be taking that contest.

Okay, so back to this evil and abundant question, which we CAN discuss, since I just created it as a little supplementary challenge to fill in the bits and pieces of waiting time during the meet. It turned out to be way more interesting than I had realized!

We began the Math Meet by discussing the "number of the day: 12." (Why, because it is December 12, or 12/12, of course!)

Like all numbers, 12 has many interesting properties. We focused on two of those properties today, which are highlighted in the Tagxedo-produced graphic above.

Twelve is an "evil number", which means that it has an even number of ones in its binary expansion, i.e., 1100_{base 2} = 1*8 + 1*4 + 0*2 + 0*1 = 12.

Twelve is also an "abundant number," because 12 is less than the sum of its proper factors, i.e., 12 < 14 = 1+2+3+4+6. In fact, it is the smallest abundant number, and therefore, of course, it is also the smallest evil abundant number, as well.

Is there a largest evil abundant number?

Some students noted that doubling an evil number always gives you another evil number! (Why?) What if you tripled an evil number? Or multiplied your evil number by other integers? What if you add two evil numbers? What if you raise an evil number to a power? Do you always get another evil number?

(By the way, you could ask the same questions about "odious numbers," which are the opposite of evil numbers--they have an odd number of ones in their binary expansions.)

Other students noted that doubling an abundant number always gives you another abundant number! (Why?) What if you tripled an abundant number? Or multiplied your abundant number by other integers?

Again, you could ask the same questions about perfect numbers, or deficient numbers.

More interesting questions: can a power of two ever be an evil number? Why or why not? Can a power or two ever be an abundant number? What about powers of three?

All great questions to think about!

Now back to judging the entries submitted in the contest.

24 is clearly evil (binary representation is 11000) and abundant (its proper factors are 1,2,3,4,6,8,12, which sum to more than 24.)

720 is also evil (binary representation is 1011010000) and abundant (its proper factors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360).

111100 turns out to be trickier. It is not clear whether it was intended to be interpreted as a binary number, in which case it would obviously be evil. If it was intended to be interpreted as a base-10 number, then it's actually not evil, because the binary representation of 111100_{base 10} is 11011000111111100. So the only way this number is a candidate is if we interpret 111100 as intended to be binary, in which case it is only equivalent to decimal 60. Now, 60 is clearly abundant, but it is less than 720.

Now, for that humongous number with all the concatenated exponents. I can tell you it is abundant, for sure, but I have no idea if it is evil or not. I am not convinced that the team that submitted it is sure whether it is evil or not, but if they can come up with a convincing proof that it is evil, I am willing to listen. Thinking systematically about some of the questions I raised above may help you sort out what is going on with your--very interesting--number. You may also want to consult the following book, which introduced the concepts of evil and odious numbers: Winning Ways for Your Mathematical Plays Volume 3, by Elwyn R. Berlekamp, John Horton Conway, and Richard K. Guy.

In the meantime, until such time as the orange team can demonstrate their candidate number is evil, 720 is the winner among the numbers submitted today.

Congratulations to the Green Team: Sean, Jason, Gideon, Frank, and Aaron. Your entry of 720 is the largest confirmed evil abundant number of those submitted today.

And, everyone, keep on thinking about this problem! Can you come up with a formula for an arbitrarily large evil abundant number that you can PROVE will work?

Princeton University Math Contest (PUMaC)

2010-11-23T18:31:00.001-08:00

Teams from around the country and as far away as Beijing, China competed at the fifth annual Princeton University Math Contest (PUMaC) this past weekend.

Congratulations to the eight Albany Area Math Circle students who did an outstanding job of representing our math circle at PUMaC! Pictured below are team members Jay White (heeg), Felix Sun (Shenendahoah), Gili Rusak (Shaker), Ashley Cho (Emma Willard), Gurtej Kanwar (Bethlehem), Matthew Babbitt (heeg), Zubin Mukerjee (Guilderland) and Preston Law (heeg).

The team tied for fourth place in the highly competitive A-division team round, tying with top teams from such distinguished places as Phillips Exeter Academy, New York City, and Beijing.

PUMaC team captain Matthew Babbitt and senior veteran Ashley Cho both brought home individual A-division medals as well on the geometry round, with Matthew tying for 4th place and Ashley tying for 7th place.

There was much friendly camaraderie in the cars travelling to and from the contest, as well as games during the breaks in the competition day. Team member Zubin Mukerjee won the chess mini-event during the lunch break.

A special highlight this year was the opportunity for team members to visit with Andrew Ardito and Dave Bieber, much beloved alumni of our math circle who are now Princeton undergraduates helping to run the contest.

Wise and heartfelt words from a veteran

2010-11-20T21:18:00.000-08:00

Kate Rudolph, one of last year's top ten winners at the 2009 Math Prize for Girls, and now an MIT freshman, came back to speak with this year's participants at the 2010 Math Prize for Girls award ceremony, held in the historic Cooper Union Great Hall.

The gold-fringed velvet covered podium in the Great Hall is an imposing and intimidating place for a young woman to speak, even one as accomplished as Kate. (MIT describes her as a "world class mathlete.")

In its 150 years of history, "rebels and reformers, poets and presidents" have spoken at that podium. Many great orators--Abraham Lincoln, Mark Twain, Teddy Roosevelt, Barack Obama, the leaders of the antislavery,civil rights, and women's suffrage movements have all made impassioned speeches in that hallowed hall. Not exactly easy acts to follow!

Kate stepped up to the challenge with poise and passion, defying the stereotypes and demonstrating her gifts with words as well as numbers. Her enthusiastic words of encouragement and advice resonated throughout the Great Hall, giving new perspectives to the hundreds of girls and parents anxiously awaiting the results of the competition.

Here is an excerpt from the inspiring, passionate, and thoughtful speech Kate had clearly put her heart into composing to share with the 2010 contestants.

[A]ll of these competitions, including the one you took today, have something in common: you’re solving “solved” problems. Someone else has already thought about the problem and knows the solution before you even get to see it. Imagine what it must feel like to be the first person, in the world, to solve a math problem.

Well, that’s what the future holds for all of you. The point of the Math Prize for Girls is to get more girls interested in math, but what for? Moving forward, the point is NOT to get you winning more math contests. It’s not even to get you writing good math contests (which is considerably harder.) The point of bringing you here and exposing you to these problems is to get you interested enough in math that eventually you want to do NEW MATH.

But how do you get there from here? You’re on the right track: seeking out challenging problems and pushing yourself to do well. What’s next? I have three main pieces of advice.

The first: work hard. Nothing worth achieving is easy to achieve. Math is not easy, and it gets harder, but you can solve any problem you come across with enough effort.

Next: do what you love. At some point during your life, there will come a time when you break down, or burn out. If you spend your time doing what you love, you will have the foundation to build yourself back up again.

Finally: work with other people. This seems sort of opposite to the concept of competition math, where you’re primarily working individually, but I can tell you that there are math problems that are so hard, if you didn’t combine forces with other people you wouldn’t get anywhere.

Look around. You may know some of the other contestants here: you may have met them in summer math programs or they may be from the same area as you. But I challenge you not to just let this be a reunion of people you already know, but a chance to meet more math girls and expand your network. When I say “work with other people,” THESE are some of the best “other people” you could find!

Finally, I think I need to acknowledge that yes, we girls are a minority in the field of mathematics. However, this is not a curse but a blessing, and I challenge you to use it! As a girl, you will have more opportunities (heck, you’re taking advantage of one of them right now!) If people set lower expectations for you because you are a girl, that is an opportunity to blow them away.

Good luck on this competition: I know you’re all anxiously waiting for the results. But more importantly, good luck as you pursue mathematics beyond this competition, beyond all competitions, and start doing some NEW MATH of your own."

More fun and games at Math Prize for Girls

2010-11-19T21:21:00.000-08:00

'Twas the night before the Math Prize for Girls, and some girls sat on the floor to build surprisingly sturdy structures from marshallows and spaghetti, while others played board games. There's a lot to be said for cultivating a relaxed playful mind--playfulness is an important part of problem-solving.

The challenging math problems that awaited them the next morning are available here.

Math Prize for Girls contestants community: who are they and where are they from?

2010-11-16T06:31:00.000-08:00

Thanks again to Advantage Testing Foundation for its vision and generous lead sponsorship of the Math Prize for Girls in 2009 and again this year. Thanks as well to the additional sponsors who have now joined Advantage Testing Foundation in supporting the event: Akamai Foundation, Canada/USA MathCamp, and Wolfram Mathematica.

This past weekend's Math Prize for Girls event provided even more opportunities for girls from all over the United States and Canada to forge new friendships and renew old ones based on their shared enthusiasm for mathematical challenges. This year's event added a lunch for contestants on Saturday as well as a "Games Night" event Friday evening for distant students whose travel plans had them staying overnight in the Big Apple.

There's a wonderful camaraderie of kindred spirits at all the mathematical events I've ever attended, but the atmosphere at the Math Prize for Girls stands out even more for all the sparkling smiles and laughter and friendly hugs. Students did not even seem to mind the long lunch lines--taking that as yet another opportunity to make new friends they might not otherwise have met. The purple hats and t-shirts were apparently major hits.

Veteran students returning for a second year welcomed the opportunities to reconnect with friends they met last year, as well as to make new friends with first-timers. Students, volunteers, and fans who knew one another from ARML or other contests like HMMT or summer programs such as Canada/USA MathCamp and HCSSiM reunited and connected up their intersecting networks of friendships.

For students from remote outposts who had never participated in a math event outside their own schools, this event was a particularly special opportunity to make new friendships with girls who shared their passion for mathematical challenges. Some girls reported that they had so much fun talking to students from all over that they have been inspired to form local math circles to recruit more kindred spirits to work together to keep that enthusiastic mathematical community experience going throughout the year in their hometowns.

So, how about a little friendly rivalry?

Which states and provinces had the most girls participating this year?

Top States and Provinces
Based on Raw Numbers of Participants

1) California and New York (tie 28 girls each)
2) New Jersey 22 girls
3) Massachusetts 18 girls
4) Connecticut 16 girls
5) Illinois 9 girls
6) Pennsylvania and Virginia (tie 8 girls each)
7) Maryland 7 girls
8) Georgia, North Carolina, and New Hampshire (tie 6 girls each)
9) Michigan, Texas, and Washington (tie 5 girls each)
10)Indiana and Ontario (tie 4 girls each)
11)Florida and South Carolina (tie 3 girls each)
12)Iowa, Missouri, Ohio and Wisconsin (tie with 2 girls each)

Other states and provinces represented at 2010 Math Prize for Girls: Alberta, Arizona, British Columbia, Colorado, Kentucky, Manitoba, New Mexico, Utah (1 each)

Of course, reasonable people may object that the rankings above do not take into account population or distance from New York City. It's hardly fair to compare New York State to Manitoba!

So I generated some alternative rankings below by adjusting for population and/or distance, using Wolfram Alpha's handy data retrieval features to get statistics on the distance of each state or province's capital from New York City as well as its population.

Top States and Provinces at Math Prize for Girls
Adjusted for Population
(Ranking based on raw numbers divided by state or province population)

1) New Hampshire
2) Connecticut
3) Massachusetts
4) New Jersey
5) New York
6) Maryland
7) Virginia
8) Manitoba
9) California
10) Washington
11) Illinois
12) Iowa

Top States and Provinces at Math Prize for Girls
Adjusted for Distance from New York City
(Ranking based on raw numbers multiplied by number of miles from state or province capital to NYC)

1) California
2) Washington
3) Texas
4) Illinois
5) Georgia
6) New York
7) Massachusetts
8) Michigan
9) Florida
10)Indiana
11)North Carolina
12)British Columbia

Top States and Provinces at Math Prize for Girls
Adjusted for Population and Distance from New York City
(Ranking based on raw numbers multiplied by miles from capital to New York City divided by state or province population)

1) California
2) Washington
3) Manitoba
4) New Hampshire
5) New Mexico
6) Utah
7) Iowa
8) Alberta
9) British Columbia
10) Illinois
11) Massachusetts
12) Georgia

Of course, reasonable people can differ about the appropriate methodology. Perhaps it is better to multiply by the square root or logarithm of the distance in miles to take into account the fact that travel times are not linear in distance. Perhaps states with boarding schools that recruit from national or international pools should have an adjustment to the population divisor to take that into account.

Can you come up with a methodological approach that puts your state or province on top? Feel free to post it in the comments below.

Put your state or province on the mathematical map next year!

And a shout-out and note of friendly encouragement to students in states and provinces that did not participate at all this year: if your state or province is small and/or far-away, it would only take one or two participants to make it rise to the top of the adjusted rankings above!

What's the first step?

If your high school does not offer the Mathematical Association of America's American Mathematics Competitions AMC10/12 contests offered each February, this is an excellent time to approach the head of your school's math department to ask about taking it. The AMC10/12 can lead to many opportunities--not just the Math Prize for Girls, but also the American Invitational Math Exam, the USA Math Olympiad, the Math Olympiad Summer Program, and even the International Math Olympiad as well as the China Girls Math Olympiad.

The per student cost for the AMC10/12 is very reasonable if you can persuade a number of your friends to join you in taking it. If your school takes advantage of the early registration discount and signs up before December 18, it works out to less than $6 per student if ten students take it at your school, about $2 per student if 100 students take it, and the cost goes asymptotically down to $1.60 per student if an infinite number of students take it at your school!

Best of all, you and your fellow students can have a lot of fun and learn a lot by preparing together. The best way to learn is to help others prepare as well. Create a mathematical community at YOUR school! Here is a resource website I've put together to help students prepare.

Photo credits: Joy Mingalingading (photo at top); Dr. Madhu Boppana (other photos)

Congratulations Ashley!

2010-11-15T06:15:00.000-08:00

Albany Area Math Circle veteran So Yeun (Ashley) Cho, a senior at Emma Willard School, brought home yet another beautiful sparkling crystal trophy this year for a performance even more outstanding than last year in an even more stellar field of over two hundred extremely mathematically talented young women from all over the country and Canada at the Math Prize for Girls held at the Courant Institute of Mathematics on Saturday.

This year, Ashley was tied for 18th place, only one question away from top 10 tiebreak standing! Last year, she was tied for 25th place, two questions away from the top 10.

Thanks to her Honorable Mention score at the Math Prize for Girls this year, Ashley will be invited to write the Math Prize Olympiad in December, a four hour olympiad-style contest with proof-based problems designed to be comparable to those on the China Girls Math Olympiad.

In both 2009 and 2010, Ashley's score at the Math Prize for Girls was the highest for anyone from New York State! The complete list of high scorers is available here.

This year's field of over 200 competitors was even stronger than last year's field, because the success of last year's event caused much greater interest and many more girls from all over the country applied to participate. The event has attracted additional major new sponsorship this year, Akamai Foundation, which also sponsors the Math Olympiad Summer Program and the US team to the China Girls Math Olympiad. Thanks to additional sponsorship, more exceptionally strong students from distant locations were able to participate this year, because all 2010 USAMO qualifiers received travel subsidies. In addition, the Math Prize for Girls accepted applications from Canadian students for the first time this year. Thus, Ashley's stronger performance this year is all the more impressive, since the field is even stronger.

Ashley has been an outstanding leader and inspirational model for her fellow students at Emma Willard and for all students in our math circle. She has also been a leader among all students in New York, with many other recognitions including qualifying for the USA Math Olympiad in 2008, team high scorer honors on our A team at the state math tournament, NYSML, last April, selection for the Upstate NY ARML A team where she contributed to the epic first-place super relay in 2009, and selection to participate in Princeton's Summer Workshop in Mathematics last summer.

Ashley has mentored and coached her fellow students on Emma Willard's Harvard-MIT Math Tournament (HMMT). Next weekend she will join seven of our math circle's strongest and most experienced students to represent Albany Area Math Circle at PUMaC (Princeton University Math Contest), an extremely challenging math contest.

Our first-timers at Math Prize for Girls this year were Sherry He and Wan Wan Fei, also from Emma Willard, Cecilia Holodak and Elizabeth Parizh from Niskayuna High School, and Gili Rusak from Shaker Junior High School. The photo at the top of this post shows Wan Wan, Albany Area Math Circle founding member Alison Miller, and Sherry celebrating along with Ashley.

Congratulations to all the participants in Math Prize for Girls this year, from Albany Area Math Circle, from all over New York State, from all over the country and Canada, too!

More information and photos will appear on this blog in the coming days!

Harvard-MIT Online Tournament at Emma Willard 11/7/10

2010-11-11T15:29:00.001-08:00

Congratulations to the brave group of Albany Area Math Circle students who spent five hours last Sunday afternoon working on an "Extreme Math" challenge--the Harvard-MIT Online November Tournament. Though most of the students were new to this kind of intense mathematical experience, they rose to the challenge with great enthusiasm and camaraderie. We had three composite teams bringing together students from Doane Stuart, Emma Willard, Guilderland High School, and Niskayuna High School.

To honor our region's grand traditions of mathematical and scientific contributions, our three teams were named after three historic scientists from our area: Charles Steinmetz, Katherine Blodgett, and Frank Benford. Charles Steinmetz, the mathematical wizard of Schenectady was a mathematician and electrical engineer who started the GE Research Laboratories, served as President of the Schenectady School Board, and taught at Union College. It was said that he figured out a way to turn imaginary numbers into electricity. Katherine Blodgett was a Schenectady native who was the first woman ever to get a PhD in physics from the University of Cambridge, and who later worked at GE where she invented a molecular process to create the world's first 100% invisible glass. Frank Benford was an electrical engineer and physicist now best known for his discovery of Benford's law, an unexpected but beautifully surprising logarithmic statistical pattern that can be used to detect financial frauds and other fabrications. (The story behind his discovery of the pattern is delightfully serendipitous: while working at the GE Research Laboratories in Schenectady, he noticed that the pages of the logarithmic tables corresponding to numbers with a leading digit of 1 or 2 were much dirtier than the pages for numbers beginning with 8 or 9, which suggested to him that numbers beginning with 1 or 2 might occur much more frequently in real world data than numbers beginning with 8 or 9.)

The students demonstrated remarkable concentration and perseverence throughout the long hours of the multi-round mathematical contest--I believe that Steinmetz, Blodgett, and Benford would be very proud of the strong and persistent efforts of the students on their namesake teams.

Students on Team Steinmetz (Blue) were: Aniket Tolpadi, Elizabeth Parizh, George Gelashvili, Peggy Hsu, Sherry He, and Yvonne Yen. Students on Team Blodgett (Red) were: Candice Chiu, Jamie Park, Justina Liu, Luxi Peng, and Sunny Yan. Students on Team Benford (Green) were: Chelsea Wu, Claire Feng, Eric Dammerman, Isaac Malsky, and Shuang Jin.

Team High Scorers:

General Round:
Elizabeth Parizh (Steinmetz Blue)
Candice Chiu (Blodgett Red)
Chelsea Wu (Benford Green)

Theme Round:
Sherry He (Steinmetz Blue)
Justina Liu (Blodgett Red)
Isaac Malsky (Benford Green)

High scorers of the meet
(based on combined total on general and theme rounds):
Sherry He (first place)
Chelsea Wu (second place)
Elizabeth Parizh (third place)
Honorable Mentions: Aniket Tolpadi, Justina Liu, Luxi Peng

Team Round Local Winner: Blodgett (Red)
GUTS Round Local Winner: Blodgett (Red)

Whole is More than the Sum of the Parts Award:
Benford (Green)

Spirit of the Meet Award: Peggy Hsu
for her awesome enthusiasm and encouragement to our many first-time participants

Many thanks to Emma Willard School for agreeing to host this very enjoyable opportunity for our newer students to really immerse themselves in a lengthy and challenging mathematical experience!

Special thanks to Emma Willard math department head Sunshine Greene for working with us to make all the advance arrangements, as well as to Emma Willard teachers Judy Price, Carmel Schettino, Meredith Legg, and Angela Richard for all their help running the event.

Thanks as well to Emma Willard Practicum Coordinator Anne Mossop for all she has done to support Emma Willard students in making connections with our math circle on Friday evenings! Emma Willard students been a tremendous and growing addition to our math circle in recent years--and we are delighted to have their talents and enthusiasm among us.

Special recognition is due to Emma Willard senior veteran Ashley Cho for all her leadership and encouragement of Emma Willard students, as well as her help in getting all the contestants to the right place at the outset of our contest.

Finally, a shout-out to Beth Schaffer, former Captain of Albany Area Math Circle, now an MIT senior. Beth launched new initiatives--the November tournament and the on-line version of the November and February tournaments--during her tenure as HMMT tournament co-director for the past two years. Both these innovations reflect her concern for outreach and inclusion.

AMC8 Tuesday Nov 16

2010-11-04T11:08:00.000-07:00

The AMC8 is coming up on Tuesday November 16. Some area middle schools will be offering this contest to their students. If you are interested in taking the contest, please make sure to check with your MATHCOUNTS coach and/or math teacher to see if your school is offering you the contest.

For those middle school math circle members attending schools that do NOT offer the contest, Albany Area Math Circle has arranged a special administration of the AMC8 to be hosted at Hebrew Academy of the Capital District.

Please use the form at this link to register your student.

Albany Area Math Circle is grateful to Hebrew Academy of the Capital District for its hospitality!

Try again! Fail again! Fail better!

2010-10-31T18:44:00.000-07:00

Students: Were you feeling discouraged by the difficulty of the problems you tried at our math circle on Friday evening?

If you found yourself struggling and flailing about and feeling lost, that means you are in the right place!

The problems we work on at math circle are supposed to be a LOT harder than the problems you get in regular school classes. Struggling, flailing about, feeling lost a lot--that is what mathematics is all about.

Mathematician Lillian Pierce has great advice on learning mathematics in an interview in the latest issue of Girls Angle Bulletin:

Enjoy math!

Especially, enjoy challenges!

Math is just like any other skill: practice counts.

Also, have courage and confidence in your abilities. Don't shy away from failing to solve something immediately: try out your ideas, make mistakes, learn from your mistakes.

The struggle itself is one of the most important parts of your practice.

Try again!

Fail again!

Fail better!

When you have been beating your head against a problem for a while, and getting nowhere, leave it and move on to other problems, struggle with those for a while, then come back with a new perspective. Sometimes just finding a partner so you can share what you've been trying can help a lot. Even if your partner is just as lost as you are, the simple act of explaining aloud what you've been trying may help to clarify the problem in your own mind. And perhaps you have a great approach but finding a small blind spot your partner can help you spot will make all the difference.

Remember: practice counts! And practice means making mistakes! It is OKAY to make mistakes, lots and lots of mistakes at our math circle meetings. If you are NOT making mistakes at our meetings, you are doing the wrong problems!

Don't be embarrassed about making mistakes at our meetings! All of us make mistakes. Celebrate your mistakes! Learning from your mistakes, your half-baked ideas, your false starts--that is the essence of problem solving.

Our math circle is a place where it's really, really okay to make mistakes! Don't be afraid. Enjoy that space and freedom to make mistakes! It's a treasure! Share your mistakes and what you've learned from them.

Signup for Harvard-MIT Math Tournament LOCAL

2010-10-29T22:25:00.000-07:00

Thanks to Emma Willard School for their gracious hospitality in accommodating our math circle's local administration of this November contest to our high school student members.

Please use the form below to sign up.

Loading...

"maverick mathematicians" and the power of grade school geometry

2010-10-18T08:50:00.000-07:00

Earlier this week, the New York Times published this obituary for Benoît Mandelbrot, excerpted below:

Benoît B. Mandelbrot, a maverick mathematician who developed the field of fractal geometry and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85. ....

Dr. Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature.

“Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found,” said David Mumford, a professor of mathematics at Brown University. “He was one of the primary people who realized these were legitimate objects of study.”

In a seminal book, “The Fractal Geometry of Nature,” published in 1982, Dr. Mandelbrot defended mathematical objects that he said others had dismissed as “monstrous” and “pathological.” Using fractal geometry, he argued, the complex outlines of clouds and coastlines, once considered unmeasurable, could now “be approached in rigorous and vigorous quantitative fashion.”

For most of his career, Dr. Mandelbrot had a reputation as an outsider to the mathematical establishment. From his perch as a researcher for I.B.M. in New York, where he worked for decades before accepting a position at Yale University, he noticed patterns that other researchers may have overlooked in their own data, then often swooped in to collaborate.

...

Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain? The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.

“Here is a question, a staple of grade-school geometry that, if you think about it, is impossible,” Dr. Mandelbrot told The New York Times earlier this year in an interview. “The length of the coastline, in a sense, is infinite.”

At last week's middle school math meet, we talked about a special kind of fractals, Pythagoras trees. The particular type of tree we investigated was made entirely out of squares and isosceles right triangles.

We started with the assumption that the biggest square in each fractal was 64, and tried to figure out how the area of the fractal grows as we add layers. One way to solve this problem is to use the Pythagorean theorem over and over and over again. That is the rather laborious approach that teachers came up with this summer at the Bard summer workshop for middle school math teachers.

Max Thomas of Hackett Middle School, however, came up with a very clever alternative approach. He noted that you can figure out that the isosceles right triangle in B1 must have area 16, because you can mentally "fold" it down into the big square below it, and easily confirm that it has area equal to one fourth of the big square. By similar reasoning, you can fold the same triangle in B1 over into the smaller squares in B1 and see that each of those two smaller squares must have an area of 32.

So, the total area of the fractal in B1 must be 64 + 16 + 32 +32 = 144. Can you extend Max's approach to figure out the areas of the succeeding fractals, and the general pattern as you add each layer of the fractals?

You can also investigate other kinds of Pythagorean trees by downloading free interactive applications from Wolfram MathWorld here.

Wolfram alpha also offers many other nice interactive fractal demonstrations here.

As Professor Mandelbrot and Max Thomas have both demonstrated, you don't always need to use high-powered mathematics to get very deep insights into fractal mathematics. Sometimes you don't even need the Pythagorean theorem, though playing with more complicated Pythagorean trees will certainly motivate more use and understanding of that idea. And if you persevere, the study of fractals can take you into more and more complex mathematics.

But first things first. Start with simple grade-school geometry and the Pythagorean theorem. See how far they can take you.

See what you can discover by investigating fractals playfully, starting with simple cases and working you way into the general patterns.

Math Marketing Done Wrong!

2010-10-14T04:37:00.000-07:00

Dear parents of students who attended our first middle school math meeet,

Thank you again for bringing your children to our first middle school math meet! They were a thoroughly delightful group to work with, and they helped our year of math meets get off to a great start!

It has come to our attention that Aileen Leventon, who is apparently a marketing person for a private tutoring business called "Math Done Right," was soliciting parents waiting to pick up their children after the meet, with information promoting that company.

None of the advisors of Albany Area Math Circle know anything about this "Math Done Right" business.

From our perspective, it was "Math Marketing Done Wrong!"

Ms. Leventon did not have our permission or endorsement to market her business to you, nor did she have permission from Hebrew Academy to market her business to you.

Please know that Albany Area Math Circle adult advisors are VOLUNTEERS! We are volunteering our time to create a vibrant mathematical community of kindred spirits who love problem solving together.

We are NOT volunteering our time to provide a marketing platform for a private business about which we know absolutely nothing.

If you encounter anyone attempting to solicit you for a private business at an Albany Area Math Circle event, please bring it to the attention of an Albany Area Math Circle advisor immediately. You can recognize us by our "Tough Traveler" ID badges (see below.)

Mary O'Keeffe
Albany Area Math Circle advisor

Thanks to Hebrew Academy of the Capital District ...

2010-10-12T19:56:00.000-07:00

... for hosting students from schools all over the Capital District at our October 2010 Middle School Math Meet!

Names and scores of high-scoring students and the value-added whole-is-more-than-the-sum-of-the-parts team award will be posted in this space later this week after the administration window ends.

Thanks to George Reuter and Mike Curry of MathMeets.com for writing a great set of problems for our students! Thanks to student coaches Matthew Babbitt and Zubin Mukerjee as well as Albany Area Math Circle advisors Bill Babbitt and Rita Biswas for helping make the meet great. A special thanks to Albany Are Math Circle Advisor and Hebrew Academy math teacher Alexandra Schmidt for all the arrangements she made for us.

Would YOUR school like to host our next monthly math meet, scheduled for Sunday November 7? If so, please get in touch with us by sending an email to mathcircle@gmail.com.

In addition to working on those Math Meet problems, we also talked about fractals and other fun mathematical topics today.

In honor of the recent 10/10/10 day, we talked about powers of ten, powers of two, and 42.

For example, we talked about how 101010 in binary is 32+8+2=42 in decimal, and of course how 42 is a delightfully special number.

(In addition to being the Answer to the Ultimate Question of Life, the Universe and Everything, we noted that 10!seconds = 42 days (exactly!) because

[10x9x8x7x6x5x4x3x2x1 seconds]÷[(24 hours/day)x(60 minutes/hour)x(60 seconds/minute)]=42 days.

We also introduced the concept of "bimal" notation, which is the binary analog of decimal notation.

In bimal, 1/2 = 0.1, 1/4 = 0.01, 1/8 = 0.001, 1/16 = 0.00001, and so on.

This allows us to nicely express the following question:

What is 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + .... (and so on forever)?

In bimal, the answer is 0.111111111111111..... (and so on forever).

But, just as in decimal, 0.999999999...... = 1, in bimal 0.111111111.... = 1.

And we talked about a special kind of fractals, Pythagoras trees. In honor of Dr. Benoît Mandelbrot, who died a few days after our middle school math meet, I have moved our discussion of that topic to a separate post, Maverick Mathematicians and the Power of Grade School Geometry.

Middle School Math Meet Tuesday October 12

2010-09-27T19:52:00.000-07:00

We again encourage our high school students to coach MATHCOUNTS teams and/or to organize and lead small middle school math circles for students in their areas.

Albany Area Math Circle is also offering something new for middle school students this year.

We will have a special monthly "Middle School Math Meet" event once a month.

Our first "Middle School Math Meet" event will be hosted by the Hebrew Academy of the Capital District on Tuesday October 12.

The meet will officially start at 4:15, but we will offer warmup activities for students who can arrive at 3:45. The meet will end by 5:30. Refreshments will be served. Students should bring pencils with good erasers. Please leave your calculators at home!

We will rotate days and locations for this monthly event in future months, including Sunday afternoons as well as weekday afternoons, so don't be discouraged if Tuesday afternoons are not good for you.

We also plan to rotate locations for this event, so please let us know if you would like to arrange for your school to host a future math meet. A special thanks to Hebrew Academy of the Capital District for "breaking the ice" and hosting the first one!

Parents of students who would like to participate in the October 12 math meet should use the form at this link to register their student.

Princeton University Math Contest (PUMaC)

2010-09-25T11:38:00.000-07:00

Albany Area Math Circle plans to participate in PUMaC again this year. This is a very challenging and exciting experience run by the undergraduate math students at Princeton University each year since 2006.

(It's exciting that two of our alumni are now undergraduate students at Princeton. Both Andrew Ardito and Dave Bieber participated in PUMaC throughout their high school years, and I'm sure they and all the students involved are eager to draw on their experiences to contribute their ideas to make this year's contest even better.)

Albany Area Math Circle teams have done very well in the past, and we plan to send two teams this year.

More information about PUMaC is available here.

Here are the key dates that Albany Area Math Circle students need to keep in mind for PUMaC:

As soon as possible, email me at mathcircle@gmail.com to let me know of your interest, even if you are not yet entirely sure of your schedule and ability to commit. We'll be happy to answer questions and to put your parents in touch with other parents whose students are considering going so they can discuss possible carpools and hotel-room sharing arrangements, etc. among themselves.

Sunday October 10: Deadline to inform me of a firm commitment to participate.

Saturday November 13 through November 19: Power Round of PUMaC All 8-person teams will work collaboratively during this time to solve and write up solutions to a multipart Power Round problem. Math circle students will do this collaboration mostly via Internet, and it's important that students who sign up for PUMaC make sure they will have time to work on the problems during this period and contribute to the solution and writeup.

Saturday November 20: All day on-site contest at Princeton University. The Power Round will be turned in at the beginning of the day. The remaining rounds (Individual Subject Tests and collaborative Team Round Test) will take place this day, along with a number of just-for-fun "Mini-Events" that don't count toward the final team ranking (Math Bowl, Rubiks Cube, Useless Math Olympiad, Chess, etc.)

For more information, you may want to talk to students who have gone in the past about their experiences. Veterans from last year who have already notified me of their enthusiastic plans to return this year are: Matthew Babbitt, Gurtej Kanwar, Zubin Mukerjhee, and Jay White. Ashley Cho is also definitely going. Once we have the team composition settled, we will hold a preliminary organizational meeting to help our first-time participating students prepare to make the most of this exciting opportunity.

I have created a special google groups email discussion list for Albany Area Math Circle students who are possibly interested in going to PUMaC this year. Even if you are not sure if you can go yet, you are welcome to join the group to find out more about preparing for PUMaC. Email me as soon as possible if you are interested in PUMaC for this year and I'll add you to the list.

UPDATE: See comments below for questions and answers from math circle students about how PUMaC is going to work.

Andrew Ardito: Soul of the Albany Area Math Circle

2010-08-04T12:39:00.000-07:00

Andrew Ardito, our math circle's captain for the past three years, has racked up an extraordinary string of accomplishments during his time with our math circle. His infectious passion for problem solving challenges has inspired many others in our math circle community, both younger and older, and we will all miss him enormously as he heads off to college this fall.

Andrew is a homeschooled student from Coxsackie whose accomplishments go well beyond mathematics. By the end of his junior year of high school, he had already reached National AP Scholar status by getting high scores on nine AP exams, and he took five additional AP exams in his senior year. Those 14 AP exams covered a wide variety of disciplines including literature, art history, US and world history, economics and government, as well as mathematics and all the natural sciences. He also managed to find time to study four years of Russian during high school. He went into special depth in mathematics and physics, taking several advanced physics classes at SUNY Albany as well as even more advanced math classes at SUNY Albany and RPI, including number theory, topology, analysis, and a graduate class in combinatorics. His many honors also include a National Merit Scholarship and a Robert C. Byrd Scholarship. In addition, Andrew has won numerous awards for chess, as well as coaching a chess club for younger students.

Andrew started out as one of the youngest members of our first middle school math circle, back in 2003. He eagerly moved on to greater and greater challenges, taking over as captain of our high school math circle in his sophomore year of high school. He also student-coached MATHCOUNTS teams throughout his high school years. In his junior year, he helped spur a reinvorigation of our middle school math circles, and he leaves a remarkable legacy of inspiring leadership behind, as he has worked with so many students who have already demonstrated great promise as mentors themselves.

He is an outstanding example of the guiding principle of our math circle: the best way to learn is to share what you think you already know with someone else, because explaining it to them deepens your own understanding.

Andrew has accumulated an extraordinary number of accomplishments during his time as a member of our math circle, both in mathematics and in other areas.

A partial list of his many honors in mathematics include:

☞ National MATHCOUNTS contestant all three years as a member of the New York State team in middle school. As a 7th and 8th grader, he won the New York State championship and made the National Countdown Round in both years, placing sixth on writtens in 2005 and and 2nd place in the country at MATHCOUNTS Nationals Countdown in 2006. He also provided team leadership to two Chapter-winning teams, one of which came in 3rd place in the state.

☞ As a high school student, Andrew coached many successful MATHCOUNTS teams, including several teams that won Chapter championships and one team that won a state championship. He also coached many students who won high individual honors at Chapter and State MATHCOUNTS contests, including quite a number of Chapter and State CountDown participants and National MATHCOUNTS contestants. His mentorship and enthusiastic example has also inspired many younger students to embrace some exciting and challenging high school contests while still in middle school, including AMC10/12, HMMT, and NYSML/ARML.

The photo above shows Gili Rusak, a 7th grader at Shaker Junior High, and Aniket Tolpadi, an 8th grader at Iroquois Middle School, working with Andrew in a middle school math circle meeting. Both Gili and Aniket qualified for the American Invitational Math Exam (AIME) this year. Gili was the only 7th grader in the state to qualify for this exam, while Aniket was one of only four 8th graders in the state to do so.

☞ Andrew has earned many outstanding honors in high school math contests: he began taking the AMC high school contests in sixth grade and has won many honors in that series: he qualified for the AIME seven times, for the USA Math Olympiad five times. In 2007, he qualified for the Math Olympiad Summer Program; in 2008, he was the top scorer in the state on the AMC12B, and he also won an AMC12 gold medal for his consecutive four years as math circle's high scorer on the 12A and/or 12B.

Andrew has consistently been among Albany Area Math Circle's top three scorers on the AMC12 in every year since he began taking that exam in seventh grade, helping the math circle teams score among the top teams in the state each year. In February 2010, in his final attempt at the AMC12, he contributed to a record best-ever team performance by any Albany Area Math Circle on any AMC math contest--the Albany Area Math Circle AMC12B team of Dave Bieber, Andrew Ardito, and Schuyler Smith placed first in New York State. Indeed their team's performance on that remarkably challenging 2010 AMC12B contest was among the top five team scores in the country. Two younger students whom Andrew has coached in the past both earned top individual honors on honor roll for AMC12A/B: Schuyler Smith tied for high-scorer in the NY-NJ region on that contest, and Matthew Babbitt earned honors as the region's top-scoring student in ninth grade or below.

The first time Andrew qualified for the USA Math Olympiad, he had to take the 9-hour contest by himself, because he was the only qualifier in our area that year. However, he has generously shared his olympiad problem-solving skills with other students, and this has resulted in the camaraderie of a growing number of math olympians in our math circle taking the contest together in every year since then. This year's qualification process was exceptionally rigorous and yet our math circle had a record-tying five students taking the USA Math Olympiad, as Andrew was joined by Felix Sun (Shenendahoah HS junior), Matthew Babbitt (homeschool freshman), Schuyler Smith (homeschool junior), and Dave Bieber (Niskayuna HS senior).

There is an ancient metaphor invoked by many philosophers, mathematicians, and scientists that seems especially apt here: "standing on the shoulders of giants."

Andrew once stood on the shoulders of earlier members of Albany Area Math Circle, and he gives special credit to founding member and "soul of the Albany Area Math Circle" award-winner Drew Besse for inspiring and mentoring him.

In turn, Andrew's shoulders have surely provided strong support to launch many other students in our math circle, who in turn launch other students, and so on and on. Although Andrew and Dave will be heading off to college in the fall, our other olympiad veterans, who also include Ashley Cho (a rising senior at Emma Willard) and Jay White (a rising homeschool senior), as well as Felix, Matthew, and Schuyler, will surely continue to provide strong mentorship shoulders to future aspiring olympians in our math circle. Andrew has also helped to encourage and inspire a growing number of participants in the USA Physics Olympiad contests: our math circle had a record four students reach the top level of that contest series this year, with Dave, Schuyler, and Gurtej Kanwar (a Bethlehem HS junior) all joining Andrew in taking the USAPHO.

☞ Andrew has consistently risen to the occasion with outstanding and enthusiastic contributions to countless collaborative math team rounds in a variety of venues. He began participating on our teams for NYSML and the Harvard-MIT Math Tournament in middle school. PUMaC, the Princeton University Math Contest, did not start until he was a freshman, but he participated in that contest, studded with a stellar field of many of the strongest math olympians in the country, throughout his four years of high school, accruing multiple top 10 honors as a sophomore, junior, and senior years, including 2nd place rankings in combinatorics (2009) and number theory (2007). His record at ARML is also especially noteworthy: in 2007 and 2010, he made the national tiebreak rounds and received Individual High Scorer of the Meet awards, while in 2008 and 2009, he earned honors as high scorer on the Upstate NY team.

As Team Captain, his leadership contributions to team rounds at NYSML, HMMT, PUMaC, and ARML have been exceptionally impressive. Competing against extraordinarily strong teams from all over the state, the country, or even the world, he has led our math circle teams to many great rankings. Special highlights for teams he has led as captain include 3rd place rank at NYSML 2009--and "Most Improved" team award, 2nd place rank at NYSML 2010, 1st place rank for NYSML local in 2009-2010, a top 10 rank at HMMT 2010, and 3rd place Power Round at PUMaC in January 2009.

The crowning accomplishment for Albany Area Math Circle during Andrew's time as captain came in the national/international ARML Power Contest in 2009-2010. That contest is a collaborative round in which all members of the math circle were able to work together, and it's key for the captain to find ways to make the most effective use of the collective talents of rookies as well as veterans. There are two rounds to that contest each year, one in November and one in February. There is extremely challenging competition from math circles and magnet school programs all over the country and the world. The top 10 teams are honored with plaques at ARML each June. Our math circle had done well in the past, but we had never made that top 10 list before. Andrew clearly had been thinking hard about how to draw on his years of experience and knowledge of other students' strengths to do well this year. In November, the team was thrilled to take eighth place on the honors list, and in February, they were even more ecstatic to learn they'd placed second on the February round, resulting in a fourth place rank overall for the year. The photo below shows happy representatives of the Upstate NY Math team from the Albany Area Math Circle accepting the plaque at the Penn State ARML awards ceremony on behalf of all members of the Albany Area Math Circle.

As I write these words in August 2010, Andrew is at PROMYS, a summer program designed for students with extreme talent and passion for mathematics. Andrew won the ARML Scholarship to attend PROMYS in 2008 as a student, and returned as an advanced student the following year. This summer, he is a member of the instructional staff at PROMYS, working as a counselor.

Next month, Andrew will go off to Princeton, where he plans to study math. Dave Bieber will be heading to Princeton as well, with plans to study computer science. (For more about Dave, see this post.) Dave and Andrew have been the heart and soul of Albany Area Math Circle since Beth Schaffer and Drew Besse graduated in 2007.

Our math circle will miss them both, but we hope they'll come back to visit during school breaks, as Beth and Drew and many of our alumni do. And our math circle students will look forward to seeing them when the team travels to Princeton for PUMaC in November.

And, if Dave and Andrew miss our math circle, Princeton now has one too. Our loss is their gain. Well, no, not really--it is not a zero-sum game, but rather a positive-sum game. Our intersecting circles enrich us all.

And, of course, both Andrew and Dave have left our math circle with a remarkable legacy--their friendly encouraging spirits and their passionate enthusiasm for challenge and their generous willingness to share their prodigious talents and their remarkable ability to help others work well together will remain behind in the hearts and souls of all the enthusiastic younger students with whom they have worked.

Pythagorean Auctions notes

2010-08-01T19:36:00.000-07:00

Notes from my Pythagorean Auctions session at the New York Middle School Math Teacher Workshop at Bard College are available here. I will annotate them more fully later this summer.

http://sites.google.com/site/pythagoreanauctions/

Pythagorean auctions and other Pythagorean excitement for middle school teachers at Bard College next week!

2010-07-21T06:06:00.000-07:00

As I said, why should students have all the fun?
Next Monday, I will be leading a session on Pythagorean auctions at the New York City Math Teachers Circle summer workshop for middle school mathteachers at Bard College.

The inspiration for running math auctions in my session came from an idea I first read about in the book Mathematical Circles (Russian Experience) by Dmitri Fomin, Sergey Genkin, and Ilia Itenberg. Further encouragement came from a very enthusiastic presentation by Anna Burago at MSRI's Great Circles 2009 conference. Anna has many years of experience with math circles, both as a student in her native St. Petersburg and now as a lead teacher for the Northwest Academy of Sciences math circle. Here is her description:

Mathematical Auction is an exciting team mathematical contest. It combines mathematics with the elements of gambling and psychological thriller. The game starts from a period of problem solving which is followed by a round of trading. The teams bid, scheme and strategize for the rights to present the solutions to the problems. Mathematical Auction is one of the favorite competitions in the Math Circles that I run.

As an economist, of course, I was intrigued by the idea of a mathematical auction, so I had to try the idea out in our math circle. Since Anna said that the auctions are especially popular with middle schoolers, we ran some math auctions at our Albany Area Math Circle middle school math circle meetings last spring--and they were indeed very well received by the students. I hope the teachers at next week's workshop will also enjoy using math auctions to explore some interesting Pythagorean mathematics.

Here are the rules for a Math Auction:

1) The auctioneer hands the teams a set of problems--about five or six problems is considered ideal. But the problems are a special kind--Russian math circle leaders call them "research problems" because they allow possibilities for partial solutions or intermediate answers which can gradually lead to a final result.

2) Teams are given a certain amount of time to work on the problems.

3) When that time is up, the auction begins. Each team starts with a certain amount of fictional currency at the outset of the auction. In honor of Pythagoras, we'll use drachmas as our fictional unit of currency in next week's workshop, so each team will have 1,000 drachmas to use in their bidding.

4) The teams then bid for the right to present a solution to each problem. The team that submits the highest bid in the initial round of the auction gets the right to present their solution. After they present their solution, the bidding reopens so that other teams who believe they can improve on that solution may do so. The team with the strongest solution to the problem wins the value of the problem. Bonus drachmas may be awarded for cool discoveries made alone the way.

The focus of the summer teacher workshop is the Pythagorean theorem, so all the problems we will be auctioning off next Monday afternoon will use that theorem in a variety of fascinating ways--many of the auction problems will connect to the presentations that will be given by other speakers later in the week.

Here is the list of workshop presentations scheduled at the Bard math teacher summer workshop next week:

Auctions of All Things Pythagorean: Spirals, Trees, Triples, Twins, Quads, Networks, and Outcastes, Mary O'Keeffe (Albany Area Math Circle)

Showing of The Theorem of Pythagoras (movie created by Tom Apostol's Project Mathematics! at Caltech with awesome animation from MacArthur "genius" prize winner Jim Blinn )

Primitive Pythagorean Triples Sheila Krilov (Hunter College High School teacher and MATHCOUNTS coach)

Heronian Triangles David Hankin (former chair of the AIME Committee and veteran teacher/math department chair Hunter College High School)

Showing of The Proof (movie about Andrew Wiles proof of Fermat's Last Theorem)

Pythagoras in Spherical and Hyperbolic Geometry, Jim & Maria Belk (Bard College faculty)

Eight Different Proofs of the Pythagorean Theorem Gary Rubinstein (Stuyvesant High School faculty)

Fermat n=4 and Some Interesting Open Problems in Number Theory Lauren Rose (Bard College faculty)

Primitive Pythagorean Triples via Unique Factorization John Cullinan (Bard College faculty)

Almost Pythagorean Triples, and Almost Isosceles Pythagorean Triples: Connecting to Pell's Equation, Japheth Wood (Bard College faculty)

All of this mathematical excitement (as well as music and film festivals) will take place on Bard's campus next week. The area near Bard, overlooking the Hudson River, is a spectacularly beautiful setting at this time of year (word has it that Chelsea Clinton will be getting married nearby shortly after the math circle teacher workshop ends!)

There may be still room for a few more math teachers to attend the workshop--and it is even possible to arrange for continuing education credit. Please pass the word along to any middle school math teachers you know who would enjoy this experience!

http://www.nymathcircle.org/2010workshop

Spectacular summer math programs in Upstate NY: Part I

2010-06-17T11:10:00.000-07:00

I'll be writing about two terrific summer math programs in Upstate New York that still have openings. One is a week-long daycamp program for middle school students and one is a week-long math immersion retreat for middle school teachers. (Because why should students have all the fun!)

This post is about the program for students. I'll write about the program for teachers later this week.

Albany Area Math Circle alumni Dave Bieber and Markus Salasoo will again offer their summer math day camp for middle school students July 12 to 16 amid the beautiful and inspiring surroundings of the Association for the Protection of the Adirondacks in Niskayuna. Parents and siblings of math campers are welcome to walk around the grounds of the adjacent wildlife sanctuary while Dave and Markus lead their students in a week of fun "think outside-the-box" mathematics.

Dave and Markus initiated this camp in 2008, and this will be their third year of running this very well-received program. Dave has written about the first year of the camp here. Dave has also been coaching the Van Antwerp Middle School MATHCOUNTS team for the past two years. The National MATHCOUNTS organizations recognized his very successful coaching with "Coach of the Week" honors in March. Dave was the first ever student coach to receive this recognition! You can read more about Dave here.

Dave and Markus started this program as high school students, and it is great to see them build on their enthusiasm and experience continuing to run it as they move on into college: Markus is a rising sophomore at Cornell and Dave will be a freshman at Princeton in the fall.

The camp is aimed at mathematically and behaviorally mature middle school students (entering 6th through 8th grades). More information and a camp application are available here.

In memory and appreciation of Prof. Leo Schneider

2010-06-06T12:37:00.000-07:00

Just two months ago, we were honored to have Professor Leo Schneider come to Albany for NYSML, the statewide math championship math meet, where our students, as well as students from all over New York State, got to see him in action as he helped to run the tiebreak rounds (above, with George Reuter) and subsequently explained the mathematics behind the solutions to those problems to an audience of hundreds of students.

Professor Schneider has composed many terrific problems to challenge and inspire high school students at ARML and NYSML over the years. In fact, he has written all of the problems used at NYSML for at least a decade, and he has also overseen the grading of the essay/proof-based Power Question during that time. He has also contributed AMC contest problems and volunteered with the International Math Olympiad. Our students have very much enjoyed working on many of his problems during official competitions, as well as learning more from those problems by working on them informally afterwards as they prepared for future competitions.

Yesterday, the American Regions Math League (ARML) national organization honored Professor Schneider by awarding him the 2010 Al Kalfus Award for Distinguished Service. Prof. Schneider was on-site to receive that honor, as well as to serve in his role as Chief Judge of the national high school math contest, including overseeing the grading of the power round on Appolonian circle packing.

Less than 24 hours later, we received the sad news that Professor Schneider passed away suddenly while traveling from ARML.

He leaves a remarkable legacy behind--thousands and thousands of students all over the state and all over the country, inspired and energized by the mathematical excitement he created in the problems he composed for them. And decades of future students will grow mathematically by continuing to work informally on those problems in the future.

Professor Moorthy, Mr. Babbitt, Professor Biswas, Beth Schaffer, and I had the privilege of meeting and dining with Professor Schneider and other NYSML officials the night before NYSML this year. His eyes sparkled as he talked about how he'd found inspiration for this year's Power Question in a visit to a factory that used computer-controlled milling machines. His motto was "There's a Power Question in everything!" and it's clear that his mind was constantly open to the possibility of interesting mathematics in every daily encounter.

Thank you, Professor Schneider. You will be missed, and we will think of you as we continue to work with future cohorts of students and to reflect on the mathematics embodied in the problems you have composed.

Hale and Farewell!

2010-05-31T11:19:00.002-07:00

Yesterday's picnic was beautiful and bittersweet as we greeted our returning alumni and officially welcomed our graduating seniors into their midst. It was a pleasure to have alumni Alison and Catherine Miller, Zagreb Mukerjee, Beth Schaffer, Liz Simon, Susanna Todaro, Yipu Wang, Lindsay White, and Tom Zink join our gathering.

Our graduating seniors are going off in a variety of directions: Andrew Ardito and David Bieber are headed off to Princeton; Heidi Chen will be at Williams; Peixuan Guo will be at Columbia; Brady Pelkey at Drexel; and Anagha Tolpadi and Eric Wang will be at Cornell.

Our sadness at seeing our seniors go is attenuated by the terrific legacy they are leaving behind--our seniors have done an outstanding job of mentoring and encouraging a record-size group of superb younger students to follow in their footsteps. A few of them are shown at left, including seventh grader Shreya Arora, standing, who received special recognition for her leadership of the delightfully named "Persistent Chickens." At left in the photo is 8th grader Cecilia Holodak, who won this year's Chapter Countdown Round, captained the first place team at Chapter, and was a member of a Science Bowl team that placed 7th in the nation. Gili Rusak (center) and Jien Ogawa (right) were the high scoring AMC8 students in the region this year. Gili also qualified for the American Invitational Math Exam (AIME) this year. Cecilia and Gili are both headed to Penn State as members of the Upstate New York ARML team this week.

Our younger students as well as our vets have already racked up an impressive array of other accomplishments, which we will recap in coming end of year posts. We look forward to seeing our younger students and our vets attack many mathematical challenges in the future.

Meanwhile, at the other end of the spectrum, it was fun to learn news of alumni who were unable to join us. Founding member Drew Besse is in California this summer, interning at Facebook. Longtime member Nicole Bieber and founding member Manisha Padi will be marching in MIT's graduation ceremonies this week. Nicole has already begun work on her master's degree in computer science. Manisha has been studying economics and mathematics as a Burchard Scholar.

Congratulations Matt!

2010-05-15T07:26:00.000-07:00

Matthew Babbitt (at left above, celebrating after NYSML with teammates Zubin Mukerjee, Gili Rusak, Cecilia Holodak, and Jien Ogawa) scored high enough on the notoriously challenging 2010 USA Math Olympiad contest to qualify for an invitation to this summer's Math Olympiad Summer Program.

Congratulations! You are among a very small group of about 57 students (from the original pool of over 221,000 AMC 10 and AMC 12 participants) invited to take part in the 2010 Mathematical Olympiad Summer Program (MOSP) scheduled to begin Tuesday, June 8 and ending Wednesday, June 30, 2010. This year’s MOSP will be held on the campus of the University of Nebraska-Lincoln.

The purpose of the program is to broaden the participants’ view of mathematics and foster their excitement toward further study. It will better prepare you for possible future participation on our International Mathematical Olympiad team as well as for possible careers involving mathematics.

Full days of classes, problem solving and tests give students extensive preparation in several important areas of mathematics, including algebra, geometry, combinatorics, number theory, and many other special topics. All members of the MOSP staff are housed with the students, and will closely interact with all the participants outside of class as well. In the past this interaction has greatly contributed to the development of America’s most talented young mathematicians.

Please note that basic MOSP expenses for food and lodging will be covered by the MAA American Mathematics Competitions. We will also reimburse your round-trip travel expenses up to $400 (see attached MOSP Acceptance and Travel Agreement). Additional information about MOSP can be found in the Student Handbook. You will also receive a set of MOSP Medical Forms that your parent/guardian will need to complete, and return to us so they arrive by May 26, 2010.

I am pleased to invite you to the 2010 MOSP, and feel that this program will offer you three weeks of camaraderie with many of our country’s top math students, and activities which will make a significant difference in your mathematical education.

Sincerely,

Prof. Steven R. Dunbar
AMC Director

Cc Zuming Feng, MOSP Academic Director

Some of the factors that have contributed to Matthew's success:

1) Matthew delights in working with other students in our high school math circle and has been a key leader in our middle school math circles as well. He exemplifies one of the mottos of our math circle: the more of your mathematical understanding you share with others, the more you have for yourself. Answering the questions of other students who are struggling with a problem you believe you have solved deepens your understanding of that problem. The relationship between mentors/mentee or collaborators is mutually beneficial: the whole really is more than the sum of the parts. The photo at the top of this post shows Matt celebrating at NYSML with some of our math circle students who have enjoyed working with Matt over the past two years, starting out in our middle school math circle, where Matt has been a leader, and have now moved up to our high school math circle: Zubin Mukerjee, Gili Rusak, Cecilia Holodak, and Jien Ogawa. His interactions with them and with many other math circle members, seasoned veterans and fresh-faced rookies alike, have advanced his understanding of mathematics. In a very real sense, all members of our math circle can claim a share of the credit for his success.

2) Matthew likes to write about mathematics! He has sharpened his mathematical expository skills in many ways.

An informal, free, and fun way to start out writing about math is to participate in the Art of Problem Solving forums, where Matthew has been an active participant. Choose an interesting problem posted by another participant who wants to discuss solutions and post your ideas about how to solve it. Or post a question of your own that you've been struggling with and would like to discuss in order to understand it better. Putting your question in writing can help you sharpen your understanding of the problem. Writing down a clear description of your attempt at solving a problem forces you to think explicitly about some of the assumptions you are making.

Once a student develops comfort in writing in that informal, friendly, and highly interactive environment, the way paved for the student to move to writing in more formal settings, such as mathematics journals that post challenging problems and welcome well-written student submissions.

The Canadian Mathematical Society publishes an excellent journal called Crux Mathematicorum with Mathematical Mayhem. They post challenging problems in each issue in their "Mathematical Mayhem" section. The currently open problems are here. (They are published in French and English, so if your French is sketchy, just scroll down the PDF to the English version.) Anyone who would like to try to solve these problems is welcome to mail in their solution to Crux before June 15. The names of all successful submitters will be published in an issue next fall. In addition, Crux publishes an examplary solution to each problem in that subsequent issue as well.

Browsing through recent issues of Crux, you can see that Matthew has submitted a number of correct solutions to problems this past year, and they even published one of his solutions as a highlighted solution as well. Check out problem M379 on pages 429-430 to see Matthew's published solution to a problem submitted by Professor McLaughlin of the University of New Brunswick. It's fun and fascinating to see the diversity of the names, affiliation, and hometowns of the other people who submitted correct solutions to the same problem. In this case, the other successful submitters are listed by Crux as: Edin Ajanovic, First Bosniak High School, Sarajevo, Bosnia and Herzegovina; George Apostolopoulos, Messlonghi, Greece; Antonio Godoy Toharia, Madrid, Spain; Richard I. Hess, Rancho Palos Verdes, CA; R. Laumen, Derne, Belgium; Richard Peiró, IES "Abastos", Valencia, Spain; Mridul Singh, student, Kendriya Vidyalaya School, Shillong, India; Neculai Stanciu, George Emil Palade Secondary School, Buzău, Romania; Edward T.H. Wang, Wilfrid Laurier University, Waterloo, ON, and Jixuan Wang, student, Don Mills Collegiate Institute, Toronto, ON. (It's interesting to note that Jixuan was a member of the Canadian team at the 2009 International Physics Olympiad, where he won a silver medal, and it looks like he is leading contender for this year's team as well. Sharpening those expository writing skills comes in handy in physics too! Jixuan has also done very well on the Canadian Math Olympiad.)

There are other journals that publish excellent problems and welcome student submissions, including the Mathematical Association of America's Math Horizons magazine, where Albany Area Math Circle student Felix Sun submitted a solution that was published as a highlighted solution last year. Other magazines where you can look for problems include: the American Mathematical Monthly, Mathematics Magazine, the College Mathematics Journal, the Harvard College Math Review, and the Pi Mu Epsilon Journal.

Stop by a library at a local college and you can easily browse through recent issues of most of these journals. The Harvard College Math Review appears to have gone into a latent stage, but you can find interesting back issues to browse here.

It should be noted that all these journals welcome submissions of original problems. Most of the problems they publish are submitted by their readers. Composing a good problem can be a great way to develop your problem solving abilities. Matthew has also had one of his problems published in Crux. (Check out Problem M410 of the November issue to see Matt's problem. The list of successful solvers and a highlighted solution submitted by a reader will no doubt appear in an upcoming issue. It will be fun to see the names and hometowns of those who have worked on Matt's problem. Maybe someday he will meet one of the solvers at the International Math Olympiad!

Name this polyhedron?

2010-05-12T11:51:00.000-07:00

Four years ago, scientists at Pacific Northwest National Laboratory announced their exciting and surprising discovery that gold atoms can also form beautiful polyhedral configurations, like the 16-atom gold molecule shown above. Previously, it had been thought that metals were too reactive to organize themselves in such orderly but hollow structures.

The American Mathematical Society covered the story as follows:

The recently constructed molecular cage, made of 16 gold atoms, has the shape of a truncated tetrahedron.

Add a new member to the family of nano-polyhedra concocted by chemists. This one is made of 16 gold atoms arranged to form a truncated tetrahedron: delete the four vertex atoms from the array corresponding to the tetrahedral number 20. The New York Times for May 16, 2006 reported the construction, which is described in "Existence of hollow golden cages," by Lai-Shen Wang (Pacific Northwest National Laboratory) and collaborators, in the May 30 PNAS. The authors report that this is the first time free-standing metal hollow cages have been detected in the laboratory. In fact their method produced a mixture of the Au16 cages with slightly larger ones made of 17 and 18 atoms. They note that these cages are presently empty, but that their calculations suggest that "these hollow golden cages can easily accomodate a guest atom with very little structural distortion to the host cages." In case you want to do this at home, "The gold cluster anions were produced by using a laser vaporization cluster source" and the results were anyalyzed by photoelectron spectroscopy, "using a magnetic-bottle time-of-flight photoelectron analyzer." No name has been coined yet for these miniature gold cages (inside diameter about 6Å or 6.10-10m) akin to the evocative "buckyball" for the Carbon-60 soccer-ball shaped molecules. In fact the Times's take on the story, written by Kenneth Chang, was "16 Golden Atoms in Search of a Catchy Name."

Work on the properties of the Carbon-60 Buckyball (aka "truncated icosahedron") won the Nobel Prize in physics in 1996. For those who like to play with mathematical ideas playfully, I highly recommend the "Oball" toy shown in the video below, loosely based on the buckyball/truncated icosahedron. We'll have some Oballs on hand during our annual picnic on Memorial Day weekend.

Perhaps work on the golden polyhedral molecules will win a prize as well, but a catchier name than "truncated tetrahedron" might help!

Congratulations and good luck to our students on the All-Star Upstate NY Math Team!

2010-05-09T12:02:00.000-07:00

Congratulations to the following Albany Area Math Circle students who have been accepted to the All-Star Upstate New York Math Team for the premier national math competition, ARML, to be held at Penn State next month:
Team veterans Andrew, Dave, Peixuan, Anagha, Schuyler, Matt, and Zubin know that there are many reasons that ARML is awesome and that our rookies have lots to look forward to at ARML, including:

1) Chance to make friends and work hard with outstanding students from all over Upstate NY while riding the bus to Penn State together and talking over the problems between rounds.

2) You can learn a ton of math (and have a ton of fun) in Friday's all-day marathon team practice at Penn State.

3) The great coaching staff includes professional teachers and college student coaches and parent volunteers as well. Albany Area Math Circle alumna Beth Schaffer (left foreground), who is also co-director of the Harvard-MIT Math Tournament, has been a student coach for the Upstate NY ARML team throughout her college years, as has Albany Area Math Circle alumnus Tom Zink, now out in the working world, but still dedicated to the team. Albany Area Math Circle advisor Bill Babbitt and Professor Rita Biswas will also travel with the team to Penn State to assist with coaching and proctoring.

Several of the veteran coaches are full-time active high school math teachers, including head coach Mr. Reuter. Professional math teacher Mrs. Sandy Ohlerich is now retired but still accompanies the Upstate NY team to Penn State each year. That is dedication--and experience--and expertise!

4) A mathematician gives a fascinating math talk on Friday night. In recent years, the speaker has been the awesome saramarie belcastro, above. Her topics have included: Surprising Binary Sequences and Mysterious Expanding Tilings and Matching Up Grids

Here's a poster for the talk Professor belcastro gave last year:

5)Last year's Upstate NY A team miraculously managed to correctly solve the 15-person Super Relay!!!! (and won ARML Frisbees!)

The Upstate NY teams have done consistently well over the years, averaging around 15th place out of 150 teams competing from around the country (and the world!) in recent years. Last year's Upstate NY team beat several teams representing entire states (including Texas!) with populations much larger than Upstate New York!

Good luck to this year's upstate New York team!

USA Math Olympiad 2010

2010-05-05T12:25:00.001-07:00

Thanks to Congregation Agudat Achim for hosting Albany Area Math Circle's five USA Math Olympiad students for the nine-hour contest last week!

Thanks to Alexandra Schmidt for helping with arrangements and taking the photos of the students talking over the problems afterwards.

As usual, the six USAMO problems were very challenging.

The problems are available at these links on the AMC website: day 1 problems and day 2 problems. Links to solutions will be posted after they are published.

Congratulations Cecilia, Martin and teammates!

2010-05-03T06:24:00.000-07:00

Albany Area Math Circle students Cecilia Holodak and Martin Shreiner are members of the Van Antwerp Science Bowl team that reached the top eight at the national contest in Washington DC this weekend. Their team will be among those honored in a final ceremony at which First Lady Michelle Obama and Energy Secretary and Nobel Laureate physicist Steven Chu will speak this afternoon.

Reporter Michael Goot covered their team in an article in today's Daily Gazette, excepted below:

Van Antwerp students score high marks in D.C.:

NISKAYUNA — Van Antwerp Middle School’s science team finished in the top eight in the country at the National Science Bowl held over the weekend in Washington, D.C.

... Teams face off against each other in a Jeopardy!-style quiz that tests knowledge of biology, chemistry, earth science, physics, astronomy and math. Each finalist school receives $1,000 for their respective science department.

The Niskayuna students placed first in their division in the initial pool play and then survived three rounds in the double elimination format. [Van Antwerp's coach Connie Soron] said she was proud of the team’s sportsmanlike attitude.

“They were graceful winners and even more graceful losers when they were eliminated. It was handshakes and good luck to the winning team.”

The students also had to construct a solar-powered car. The students had some difficulty when the piece that holds the motor in place broke off just before the first time trial, according to Soron. The team had to miss the first heat while they fixed the car.

Soron credited the students for thinking on their feet.

“What’s so great about this competition is it challenges middle school students to problem solve real-life situations and find a way to accomplish their objective,” she said.

Even though the students’ car had a good time in the second heat, one of the car’s wheels went off the track in the third one.

The team has been practicing since January, spending free periods and after school getting ready for competition.

“I read a lot of books,” said 13-year-old seventh-grader Martin Schreiner. [at right above]

Eighth-grader Cecilia Holodak, 13, said she learned a lot from the experience.

“I enjoyed being here and meeting people like me that are also interested in science and math,” she said. “I enjoyed being able to meet some adults that are also in careers in math and science.”

The team also includes Andrew Stewart, Aiden Wolfe and Alexander Young.

Cecilia and Martin were also members of Van Antwerp's Chapter Championship MATHCOUNTS team, coached by Albany Area Math Circle senior Dave Bieber. Cecilia captained that winning team and also won the Countdown Round at chapter, and was also a high scorer on the Albany Area Math Circle Octahedra team at the high school state championship math meet, NYSML. Martin's voracious reading habits no doubt contributed to his strong performance in the Capital District regional spelling bee in March.

Celebrating teamwork and mathematical problem solving

2010-04-24T10:24:00.000-07:00

Quest of 3 genome musketeers
Pals who transformed biomedical research share Albany Med prize

By CATHLEEN F. CROWLEY, Albany Times Union Staff writer

ALBANY -- Three good friends reunited Friday at Albany Medical Center. Three decades ago, they were the cheerleaders and the brains behind the effort to map the human genome.

On Friday, they picked up the Albany Medical Prize in Medicine and Biomedical Research, which at $500,000 is the largest cash prize in medicine in the United States.

A few minutes into their "grand rounds" lecture -- a formal medical tradition where wisdom is shared among colleagues -- a voice announced over the Albany Med loudspeaker that fire alarm testing would begin immediately.

The scientists roared with laughter.

"We are the three genome musketeers," said Dr. Francis S. Collins, "We've been setting off fire alarms for 30 years."

In a nutshell: David Botstein, a geneticist, was one of the first people to suggest the idea of mapping the human genome; Eric Steven Lander, a mathematician, created new algorithms for analyzing genes and mapping complex multiple-gene diseases; and Collins, a physician and biologist, created faster mapping techniques and eventually oversaw the world-wide Human Genome Project from a post within the National Institutes of Health.

"They collectively unlocked and then opened the door that had previously barred us from understanding disease processes at the most basic genetic level," said James J. Barba, president of Albany Med.

Eric Lander, the mathematician on the prize winning team (pictured at left above), got a running start in developing his mathematical problem skills, as well as his teamwork and leadership skills, as a leader of his math team at Stuyvesant High School in New York City. The USA Math Olympiads were just starting up when he was in high school, and he was among the first Americans to take those contests and to represent the USA at the International Math Olympiad in 1974.

This coming Tuesday and Wednesday, 300 students across the country will be taking the USA Math Olympiads. Six of the highest scoring students will follow in Eric Landers' high school footsteps and qualify to represent our country at the 2010 International Math Olympiad to be held in Kazakhstan in July.

Congratulations and best wishes for a great adventure in problem solving in the coming weeks to all the students writing the USAMO this week, especially those from New York State, listed below, and--of course, especially to the five students from Albany Area Math Circle.

We know that the problem solving skills that all our New York State mathletes have already demonstrably acquired can be put to many important uses in the future. Our state and our country and our world have many problems to solve.

Albany Area Math Circle, Niskayuna NY:
Andrew Ardito
Matthew Babbitt
David Bieber (Niskayuna High School)
Schuyler Smith
Felix Sun (Shenendahoah High School)

Columbia Grammar & Prep School New York NY
Reed LaFleche

Comsewogue High School Port Jefferson NY
David Lawrence

Corning-Painted Post West High School Painted Post NY
Vasily Kuksenkov

Garden City High School, Garden City NY
Jan Gong

Great Neck South High School, Great Neck NY
Keaton Stubis

Hackley School Tarrytown NY
Michael Celentano

High School for Math, Sci & Engineering New York NY
Mo Lam

Hunter College High School New York NY
Andre Arslan
Meena Boppana
Paul Handorff
Bohao Zhou

New Hyde Park Memorial High School Hyde Park NY
Michael Hodgson

Penfield High School Penfield NY
Allen Liu

Stuyvesant High School New York NY
Milo Beckman
Junghwa Cha
Lijin Chen
Daniel Mendelsohn
Joseph Park Joseph
Yevginey Rudoy
Andrew Ryba
Zachary Young

The Dalton School New York NY
Alexander Iriza

Vestal Senior High School Vestal NY
Colin Lu

Information for USAMO-takers

2010-04-17T08:28:00.000-07:00

Albany Area Math Circle is honored and proud to have five USA Math Olympiad (USAMO) qualifiers this year:

Andrew Ardito

Matthew Babbitt

Dave Bieber

Schuyler Smith

Felix Sun

For their benefit, and the benefit of other USAMO takers across the country, I am listing some information designed to be helpful.

The italicized information below comes from page 14 of the USAMO Teachers' Manual, which all students should read carefully before taking the USAMO. I have also boldfaced especially important information.

USA(J)MO 2010 Teacher Manual
MAA American Mathematics Competitions USA Mathematical Olympiad
S-II – Instructions to be Read by USA(J)MO Participants

1. The space in the upper right-hand corner of your answer sheets is for your Student Number. You and your USA(J)MO proctor will be informed by mail of your assigned student number. The number at the top center is the Problem Number. Do NOT write your name or school anywhere on the answer sheets; all your papers must be anonymous at the time of the grading.

Write only your Student Number and Problem Number (in a similar location) on any additional papers you hand in.

2. There are six equally weighted problems, for which you will be allowed a total of nine hours. You will be allowed 4.5 hours on Tuesday, April 27, 2010 (12:30pm –5:00pm EDT or equivalent in your time zone) for Problems 1, 2 and 3, and 4.5 hours on Wednesday, April 28, 2010 (12:30pm–5:00pm EDT or equivalent in your time zone) for Problems 4, 5 and 6. Each problem should be started on the corresponding numbered answer sheet. You may write on only the front of the sheet. During each session, carefully look over all the problems. Then work on those which you can work well or start well.

Concurrently, be aware of the total time you allocate to each problem.

3. You will be scored on your method of attack, clarity of reasoning, evidence of ingenuity, inventiveness, and general insight. In order to obtain full credit, all the claims in your solution must be PROVED. When in doubt, you should include details rather than leave them out. Examination of special cases or generalizations may lead to fruitful ideas on how to begin a problem, and partial credit may be given for constructive progress toward a solution. An unusually elegant proof or a carefully stated non-trivial extension with proof may play a role in breaking an eventual tie.

4. Your papers should be CLEAR, CONCISE, COMPLETE, and written DARKLY, keeping in mind it is a faxed copy being graded, not the original! This includes MATHEMATICAL CLARITY, GOOD ENGLISH and LEGIBILITY. Points will be deducted for inadequate or poorly written explanations, as well as for incorrect mathematics. Therefore, use scratch paper freely before writing the solutions you submit, and submit ONLY the final work you wish to have graded. Solutions written in languages other than English will not be graded. Please leave a 1” margin on all sides of the Answer Sheet and on any additional pages and write DARKLY and LEGIBLY, so your faxed copy can be easily read. A #2 lead pencil, black ink pen or marker fax best.

5. NO notes, headphones, cell phones, ipods, books, slide rules, mathematical tables, calculators or calculator watches are allowed during the exam. The only instruments permitted are writing and drawing instruments (ruler, compass, protractor, graph paper, carbon paper). Students learning English as a second-language, who are taking the USA(J)MO for the first time are permitted to use a non-technical translation dictionary during the exam. However, the proctor must examine and keep the dictionary in his or her possession for the 24 hours preceding the USA(J)MO. Your solutions must be faxed to 303-374-6339 immediately at 5:00pm EDT or equivalent in your time zone each day.

6. The USA(J)MO will be administered in two sessions. Students should come prepared with a sack lunch and/or snacks because there is no lunch break during the exam (exceptions will be made for restroom breaks). Your proctor is required to be present during the entire course of the exam for your papers to be valid, but is not permitted to answer any questions about the test. You are not allowed to talk to any other student while the exam is in progress. If you feel that a problem is not stated clearly, note this on your answer sheet and try to make a non-trivial restatement of the problem. Then try to solve the restated problem.

7. You will start the exam when your proctor gives the signal. When the proctor announces after each session that 4.5 hours are up, immediately cease writing. Double-check that your Student Number on your answer sheets matches with the one assigned by mail. Next, immediately hand all Answer Sheets to the USA(J)MO Proctor (even if some sheets are blank) to be faxed to the AMC office.

8. You may keep the problem sheets. Additional copies, a set of solutions, and the results (including your score interval) will be mailed to your Exam Manager after Wednesday, May 12, 2010.

9. The USA(J)MO is graded more strictly than most school examinations, so it is typical for students to overestimate the scores they will receive. The decisions of the graders are final and may not be appealed.

Clarity of exposition is essential: the burden of proof is on you to demonstrate that you understand the mathematical ideas you are using. Remember that the USAMO graders are human beings--they can't read your mind! Your work will not get the credit it deserves unless you have written it up in a clear and well-organized manner than allows the USAMO graders to follow the logic of your reasoning.

Richard Rusczyk and Mathew Crawford have posted an excellent guide on How to Write a Solution on the Art of Problem Solving website. You are strongly advised to read and/or re-read that guide before the USAMO. Their article includes many excellent cautionary notes of things NOT to do and good examples of how to improve the clarity of your presentation, to make sure your work gets the credit it deserves.

You should also be aware that USAMO grading is exceptionally rigorous.

Unlike a typical school essay exam, in which teachers may be struggling to give the benefit of the doubt for partial credit wherever possible, USAMO graders are notoriously stingy.

Each question is worth a maximum of 7 points, so the total number of points theoretically available is a 42. But even though it's a very strong group of students taking the contest each year, 0's are very frequent, even among students who thought they had "solved" one or more problems.

Zuming Feng, the Head Coach of the US International Math Olympiad team and academic director of the Math Olympiad Summer Program has posted the following advice on the Art of Problem Solving AMC discussion forum:

To be deducted (and usually) by lots of points): real math errors in logic, and real mistakes in calculations, unclear reasoning between the steps, claiming facts with no proofs (facts are sometimes restating the core parts of original the problems, etc.) Most of the time, we put your solution into two categories: top down (7-, which means you have all the ideas, in correct order, to solve the problem) or bottom up (0+, which means you are missing main ideas to solve the problem), it is very hard to get to 2 points if the solution is in the second category.

An additional resource: Thomas Jefferson High School's math team leaders have generously posted their advice on preparing for USA Math Olympiad at the links listed below:
TJ USAMO Practice: Proofs
TJ USAMO Practice: Inequalities
TJ USAMO Practice: Induction
TJ USAMO Practice Test
TJ USAMO Practice: Cyclic Quadrilaterals
TJ USAMO Practice: Pigeonhole
TJ USAMO Practice: Geometry practice
TJ USAMO Practice: Functional equations

Richard Rusczyk and other high scorers on past USAMOs have provided lots of great advice in their AOPS math jam linked here.

Thanks to NYSML for coming to Albany

2010-04-16T09:08:00.000-07:00

Thanks to all the teams that came to UAlbany last weekend for the New York State Math League (NYSML) last weekend: Bergen County AAST Mu A, B, & C, Dutchess-Ulster-Sullivan-Orange (DUSO) Math League A and B, Genesee Valley BOCES, Ithaca High School, Monroe County Math League A and B, Nassau County Math League, New York City Brooklyn/Staten Island, New York City Clio, New York City Manhattan, New York City Queens/Bronx, New York City Leo & Louie, Onondaga County Math League A and B, Rockland County Math League, Southern Tier Math League A and B, and Westchester-Putnam County Math League A and B.

From Albany Area Math Circle's perspective, your coming was the most exciting visit to Albany since Henry Hudson sailed up the river in 1609.

Top Team Results are listed here. Top individual results are listed listed here. Full results for all teams and individuals will be available on the NYSML website soon.

Thanks to Professor Leo Schneider for writing yet another great set of problems for NYSML 2010. It was a pleasure for us to meet him, and to learn that his motto is "There's a Power Question in everything," as he discovers possible topics for future power rounds in a wide variety of everyday situations.

This year's Power Question was inspired by the mathematics used in computer-controlled steel milling machines. Professor Schneider is shown here with his wife Susan and Albany Area Math Circle advisor Professor Mukkai Krishnamoorthy, who enjoyed working with a group under Professor Schneider's direction to grade the Power Question, a one-hour essay-like component of the contest, "in which the teams work collaboratively to answer a multi-part set of problems calling for creative thinking, elegance of presentation, and accuracy of solutions," according to the NYSML website.

There are few if any other state-level contests that offer anything like the NYSML Power Question to their students, and its inclusion in NYSML for the past four decades is a testament to the distinguished tradition of problem solving in New York State, a tradition celebrated and encouraged by Professor Nura Turner of UAlbany, who was on the first USA Math Olympiad Committee at the same time that NYSML started up in the early 1970s.

Thanks to all the wonderful NYSML officials who volunteered their time to make this competition possible, especially NYSML President Jason Mutford, NYSML VP/Meet Leader and President-elect George Reuter, NYSML Treasurer and Executive Officer-elect Mike Curry, and NYSML Secretary and Treasurer-elect Toni-Lynn Swanson.

Thanks as well to the outstanding coaches from all over the state who also give up countless hours of their time each year to prepare their teams and make arrangements to travel with them to NYSML.

We'd especially like to thank Anchala Sobrin, NYSML Vice-President-elect and President of the DUSO Math League (the 2009 Host Site), for all the advice, encouragement, and assistance she provided to us throughout our planning process.

Finally, we'd also to recognize the leadership of the New York City Math Team and NYC Head Coach Jim Cocoros for continuing a grand tradition that has inspired and challenged the rest of the state for four decades.

Albany Area Math Circle

host team NYSML 2010

Upstate NY solidarity does a double take!

2010-04-15T06:17:00.001-07:00

Albany Area Math Circle students happily congratulate their fellow Upstate New Yorker, Allen Liu from Monroe County Math League, after he won the state high school NYSML championship hosted at UAlbany last Saturday (above) and the state middle school MATHCOUNTS championship last month (below).

At NYSML and MATHCOUNTS, Allen was on teams that competed with Albany Area Math Circle teams. At ARML, the national version of NYSML to be held at Penn State on June 5, all Upstaters will be on the same all-star Upstate New York Math Team. The head coach of the Upstate NY Team, George Reuter, looks ecstatic about the team's prospects, as do the members of the Upstate NY Math Team, who look forward to making new friendships and renewing old ones as they work with kindred spirits across Upstate New York.

Heads up to our friends on the downstate teams and AAST: the math leagues from Upstate NY congratulate your teams on your awesome performances at NYSML, but we are also looking forward to ganging up and meeting you again at ARML!

If you loved NYSML, this man is looking for you

2010-04-14T10:51:00.000-07:00

Mr. Reuter, the NYSML President and leader of last Saturday's New York State championship math meet at UAlbany, wears many hats.

In his day job during the school year, he is a math teacher at Canandaigua Academy. During the summers, he is one of a select group of International Baccalaureate teachers who teaches in the Oxford Study Courses program for overseas pre-IB students hosted at Harvard and MIT. (His students in that program were the ones who made the hat shown in the picture above.)

He and his wife also have five children (including toddler twins!) and they are expecting their sixth child later this year. He wrote the NYSML Seasonal contest problems. He's writing a book.

Somehow he manages to keep his amazing sense of humor in the face of it all. His past and present students have created a Facebook fan page to collect some of the funny things he says. Here are a few of his bons mots:

Reuter: "I WILL get down to 6 pounds 11 ounces. I was there once and I'll be there again!"
Carissa: "You'll die first."
Reuter: "Are you wishing death upon me?!"

"During my exams you may become very religious, looking up to the heavens and down to your paper, but please not to the right or the left, it makes me nervous. Please separate your desks by a space wider than my hips, and remember, I’ve had three kids and two more are due this month. I’ll be around to answer your questions as you have them, and I would wish you good luck, but STUDYING WOULD HAVE BEEN FAR BETTER."

His ideas of fun things to do in his free time include wearing yet another hat as Head Coach of the Upstate NY ARML Team. Other coaches of the Upstate NY team include veteran high school math teachers (some of whom are retired but still love doing this--like Mrs. Ohlerich--yay for mathlady!) and college student coaches such as Albany Area Math Circle alumna Beth Schaffer (an MIT junior who has been co-director of the Harvard-MIT Math Tournament the past two years) and Albany Area Math Circle's very own charter member Tom Zink, now a software engineer in northern Virginia.

All these wonderful and dedicated folks can think of nothing they'd rather do in early June than volunteer their time to spend many hours riding chartered buses with dozens of math-loving students from Upstate NY to Penn State for ARML on the Thursday after Memorial Day, then help them prepare with a day long practice at Penn State on Friday, chaperone them at night in the Penn State dorms, then assist with the contest administration as graders and proctors on Saturday, then cheering them on and getting ice cream at the famous Penn State College of Agriculatural Science Creamery, the largest university creamery in the nation, then board the bus for the long ride home. Are we having fun yet? The coaches clearly are! It is clearly a labor of love for them. They come back year after year. And the students have a blast as well, making new mathy friends from all over Upstate.

Could this be the year that Upstate NY beats NYC? Who knows?

As Coach Reuter says, students from every league outside of New York City and Long Island are eligible to band together on the Upstate NY team and gang up on NYC and the rest of the teams from around the country. So the Upstate NY math team is an all All-Star team that will bring together the top students from Dutchess-Ulster-Sullivan-Orange County Math League, Monroe County, Ondondaga County, Rockland County, Westchester-Putnam County, and so on, as well as Albany Area Math Circle.

The format of ARML is just like NYSML, only the problems are somewhat harder, because it is a national/international competition that attracts teams from all over the country and the world. But it all started with NYSML. Other states wanted to participate in NYSML, so our New York state championship math meet (NYSML) became the model for the premier national high school championship math meet, American Regions Math League (ARML).

If you love the idea of spending three days working on really hard math problems (same format as NYSML but harder) with kindred spirits from across Upstate NY who share your passion, and making new mathy friends from all over, here is an application for the Upstate NY ARML team. Send it off to Mr. Reuter ASAP; the deadline is coming up on April 26, but sooner is better!

NYSML high-scoring students from Albany Area Math Circle

2010-04-14T09:28:00.000-07:00

Perfect scorers (10 Questions Correct)

Matthew Babbitt, 9th grade heeg
Eric Wang, 12 grade Shenendahoah High School

9 Questions:

Andrew Ardito, 12th grade heeg
Ashley Cho, 11th grade Emma Willard School
Peixuan Guo, 12th grade Bethlehem High School

8 Questions:

David Bieber, 12th grade Niskayuna High School
Heidi Chen, 12th grade Emma Willard School
Gurtej Kanwar, 11th grade Bethlehem High School
Paul Rapoport, 11th grade Albany Academy
Schuyler Smith, 11th grade heeg
Wyatt Smith, 10th grade heeg
Felix Sun, 11th grade Shenendahoah High School
Jay White, 11th grade heeg

7 Questions:

Cecilia Holodak, 8th grade Van Antwerp Middle School
Zubin Mukerjee, 9th grade Guilderland High School
Adam Parower, 12th grade Shaker High School
Noah Rubin, 11th grade Guilderland High School
Troy Wang, 8th grade Acadia Middle School
Jason Xu, 11th grade Niskayuna High School

6 Questions:

Gabriel Holodak, 10th grade Niskayuna High School
Brad Johnson, 10th grade Niskayuna High School

5 Questions:

Greg Hickey, 9th grade Shaker High School

Peiting (Peggy) Hsu, Emma Willard School

Preston Law, 9th grade heeg

Brady Pelkey, 12th grade Hudson Falls High School

Philip Sun, 7th grade Acadia Middle School

Aniket Tolpadi, 8th grade Iroquois Middle School

4 Questions:

Bea Malsky, 11th grade Guilderland High School

Elizabeth Parizh, 9th grade Niskayuna High School

Gili Rusak, 7th grade Shaker Junior High
Ved Tanadve, 11th grade Guilderland High School

William Wang, 6th grade Farnsworth Middle School

Yuqing Wu Emma Willard School

Student names listed in blue were perfect scorers. Student names listed in red were high scorers on their respective teams. (In keeping with the NYSML tradition of "no duplicate awards," students with perfect scores are not eligible for "high scorer on the team" honors.)

We would like to congratulate all students on Albany Area Math Circle's three NYSML teams this year, whether or not you were listed on the high scoring honors lists above, whether you scored two points or ten points.

Selection for the AAMC teams required meeting very high standards of mathematical and behavioral maturity, especially since we were the host team this year--you more than lived up to our expectations and we are proud of each and every one of you. Every single student on each of our three teams made contributions to their team's score this year.

Your team leaders, Andrew Ardito, Dave Bieber, Anagha Tolpadi, Noah Rubin, Brady Pelkey, and Wyatt Smith did an outstanding job of coordinating your work on the Team and Power Rounds and there were many notable successes on the relay rounds as well.

Drum roll please: the mathiest person in New York State is ....

2010-04-13T19:26:00.000-07:00

As NYSML Meet Leader and President-elect George Reuter put it, he was about to "crown the mathiest person in New York State" at the New York State Math League state high school championship math meet on Saturday.

Hundreds of New York State's strongest and most enthusiastic math students had gathered in the UAlbany Campus Center ballroom, waiting expectantly for the exciting tiebreak round that would determine which of the perfect scorers would be declared the individual winner of the state championship math meet.

Meet Leader George Reuter called forward the following students with perfect scores on the individual written round to the front of the auditorium for the tiebreak problems.

Perfect Scorer List

Albany Area Math Circle A: Matthew Babbitt, Eric Wang

Bergen County Academies for the Advancement of Science & Technology Mu A: Jin-Sung Na, Alex Zhu

Monroe County A: Allen Liu

Nassau County A: Michael Hodgson, Keaton Stubis

New York City Brooklyn/Staten Island: Yevgeniy Rudoy, Mikhail Rudoy, Yichi Zhang

New York City Clio: Junda Huang, Hon Wei Khor

New York City Louie & Leo (Alternate 1): Max Weinrich

New York City Manhattan: Andre Arslan

NYC Queens/Bronx: Billy Lam, Kevin Peng

Westchester County A: Brian Froehlich

Professor Leo Schneider, the author of all NYSML problems for many years, conducted the tiebreak round. After an initial question, the field of finalists narrowed to three and the state title hung in the balance, hinged on submitting the first correct answer to the following question:

At the end of the allotted time of four minutes, the judges examined the answers which had been submitted, and a clear winner emerged and was declared the champion:

Allen Liu from Monroe County

The audience's jaws dropped in astonishment: Allen is only a sixth grader--to my knowledge he is the first sixth grader to win NYSML, quite possibly even the first middle school student ever to do so--and yet he had clearly concocted an elegant and sophisticated approach to answering the problem in order to arrive at the correct answer so efficiently. (If you can't see how to do this problem in four minutes, you have a lot of distinguished company! Prof. Schneider presented a detailed solution for the benefit of the rest of us mere mortals. You can see the answer and the beginning of his solution approach here.)

The photo below shows NYSML meet officials George Reuter and Mike Curry presenting Allen with his prizes, which include a scholarship check and a state high school math meet champion T-shirt that will surely fit him some day eventually down the road. (Allen should look a bit familiar to readers of this blog, because he won the New York State MATHCOUNTS middle school competition held last month. In addition, he has qualified for the USA Math Olympiad for the second consecutive year.)

You may notice that George Reuter is looking especially excited--that excitement might stem from the fact that he is also the coach of the Upstate NY Math Team that will travel to compete at the national version of this contest, ARML, to be held in early June. Allen is from the Rochester area and was on the Upstate NY ARML team last year. Allen has demonstrated outstanding maturity, grace, poise, and decorum as well as great mathematical problem-solving abilities. He will clearly be a huge asset to the Upstate NY team this year and for many years to come.

The remaining students with perfect scores from the written individual round were all officially declared as tied for second place and also received plaques from NYSML Meet Leader George Reuter. For the first time ever, the perfect scorer list included students from our math circle: heeg freshman Matthew Babbitt (in the plaid jacket immediately below) and Shenendahoah High School senior Eric Wang (shown at bottom holding his plaque.) A complete list of students with perfect scores from all leagues will be posted here as soon as I receive a copy from the meet officials.

Thanks to our UAlbany student guides!

2010-04-12T12:35:00.000-07:00

We had a terrific group of UAlbany students helping out as guides, greeters, and assistants at NYSML 2010 last Saturday, including Tali Gellert, who designed the banner below to welcome NYSML students from all over New York State. Thanks as well to Christina Smith, who helped get out the word to recruit our excellent volunteers.

Alpha Kappa Alpha: Chantell Hazell

Delta Delta Sigma: Meredith Nardozza, Cassandra Toth

Sigma Iota Sigma Multicultural Sorority: Gifty Ameyaw, Jamilia Martineau-Lopez

UAlbany Presidential Honor Society: Richard Buzkin, Tali Gellert, Brianna Jilson

Students in the Financial Analyst Honors Program of the UAlbany College of Business: seniors Michael Arias, Jonathan Nardi, and Daren Pon; juniors Rory Blake, Thomas Boeje, Joseph Duran, Jonathan Mangiapane, Chad Schneider, and David Siegel, and senior business major Rostislav Spitchka.

NYSML Appreciation

2010-04-11T18:15:00.000-07:00

We all owe an enormous debt of gratitude to UAlbany Prof. Biswas and Albany Area Math Circle advisor Mr. Babbitt, the co-chairs of our Host Site Committee, for the months of work and planning they have put into making our dreams and vision for hosting NYSML a reality. When Albany Area Math Circle started up in 2001, Prof. Moorthy and I never dreamed we would see our tiny math circle flourish to the point of hosting NYSML, let alone fielding three teams of awesome students.

We are also grateful to our wonderful supporting team of alumnae, parent, and community volunteers, without whose efforts this NYSML would not be possible:

Site Committee Housing Coordinator: Dr. Susan Bieber

Alumnae General Factota: Catherine Miller and Beth Schaffer

Greeters: Elena Dolginova, Nancy Newman, Suzanne Rapoport

Lead Zone Proctor: Alexandra Schmidt, Hebrew Academy of the Capital District

Zone Proctors: Eric & Susan Bieber, Dave Holodak, Rupinder Kanwar, Shuang Liu, Debby Pelky, Lois & Richard Rubin, David & Nancy Rudinger, Anil & Anjana Tolpadi

Lapboard/Clipboard Czar: Charles Law

Scoring Room: Eileen and Tony Ardito, Elaine Hickey; Prof. Moorthy (Power Question grader)

We are deeply grateful to UAlbany for its hospitality, to the many UAlbany administrators and staffers who have worked with us for many months to make our vision and dreams for this NYSML a reality, especially Diane Dumesnil of the College of Nanoscale Science & Engineering and to Roman Dubiel of Undergraduate Admissions, as well as to Mary Tarsa, Lisa Scholz and Sally Mills of the School of Business.

We also deeply appreciate our awesome team of sponsors:

Thanks to our sponsors:

The College of Nanoscale Science and Engineering (CNSE)

The Bieber Family

UAlbany Undergraduate Admissions

The New York City Math Teachers Circle

Art of Problem Solving

Tough Traveler®

Sustaining Friends and Families of Albany Area Math Circle:

Robert P. Ingalls, Mukkai Krishnamoorthy, Mary O'Keeffe,
Ardito family, Babbitt family, Bieber family, Biswas-Mukerjee family, Hickey family, Guo family, Kaur family, Law family, Lesh-Shreiner family, Liu family, Liu-Gu family, Parizh family, Pelkey family, Reitz family, Scheib-Holodak family, Smith family, Sun family, Tanadve family, Tolpadi family, Wang family, White family

Contributing Families of Albany Area Math Circle:

Buff family, Cao family, Chen family, Foyt family, Hammar family, Hsu family, Ingalls family, Job family, Li family, Magai family, Monteith family, Ogawa family, Parower family, Rapaport family, Richman family, Rubin family, Rusak family, Soedjak family, Wajda family, Xu family

NYSML 2010 Top Team Results

2010-04-11T15:55:00.000-07:00

Here are the results for top team honors for the 2010 New York State Math League math meet championship held yesterday at the University at Albany.

A Division Honors:

New York City's teams from Brooklyn/Staten Island, Manhattan, and Queens/Bronx took first place A-division honors at NYSML with scores of 269/261/255.

Albany Area Math Circle A took second place honors in the A division with a score of 245.*

Nassau County A took third place honors in the A division with a score of 236.

B-division Honors:

B division honors went to Dutchess-Ulster-Sullivan Orange (DUSO) A in first place with 177, Alternate 1 in second with 171, and Westchester Putnam B in third place with 146.

Ithaca High School ranked fourth in the B-division, only one point behind Westchester-Putnam B and received most improved honors for its score of 145. Albany Area Math Circle's two B-division teams, Octahedra and Tetrahedra, ranked next with scores of 133 and 132.

Bergen County AAST:

Bergen County Academy for the Advancement of Science & Technology (AAST) in New Jersey also had three teams participating in the meet. Bergen AAST Mu A turned in an outstanding performance of 267 points, right behind NYC Brooklyn/Staten Island.

Complete results for all 27 teams competing in the meet will soon be available at www.nysml.com. Congratulations to all participating teams and coaches.

*Thanks to a very gracious proposal made by NYC Head Coach Jim Cocoros last year, and adopted by a vote of NYSML members at last year's meeting, there is now a "no duplicate awards policy" for top team honors. This means that any given league may only win one set of honors. Thus all three of New York City's top ranking teams share first place honors.

NYSML team rosters

2010-04-09T03:40:00.000-07:00

Albany Area Math Circle A

Andrew Ardito heeg (Captain)
David Bieber Niskayuna High School (Coordinator)
Matthew Babbitt heeg
Shiwen (Heidi) Chen Emma Willard School
So yeun (Ashley) Cho Emma Willard School
Peixuan Guo Bethlehem High School
Gurtej Kanwar Bethlehem High School
Preston Law heeg
Zubin Mukerjee Guilderland High School
Paul Rapoport Albany Academy
Schuyler Smith heeg
Felix Sun Shenendahoah High School
Eric Wang Shenendahoah High School
Jay White heeg
Jason Xu Niskayuna High School

Albany Area Math Circle Octahedra

Anagha Tolpadi Niskayuna High School (Captain)
Noah Rubin Guilderland High School(Coordinator)

Shreya Arora Iroquois Middle School

Cecilia Holodak Van Antwerp Middle School
PeiTing Hsu Emma Willard School
Ann Job Shaker High School
Arun Job Shaker High School
Beatrice Malsky Guilderland High School
Isaac Malsky Farnsworth Middle School
Elizabeth Parizh Niskayuna High School
Noah Rubin Guilderland High School
Ved Tanavde Guilderland High School
William Wang Farnsworth Middle School
Yuqing Wu Emma Willard School

Albany Area Math Circle Tetrahedra

Brady Pelkey Hudson Falls High School (Captain)
Wyatt Smith heeg (Coordinator)
Matthew Gu Farnsworth Middle School
Greg Hickey Shaker High School
Gabriel Holodak Niskayuna High School
Bradley Johnson Niskayuna High School
David Luo Acadia Middle School

Jien Ogawa heeg
Adam Parower Shaker High School
Gili Rusak Shaker Junior High School
Philip Sun Acadia Middle School
Aniket Tolpadi Iroquois Middle School
Troy Wang Acadia Middle School
Isaac Smith heeg

You are an amazing community of students. Your advisors delight in the joy we have seen in you take in your collaborative problem solving at our weekly meetings and in the bonds of friendship and camaraderie we have seen form over the years. We hope to add additional students to fill Octahedra and Tetrahedra out to full strength, and we have confidence that you will welcome them and make them feel at home. (UPDATE: Thanks to DUSO Alternate Emily Shebby and Westchester Alternates Andrew Huang and Dan Herman for filling out Tetrahedra and Octahedra to full strength.)

We are proud of you, and we are proud of your veteran leadership team: Andrew, Dave, Anagha, Noah, Brady, and Wyatt.

If you are looking for help or directions at NYSML

2010-04-08T13:00:00.000-07:00

Here's how to find the people who can help you.

Our small army of volunteers will be wearing distinctive badges like the ones on the table above, made by our awesome sponsor Tough Traveler, in their Schenectady factory.

Some of them, like our Lead Zone Proctor Alexandra Schmidt, a math teacher from Hebrew Academy of the Capital District, also like to wear math t-shirts, so they'll be wearing the same light blue Albany Area Math Circle T-shirts that our students wear to help them stand out doubly from the crowd.

Our UAlbany student guides will carry pennants that look like this:

If you are looking for definitive answers to those all important questions like "Where is our team's classroom?" or "Where is the gym?" or "Where is the restroom?" or "Where am I supposed to be right now?" or "The light went out in our classroom? How do we get it turned back on" or "How long until lunch?" or "Why is there no proctor in our classroom yet?" or "I am an alternate, but I don't remember what team I'm supposed to be working with?" these folks can help you.

If your question relates to the UAlbany campus (like location of buildings and restrooms), your campus guides with the purple and gold Athena pennants are the best go-to people. If you question relates to the NYSML contest (like "Where am I supposed to be right now?" the folks with the Tough Traveler badges are the best bet.) For the most challenging questions, look for volunteers like Alexandra who are wearing light blue math circle shirts AND Tough Traveler badges.

These awesome volunteers will either know the answer to your questions OR they will know how to contact someone who can answer them!

Thanks to all our great volunteers.

Albany Area Math Circle students: NYSML information

2010-04-08T05:19:00.000-07:00

We are inviting a few excellent students from our area to fill out our Albany Area Math Circle Tetrahedra and Octahedra teams to full strength. Here is some basic guidance and orientation for them. Veterans and team leaders, please read this as well and be prepared to fill in the gaps so all students on your team can have an outstanding experience at NYSML!

A brief outline of the day:

7 a.m. to 8:15 Campus Center Food Court Plan to arrive before 8 to check in with your team leadership, which will be sitting at the round table at the base of the steps leading down to the basement Food Court.

8:15 Go upstairs to the ballroom for the opening assembly. Teams have assigned seating areas. Look for your team signs and the light blue shirts and sit with your team!

8:30 to 8:45 Opening Assembly

8:45 to 8:55 Teams travel with their campus guides and team proctors to their assigned classroom for the Team and Power Rounds. Albany will be dismissed first, because its teams will have the furthest to travel to their assigned rooms. Albany A and Albany Octahedra are on the second floor of Social Sciences building. Albany Tetrahedra will be on the first floor of Social Sciences.

9-10:30 Team and Power Rounds. For these two rounds, the entire 15-person team works together. Each 15-person team has a classroom to itself. You may use the whiteboard or chalkboard. On the Team Round, your team will have 20 minutes to solve 10 problems with answers in short order format. On the Power Round your team will have 1 hour to solve a multipart problem. In the Power Round, your answers will be lengthy. In some cases, you will need to show your work in clear detail. In other cases, you will need to provide a proof. Less experienced students usually work on the earlier parts of the Power Round, which are more computational in nature. More experienced students usually work on the more difficult proofs in the middle and later part of the Power Round. Everyone has something to contribute!

Time to walk over to the gym for Individual and Relay Rounds. This is a good time to eat a snack or drink from your water bottle as you walk.

10:50-12:30 For these rounds, you will be sitting on bleachers using a lapboard or clipboard.

Individuals are like Targets from MATHCOUNTS, because you get one pair of questions at a time. But they are much harder! Don't be discouraged. Advice for new students: look over BOTH problems before you start working. For a new student, getting even one problem right is an accomplishment, so don't rush through both of them. Better to do one of them thoroughly and carefully, checking your work, than to rush through both and get them both wrong.

Relays--for more information about relays, see this post from last year.

http://albanyareamathcircle.blogspot.com/2009/03/blog-post.html

After Relays, you will be dismissed to walk over to the College of Nanoscale Science and Engineering, where you will be treated to a great talk on nanotechnology by Prof. LaBella, followed by an excellent lunch.

Then back to the Campus Center for the Closing Assembly, which includes Buzz, Tiebreaks, and Awards. That closing assembly should run 2:10 to 3:30 and your parents are welcome to watch!

A few more important notes:

Whether you are a veteran or a first-timer, please read the contest rules here:

http://nysml.com/NYSML_competition_rules_2010.php

and also read this important information:

http://nysml.com/NYSMLTERMINOLOGYSHEET.pdf

If you are first-timer, please make a note of the things that are confusing to you and ask a veteran to explain it on Saturday morning before the meet starts (or ask a vet by email.)

Don't worry about the things that are completely over your head. If you haven't learned trig yet, just plan to skip over those questions, and spend your time on other questions that might be more accessible to you.

If you are a veteran, think about the rules and conventions that were confusing to you and make sure you have thought about how to explain them to newer students.

Things to bring: pencils, erasers, water bottle, snacks

Things to LEAVE HOME: your calculator! NYSML is a calculator-free zone!

Things to wear: layers (you never know about the weather/climate control), comfortable walking shoes, and your light blue team t-shirt. Wear your light blue Albany Area Math Circle t-shirt. If you don't have one, email Mr. Babbitt to let him know your size and we'll have one waiting for you with your team captain.

Thing to remember: Most importantly--encourage your teammates! The problems are hard--it's easy to get discouraged, especially when you realize you made a silly mistake
(as all of us do!)

Remember my motto: Have a good time! Make some new math friends! Share some Aha! experiences and cool insights you got between rounds. Celebrate your mistakes and learn from them.