Thursday, December 7, 2006

2005-2006 AAMC Year in Review

The Albany Area Math Circle continued to grow and thrive in its fifth year.

From the original eight students, the group has grown to over 20 students attending our weekly meetings at RPI in 2005-2006. AAMC's intrepid and enthusiastic problem solvers collaboratively solved hundreds of challenging problems in number theory, geometry, probability, algebra, combinatorics, and advanced topics over the course of the year's weekly meetings.

Seasoned veterans mentored eager newcomers, and the intersecting circles of mathematical insight and understanding grew beyond AAMC as many of our members also participated in their school's local math teams or coached teams of younger students outside of math circle.

Captains and senior veterans Beth Schaffer and Drew Besse have done a wonderful job of carrying forward the legacy left by older alumni and there is now an extraordinary new cohort of talented young problem solvers.


In November 2005, 26 students took the AMC8 under AAMC's auspices. Five students received individual scores qualifying for Certificates of Distinction: Andrew Ardito, David Bieber, Schuyler Smith, David Burns, and Anagha Tolpadi. Five students received individual scores qualifying for Honor Roll: Matthew Babbitt, Leah Trouwborst, Luke Trouwborst, Manvi Goyal, and Joel Shapiro. Sixth grader Monil Patel qualified for Merit Roll recognition for young students, as did Matthew Babbitt.

The AMC8 team of Andrew Ardito, David Bieber, and Schuyler Smith received national recognition on the AMC8 School Honor Roll, one of only three teams receiving this honor in New York State.

Andrew Ardito received an award as high scoring individual in New York State on the 2005 AMC8, making the second consecutive year in which AAMC members had won this honor. (Andrew and David Bieber had been NYS individual high scorers the previous year.) Matthew Babbitt's score was the high score for sixth graders in New York.


The AAMC team of Andrew Ardito, Robin Meyers, and David Bieber ranked FOURTH PLACE out of the 156 teams statewide on the MAA/American Mathematics Competitions AMC12B exam.

The AAMC team of Drew Besse, Catherine Miller, and Andrew Ardito ranked 20th out of 122 teams statewide on the AMC12A exam.

Drew's individual score ranked among the top 12 out of 3,656 scores statewide on the 12A exam. Andrew and Robin's individual scores ranked among the top 26 out of 5,617 scores statewide on the 12B exam.

Andrew was the highest scoring 8th grader in the state on both the AMC12A and the AMC12B exams. David Bieber did not take the AMC12A, but he was the second highest scoring 8th grader statewide on the AMC12B exam.

Schuyler Smith was the highest scoring 7th grader in the state on both the AMC12A and the AMC12B.

Matthew Babbitt was the highest scoring 6th grader in the state on the AMC12A and the AMC12B exams.

The following AAMC students qualified for the American Invitational Math Exam (AIME): Andrew Ardito, Anthony Ardito, Drew Besse, David Bieber, Nicole Bieber, David Burns, James Dick, Eugenia Gisin, Yunjee Kang, Stephen Krewson, Soohyun Lim, Robin Meyers, Catherine Miller, Rachel Rudinger, Markus Salasoo, Beth Schaffer, Nan Shan, Schuyler Smith, Anjana Tayi, Anagha Tolpadi, and Luke Trouwborst.

In addition, several students in 10th grade or below received commendation certificates for their AMC12 scores: Matthew Babbitt, Jean Kang, Roshal Patel, Justin Staver, and Leah Trouwborst.

Chapter MathCounts

This year's chapter competition was the biggest ever, with 23 teams and 143 individuals from all over the Capital District. AAMC students and teams coached by AAMC members took many top honors, including 11 of the top 20 individuals and three of the top five teams.

AAMC student MathCounts coaches included Beth Schaffer, Catherine Miller, James Dick, and Stephen Krewson. AAMC parent MathCounts coaches included Eileen Ardito, Anil Tolpadi, and Lembit Salasoo.

Harvard-MIT Math Tournament

This year's competitive field at HMMT was the strongest and biggest on record, but the AAMC teams proved once again that the whole can be stronger than the sum of the parts! The A team (Andrew, Anthony, Drew, David, Nicole, Soo, Robin, Beth) took 8th place in the GUTS round and 9th place in Team Sweepstakes. The B team ( Eugenia, Rachel, Markus, Nan, Anjana, Melissa plus 2 non-AAMC students assigned by the HMMT organizers) took 8th place team in their division. Drew Besse received 8th place individual honors in Combinatorics. Andrew Ardito, David Bieber, and Drew Besse tied for first place in the Logic Puzzles mini-event.


We had a record group of over 20 AIME qualifiers this year. Four students received especially commendable AIME honor roll scores: Andrew Ardito (8), Drew Besse (7), David Bieber (6), and Beth Schaffer (8).


We had a record number of AAMC members participating in the New York State finals of MathCounts. Four of the top seven mathletes at the MathCounts state finals were AAMC students (Andrew Ardito, David Bieber, Schuyler Smith, and Eric Wang.) Given that the Albany area is only a very small percentage of the state population, that is a truly extraordinary record! Two additional AAMC members finished among the top 25 (Felix Sun and Matthew Babbitt.) Schuyler and Felix were seventh graders. Matthew's performance was particularly noteworthy and very promising as he was only a 10 year-old sixth grader at the time.


For the second consecutive year, the AAMC team won first place in division B at NYSML. This year's competition was significantly harder than the previous year's test, but AAMC's team score represented a much larger margin over the rest of the division than the previous year. It is entirely appropriate that the AAMC team will compete in division A next year. AAMC will be the only upstate NY team competing in division A in 2007.

Students on our NYSML team included: Andrew Ardito, Anthony Ardito, Matthew Babbitt, Drew Besse, Eugenia Gisin, Jean Kang, Yunjee Kang, Soohyun Lim, Catherine Miller, Rachel Rudinger, Markus Salasoo. Beth Schaffer, Nan Shan, Eric Wang, and Melissa Wu. Alternate members were: Swapna Arora, Paul Rapoport, and Hyeon Soh.


Andrew Ardito became the third member in AAMC history to qualify for the USA Math Olympiad. This is even more remarkable since he was only an eighth grader at the time.


Two Albany Area Math Circle members, Andrew Ardito and David Bieber constituted half of the four-person NYS MathCounts team representing our state at the National Competition in Arlington Virginia in May. Before they left for nationals, the Albany Times Union ran a photo-story about the two boys. The photo above by Times Union photographer James Goolsby accompanied reporter Kelly Vadney's article, Math Talents Add Up to State's Best.

In his third trip to Nationals and second trip to National Countdown, Andrew blazed through the countdown round till he reached an incredibly exciting and breathtakingly close final round. In 2nd place after a very tight final head-to-head against the eventual winner.

Andrew won a $6,000 college scholarship as well as a $3,000 scholarship to attend the 2006 Awesome Math summer program.

In addition, Andrew and the other top national finalists made a trip to the White House for presidential congratulations.

Both Andrew and David came back with many wonderful memories, new friends, TI calculators, and lots of state pins traded from mathletes all over the country. As well, both of them have learned amazing amount of math and developed their problem-solving skills during the course of the past three years.

Profile: Beth Schaffer, Captain & Driving Force

As AAMC goes into its sixth year, it has had four captains in the course of its history: Tom Zink (2001-02), Raju Krishnamoorthy (2002-05), Drew Besse (2005-07), and Beth Schaffer (2005-07). (Starting in fall 2005, AAMC had grown to the point where two captains were called for.) The first three names on the list were charter members, whose profiles have already been posted below.

Beth Schaffer, a senior at Guilderland High School, joined AAMC in her freshman year, and quickly became one of AAMC's most enthusiastic and dedicated members. Her infectious enthusiasm and encouragement, her generous willingness to share her knowledge with others, and her energetic outreach and recruiting efforts have contributed greatly to Albany Area Math Circle.

As an AAMC team member, she has participated in HMMT (04, 05, 06) and NYSML (04,05,06), making significant contributions to the team each year. In 2004, she was a member of the fourth place team under Raju's leadership at HMMT, and in 2006, with a much harder competition and larger field of teams, Beth and Drew captained the AAMC team to a 9th place sweepstakes finish at HMMT. In 2005, she was a member of the division-B winning AAMC team at NYSML. In 2006, Beth and Drew captained the AAMC team to a repeat division-B championship (which means the team will compete in the A-division in 2007!) Beth also won an individual high scorer of the meet award at NYSML 2006.

Consistently strong AMC12 scores have qualified Beth for AIME every year since freshman year and she has also been a member of the Upstate NY ARML team in each of the past two years. She won Silver Awards USA Mathematics Talent Search in 2004-05 and 2005-06.

Beth's boundless energy and enthusiasm for math spills over way beyond AAMC. She has coached MathCounts teams throughout her high school career and her teams consistently place high, with many of the students she has coached landing in the Countdown Round at chapter. She has a large and very devoted fan club of younger mathletes. Two years ago, she took the initiative to launch and run Mathematical Explorations, a summer math workshop for middle school students. In 2004 and 2005, Beth attended MathCamp, an amazing summer program. Beth and two friends from the Upstate NY ARML team have recently created {a nonempty set} an on-line math contest designed for middle school problem solvers.

In 2006, Beth was one of 75 top math and science students chosen from all around the country and around the world selected to participate the Center for Excellence in Education's MIT Research Science Institute , the top research program in the country for high school scientists.

Beth is an outstanding example of an AAMC success story and a testimony to the legacy left behind by our charter members.

When Beth first came to AAMC as a freshman taking honors 9th grade math, she found herself in a room full of mostly older students she didn't know, most of them much more experienced in advanced problem-solving, some of them already taking college classes. It was scary and intimidating to ask for help--it's all too easy to worry about whether you are asking a "dumb question." But Beth was brave and undaunted and our charter members were kind and generous with their help. She asked lots of questions--and answering those questions benefited both the veterans and Beth. The vets benefited because explaining math to Beth deepened their own understanding. And Beth obviously benefited too, because now she is one of the senior vets answering questions from the rookies.

UPDATE September 2007: Beth continued her strong of amazing accomplishments during her senior year and earned many honors, including designation as a US Presidential Scholar, which brought her to Washington, DC, where she met both President Bush and Senator Hillary Clinton, as well as other officials. (The photo shows Beth on the left with Sen. Clinton and the other US Presidential Scholars from New York.) Beth is now a student at MIT and a member of Prof. Richard Stanley's Freshman Problem-solving Seminar.

Monday, December 4, 2006

AAMC Charter Members: Then and Now

As this March 2002 photo shows, the original members of AAMC were mostly younger students. We had two seniors (Warren Hayashi and Tom Zink), one junior (Katherine Brainard), two sophomores (Ben Levinn and Alison Miller), one freshman (Raju Krishnamoorthy), one eighth grader (Manisha Padi), and one seventh grader (Drew Besse.)

In the picture above, they are looking simultaneously stunned and ecstatic as they celebrate their very surprising second place in the Harvard-MIT Math Tournament team round. (Katherine is holding the plaque. Raju is mostly hidden behind Alison. Ben is unfortunately not in this photo because he and his dad had already left for the long drive back home. Ben had done the daylong contest as a day trip. He and his dad had left their home at 5 a.m. that morning. The competition was scheduled to end at 5 p.m., but the organizers were running behind schedule and tallying results seemed to be taking them forever. The contest was on a Sunday that year, so there would be work and school the next morning. It had seemed quite sensible for the two of them to leave before the awards were finally announced. Nobody had dreamed that our brand new, mostly young and inexperienced AAMC team would have much reason, other than curiosity about which other teams would take top awards, to stick around for the award ceremony!)

The team round success came as a huge shock, since the HMMT organizers had given no advance warning of their change from the old short answer format of the team round to a proof-based format. The teams only learned of this new format at the instant that the proctors tore open the exam envelopes and read the instructions aloud before handing out the problems. Our young and inexperienced AAMC team had gasped in shock when they heard the proctor read the new team round rules. They had only begun practicing together a few months before. They had not yet done any practices of written proof-based collaborative contests together. After they picked their jaws up off the ground, they set to work, determined to make the best of the situation, and wound up with an extraordinary finish.

How did all this happen? It still seems sort of like magic.

Our math circle had only started meeting a couple months before the 2002 HMMT. Very few of the students knew one another before they attended our first math circle meeting in December 2001. (It's hard to believe, but this month we celebrate the fifth anniversary of our weekly three hour math circle meetings!)

Nobody quite knew what to expect at that first meeting in December 2001. It was intimidating and awkward working together in an unfamiliar room on impossibly hard problems with a bunch of people you'd never met before from schools scattered around the Albany Area.

Halfway through the three hour practice, pizza arrived, thanks to Ben's dad's heroic arctic pizza run, as he made the first Siberian tundra treks across the frigid RPI campus bearing boxes of steamy hot pizza. He would make many more such treks over the next three winters. After the pizza break, Dr. O'Keeffe and Prof. Moorthy tried to encourage the students to write up some tentative answers on the white board, even if they weren't sure they were right. "It's really okay if they're wrong," they would say--"you've got to start the discussion somewhere. It would be boring if people just wrote up right answers all the time. That's not the point of working together. The point is for the whole to be greater than the sum of the parts."

After some initial hesitation, during which everyone seemed frozen to their seats, they began bravely coming up to the board to write up their tentative solutions, and the ice broke.

Slowly but surely, mathematical magic happened as the students began to work together. Everyone contributed lots of "helpful wrong answers." Promising ideas emerged as students compared their approaches, and joyfully made more mistakes together, and got more insights, and made more mistakes, in a sometimes seemingly unending process.

Dr. O'Keeffe had an infuriating habit. If there were two different student answers posted on the whiteboard and one was wrong and the other correct, she would never just announce the correct one and move on. Instead, the students who had come up with the answers had to work through their solutions together to try and reach consensus and understanding as to which was correct.

Students took turns presenting their work on the white boards or on an overhead projector so others in the group could understand their solution approaches. Then, the ultimate reward: "A shared Aha!" moment of joint discovery as several students who had been struggling together on a common problem realized they'd finally cracked a problem and it suddenly all looked beautifully simple and crystal clear.

And then, suddenly, it was 8 p.m. and time to go home--it had been three hours. (But it was never long enough for the students, especially for Tom Zink, who would email Dr. O'Keeffe in the wee hours of the morning during the following days with his latest ideas about any remaining problems that had stumped the whole group. Every morning, she knew she would find more emails from Tom with time stamps of 4 or 5 in the morning--a new idea had woken him and he wanted some feedback on his idea!)

The students had no way to know that they would be working together on a proof-based team round in March--they were just trying to work together to figure out good approaches to solving short answer challenges--but in the process, they learned the key mathematical communication and collaboration skills that stood them in good stead in the surprise proof-based HMMT team round. They laid the foundation for a math circle that continues to thrive and grow later as students continue to share "Aha!" experiences five years later.

Charter member alumni updates five years later: The group continues to grow and thrive five years later. About 20 students regularly attend Math Circle meetings, but Drew Besse is the only one of the charter members still in high school. The others have gone off to college. It's delightful to reflect back on their contributions to math circle and their subsequent experiences, and to see the many threads connecting across the years.

Tom Zink majored in math at RPI and is now a graduate student and TA. Tom was a star member of RPI's Putnam teams during his undergraduate career.

Tom was a very clear choice for our first captain of AAMC. When AAMC started up in 2001, he was already a very experienced senior at Averill Park High School. He came to AAMC with many years of successful problem-solving, including Countdown finishes in regional and state MathCounts, ARML experience, and AMC and AIME honors (only narrowly missing USAMO qualification due to the vicissitudes of the index system). Tom had the highest score on the statewide division-winning composite Capital District NYSML team at 2002 NYSML, where he also distinguished himself in the Buzz Round. Most importantly, his enthusiasm was extreme and infectious and he successfully recruited his schoolmate, Ben Levinn, to join math circle as well. Tom was a key contributor to the Upstate NY' ARML A team's best finish in many years in 2002 and he has continued to coach the Upstate NY ARML teams throughout his college years.

Warren Hayashi is now a senior biology major at RPI.

Warren had done very little contest math before he joined AAMC in the middle of his senior year at Niskayuna High School, so he was understandably doubtful about this HMMT undertaking. This was especially true as he only joined AAMC a few weeks before HMMT. Warren was an amazingly quick study and a very brave and kind soul as well, so he quickly agreed to join in on the fun and challenge of HMMT. Thanks to Warren's willingness to take the plunge, our math circle was able to field a full team of eight. Quite appropriately, as you can see in the photo above, Warren wore his Superman tee-shirt to HMMT, where he took fourth place individual honors in the general contest and contributed to team honors as well.

At RPI, Warren has displayed an impressive variety of talents. He worked on a math research team that produced results published in A Probabilistic Approach to Finding Geometric Objects in Spatial Datasets of the Milky Way. His Superman shirt is especially apt in the light of his later remarkable leadership and accomplishments as captain of the RPI ambulance team, described in this article.

Katherine Brainard is now a senior math and computer-science major at Stanford, simultaneously working towards an MS in computer science. She continues to mentor younger students while coaching a nearby high school debate team. She has also worked as a TA in computer science classes. Last summer, she interned at Microsoft. Earlier this fall, she was named a Siebel Scholar, an awesome award carrying a $25,000 scholarship for the top graduate students in computer science across the country.

Katherine got plenty of practice in multitasking during high school. During her two years with AAMC, she also served as president of the Niskayuna High School debate team, taking special pleasure in mentoring younger debaters. Despite the demands of a heavy debate tournament schedule in which she won many won many debate tournaments and recognition and qualification at the national level debate finals. Katherine also contributed greatly to AAMC's team successes at HMMT in 2002 and 2003.

She finished with individual honors in geometry at HMMT 2003, with a score tied for 7th place--to get an idea of that accomplishment, note that one of the students with whom she tied went on to earn a silver medal at the IMO that summer. She also contributed to the 2002 Upstate NY ARML team, but had to forgo 2003 ARML after winning berths at two national debate tournaments that June. Most importantly for our math circle, she was a great collaborator with the other students working on challenging problems at our Sunday evening meetings. (She is pictured above explaining her solution approach to Alison and Manisha.)

It was fascinating to watch Katherine switch mental gears between math and debate. She would often arrive at AAMC meetings fresh from a debate tournament, with the arguments still flowing through her head. But she would walk into Lally 002 and immediately plunge into the math. On the way home, informal political debates sometimes resurfaced in the carpool with fellow debater Manisha Padi (and later Denise Zong as well!) Conversation in the car was always lively when Katherine was along.

Ben Levinn is now enrolled in the accelerated BS/PhD program in computer science at RPI. Ben is also working as a TA in computer science. In his spare time(!), he works on the editorial staff of the RPI newspaper and serves as an officer of a community service organization. Earlier this year, Ben was inducted into RPI's highest honor society, the Phalanx Society. Only 27 students (limited to juniors, seniors, and grad students) were inducted and Ben's selection as a junior is an especially noteworthy accomplishment. He is a star student whose profile will soon appear here.

Ben contributed enormously to AAMC's team round successes for three years before he headed off to fulltime college. He also had many individual accomplishments. Ben was one of four high scoring students on the 2004 AMC12 that brought national recognition and a Sliffe award to our math circle. While still enrolled in Averill Park High School and dual-enrolled at HVCC, Ben was the 2003 state champion in the 2-year-college math contest. In addition to winning individual recognition in AMC and AIME, he contributed to many AAMC successes in Power Rounds, Team Rounds, and GUTS contests. (Not only were his mathematical skills invaluable, his varsity track and cross-country running skills came in handy on the GUTS rounds at HMMT! Part of the GUTS contest involves designating a runner to dash up and down the steps of the huge auditorium delivering the team's answers and picking up the next set of problems. Ben was a natural choice for that role, but didn't break a sweat before sitting back down with the team to work through the next batch of problems he'd just brought back to the team.)

Ben was also an exceptionally generous and helpful mentor to one of our younger students, Andrew Ardito. Many math circle members have delightful memories of the two of them sitting and working side by side during Ben's senior year of high school. Somehow, Andrew always found Ben's explanations the most helpful in his first year at AAMC, and the two of them were an extremely effective mini-team. Ben deserves some of the credit for Andrew's later accomplishment in qualifying for USAMO last spring.

Alison Miller is a junior majoring in math at Harvard. She has also been doing math research at summer programs in Duluth, Minnesota and Madison, Wisconsin. She will be presenting some of her results in a session at the joint math meetings in New Orleans in January. She hopes to give a brief practice presentation (15 minutes) of that talk to the Albany Area Math Circle when she's home on break later this month. A paper she wrote with two other undergraduate co-authors is here. (One of her coauthors is Aaron Pixton, whom many AAMC members know from the Upstate NY ARML team.) This month, she is giving a talk to the Harvard Math Table. She has also enjoyed a variety of interesting activities with the Harvard-Radcliffe Science Fiction Association, including participating in the IgNobel Prize ceremonies and the MIT Mystery Puzzle Hunt.

During her final two years of homeschooling before college, Alison coached Albany Area Math Circle's junior varsity group for younger students as well as coaching MathCounts at Iroquois Middle School. Like a number of other AAMC alumni, she later enjoyed working as an undergraduate TA. She still very much enjoys working with current AAMC students when she's home on breaks.

Raju Krishnamoorthy is now a sophomore at MIT. Raju took over as AAMC captain after Tom graduated. Raju made huge contributions to the success of AAMC, with his generous willingness to help other students and to share his prodigious talents. Raju had an amazing ability to explain the most difficult problems to our younger students. His modest unassuming manner was in stark contrast to his brilliant problem-solving abilities. He inspired everyone around him.

He was an outstanding captain of AAMC for three years. He clearly deserved AAMC's first-ever MVP award in spring 2005 , when his leadership helped the AAMC team win first place in their division at NYSML. His accomplishments also included many individual honors, including USAMO qualification, winning Chapter and State Countdown championships, and representing New York State on the four-person team at National MATHCOUNTS. Raju was one of the four high scoring students on the 2004 AMC12 team that brought national honors and a Sliffe award to our math circle. He also contributed to the success of Upstate NY ARML teams during all four years of high school.

While still only a Troy High School senior dual-enrolled in part-time courses at RPI, he was a member of RPI's 2004 Putnam team, helping it achieve 19th place out of 400 teams throughout North America.

In 2005, Raju was selected as one of 16 top high school mathematics students from around the country and around the world as a junior fellow of the Clay Mathematics Institute Research Academy. At the academy, Raju was a member of MIT Prof. Richard Stanley's combinatorics research group.

Raju is a terrific public speaker: his inspirational speeches at the 2002 Chapter and State MathCounts competitions. encouraged hundreds of younger students from all over New York. Raju is also a gifted musician and juggler.

Raju gives a great deal of credit for his mathematical interests and successes to two very special and crucial early influences, his father and his MathCounts coach, Mrs. Nancy Smith, a teacher at Doyle Middle School in Troy. Raju's stellar contributions to Albany Area Math Circle and the terrific inspiration and legacy he has passed on to younger students give remarkable resonance to their special influence.

Manisha Padi is now a freshman at MIT. She contributed to team successes at HMMT, NYSML, and ARML during her early years with AAMC. She also participated in PROMYS as well as debate. For her last two years of high school, she worked as part of a research team for Professor Ajayan's award-winning Carbon Nanomaterial Research Group at RPI.

Drew Besse was once the youngest member of AAMC. Now he is the oldest and the only remaining charter member. A lifelong homeschooler, Drew started with AAMC as a 12-year-old seventh grader and is now a 12th grade student dual-enrolled in part-time classes at RPI.

After Raju graduated from Troy High School and headed off to MIT, Drew and Beth Schaffer became co-captains of AAMC, and the two of them have taken an active role in mentoring the many younger students at AAMC as well as coaching MathCounts teams.

Drew has spent four summers at MathCamp. and now has many years of both individual and AAMC team high honors and accomplishments to his credit. He used to have a hat full of AMC school winner and distinction pins, but over the years he has accumulated so many pins that they'd probably weigh his head down if he tried to put them all on his hat now! Drew was one of four high scoring students on the 2004 AMC12 that brought national recognition and a Sliffe award to our math circle.

Drew is looking forward to making his fourth annual trip with the MathCamp team to the MIT Mystery Puzzle Hunt in January 2007. Since he's still a very active leader of AAMC, I'll have lots more to say about Drew and other current students in future posts.

We are always happy to have our alumni join us when they are on break from college. The photo below shows Ben, Raju, and Alison in January 2006, revisiting old times while working on math problems together at an AAMC meeting during their winter break.

Our alumni have left a remarkable legacy in a math circle that continues to grow and thrive after their departure! Future articles posted here will describe our wonderful current students.

sPosted by Picasa