Celebrating teamwork and mathematical problem solving

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

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

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!

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

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

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 ....

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.