Monday, May 31, 2010

Hale and Farewell!

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.

Saturday, May 15, 2010

Congratulations Matt!

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.


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!

Wednesday, May 12, 2010

Name this polyhedron?

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!

Sunday, May 9, 2010

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

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!

Wednesday, May 5, 2010

USA Math Olympiad 2010

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.

Monday, May 3, 2010

Congratulations Cecilia, Martin and teammates!

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.