The Advantage Testing Foundation Math Prize for Girls Community

Wise and heartfelt words from our alumna speaker, Luyi Zhang

2012-02-03T21:55:00.000-08:00

Thank you so much for the opportunity to be here — it is truly an honor, a privilege, and a delight to be speaking to all of you today.

You all have worked so hard and come so far to be here – today – now. Think about it – all the classes you’ve taken, all the techniques and strategies you have learned, and all the problems that you have worked through that have ultimately gotten you here today.

Collectively, as a group, we have solved millions of math problems amongst all of us. It’s pretty cool, isn’t it?

I know that you all are motivated to learn math and solve problems, like the ones earlier today, to the best of your ability – and right now, as we near the announcement of the awards, many of you are probably wondering how you placed and scored.

The thing about scores is that they’re hard to tame because they fluctuate – we all have good days and bad days.

But you know, the truth is that even if you miss a problem because of a small error or oversight, that problem hasn’t changed your math ability – you’re still just as capable; in fact, you know even more now because you will have learned how to solve the problem correctly for next time. And that’s what matters. Regardless of your score today, please know that you all have so much potential within you, and that potential will still be there for you – it always will.

Now, take a moment to look around you. Here, at Math Prize, you’re surrounded by girls from all across the nation who are as passionate and dedicated to math as you are. You’re part of a very special community, and you have such a wonderful opportunity to meet and get to know the people around you. Cherish this opportunity – reach out to people. The connections that you form here this weekend have the potential to grow into truly strong and meaningful bonds over time.

And over time, within a math community, you also have the opportunity to work with each other and share unique insights and ideas. By collaborating thoughtfully with each other, we can make more progress, develop stronger solutions, and delve even deeper in our understanding.

So work with each other.

Be patient and persevering.

Help each other out.

And most importantly, above all else, care about each other. It’s always worthwhile to go out of your way to be genuinely nice to the people around you – because gestures of honest kindness can mean so, so much to people. You never know how your sincere encouragement or heartfelt compliment might totally make someone’s day.

You all are so lucky to have come so far and to be where you are right now – your knowledge and past experience empower you. Now, from here on forward, use that power to stride forth and spread goodwill. How can you make the most of your experiences and form caring, meaningful connections with the people around you? How can you give back and make the community around you a better place?

And finally, what small steps can you take to help fill the community around you with a little more true, genuine joy?

We’re nearing the end of our time together this weekend. At the end of the day, after all the awards have been announced, words will have dissipated into air and trophies will have separated into homes across the nation. But the experiences that you all have shared and all the connections that you have made with each other will remain. Take a moment to think about all the people you’ve met and all the camaraderie that you’ve shared this weekend. Take a moment to remember all the positive experiences, mathematical or otherwise, that you’ve taken part in over the years, and to appreciate the teachers, parents and guardians, coaches, friends, and others in your life who have guided you and supported you along the way.

And from here, go forward with fervor and hope – let your passion drive you and inspire you; find what you truly love and give forth your full honesty and care. And finally, find the joy within what you do, and then share it with those around you, so that they can experience the delight, too.

Thank you.

Luyi, sharing the joy with three other MIT volunteers, Joel Lewis, Yota Kato, and Felix Sun.

About our 2011 alumna speaker: Luyi Zhang, an alumna of Math Prize for Girls 2009 and 2010, is now a freshman at MIT. Luyi’s accomplishments at math competitions include qualifying for the USA Math Olympiad and a special commendation for her solution on a USA Math Talent Search problem.

Luyi has now gone beyond just solving other people’s problems. As true mathematicians do, she now invents her own original problems—and one of those original problems appears on this year’s USA Math Talent Search.

Even back in high school, Luyi had already proven that she was an extraordinarily capable and enthusiastic educator. She is a teaching assistant (TA) at the Art of Problem Solving, where her boss, Richard Rusczyk, says she is one of their all-time favorite TAs. Her students heartily agree. Luyi’s Geometric Delights blog has attracted an international following and resulted in an invitation to present at a national conference held in Ithaca NY this summer. For the past two years, she has also taught disadvantaged middle school students in her hometown of New Haven through an internship with the Breakthrough Collaborative.

Through everything she does, one thing clearly shines through: Luyi’s infectious enthusiasm for inspiring and encouraging others to use their capabilities to their fullest. She represents the very best of the positive spirit and energy that makes Math Prize Prize for Girls so rewarding for everyone involved with it.

MPGers present their research at the Joint Math Meetings!

2012-01-06T21:55:00.000-08:00

Four alumnae from Math Prize for Girls presented their research in a poster session at the Joint Math Meetings (the largest annual professional math meetings in the world, jointly sponsored by the American Mathematical Society and the Mathematical Association of America) in Boston today.

Jessica Oehrlein (Oklahoma School of Science and Mathematics, advised by Aaron Potechin of MIT, at Research Science Institute) presented presented her graph theory research on Book Thicknesses of Subdivisions of Graphs.

A book embedding of a graph is an embedding of the graph in multiple half-planes called pages. The vertices of a graph G are labeled and placed in order on a straight line called the spine. A page is the spine and some subset of the edges of G such that no two edges cross. The minimum number of pages necessary to embed G in a book is the book thickness or stack number of G, denoted sn(G). A subdivision of a graph G is the addition of vertices to existing edges of G. We show that the book thickness of any subdivision of G is at most 2sn(G).

Sheela Devadas (Lexington High School, advised by Steven Sam of MIT, on a problem suggested by MIT Professor Pavel Etinghof) presented her abstract algebra research project on Modular representations of Cherednik algebras associated to symmetric groups.

We study lowest weight irreducible representations of rational Cherednik algebras attached to the symmetric group S_n in characteristic p, focusing specifically on the case p ≤ n, which is more complicated than the case p > n (since S_n modules are not semisimple.) The goal of our work is to calculate characters (and in particular Hilbert series) of these represenations. By studying the kernel of the contravariant bilinear form on Verma modules, we proved formulas for Hilbert series of irreducible modules in a number of cases, and also obtained a lot of computer data which suggests a number of conjectures. Specifically, we find that the shape and form of the Hilbert series of irreducible represenations and the generators of the kernel tend to be determined by the value of n modulo p.

Caroline Ellison (Newton North High School, advised by Giorgia Fortuna of MIT, as part of the PRIMES program) discussed her work on a problem originally suggested by MIT Professor Richard Stanley, The number of nonzero coefficients of powers of a polynomial over a finite field.

Coefficients of polynomials over finite fields often encode information that can be applied in various areas of science; for instance, computer science and representation theory. The purpose of this project is to investigate these coefficients over the finite field F_p. We use Stanley's matrices to find what we conjecture to be an approximation for the sum over n of the number of nonzero coefficients of P(x)ⁿ over F_p. This leads to questions in representation theory and combinatorics. We hope for further research in this area to find a relationship between the number of nonzero coefficients in the expansion of a polynomial to the n^th power and the digits of n base p.

Caroline's slides from an earlier presentation are available here, and her complete paper is available here.

Christina Chen (Newton North High School, advised by Tanya Khovanova in the MIT PRIMES program on a problem suggested by Professor Daniel Klain of the University of Massachusetts at Lowell) presented her geometric work on Hiding Behind but Not Hiding Inside: Maximizing Volume Ratios for Shadow Covering by Tetrahedra.

Define a body A to be able to hide behind a body B if the orthogonal projection of B contains a translation of the corresponding orthogonal projection of A in every direction. In three dimensions, it is not easy to observe that there exist two objects such that one can hide behind another and have a bigger area than the other. We calculated two three-dimensional examples, one of which is a Minkowski interpolation of a tetrahedron and a ball that can hide behind the tetrahedron and has 12% more volume than the tetrahedron and the other of which is a Minkowski interpolation of a tetrahedron and an inverted tetrahedron that can hide behind the tetrahedron and has 16% more volume than the tetrahedron. The second example has the highest volume ratio calculated up to this point and is conjectured to be the best possible.

Christina's slides from an earlier presentation are available here, and her entire paper is available here. A related paper coauthored by Christina, Tanya Khovanova and Daniel Klain is available here.

Both Caroline and Christina have shared on the PRIMES website that they were initially rather nervous a year ago, when they began working on their research projects. They had a lot of prior success with math competitions, but the idea of math research, solving problems that nobody had solved before, problems that might not have solutions was daunting. Both are now very enthusiastic about their experiences, and they celebrate the messiness and the setbacks along the way as well as their eventual successes.

Caroline wrote:

At first, I was definitely nervous; I didn't think I would find anything at all, and I didn't think I could really write a paper or give a math talk. It turns out I was wrong on all counts.

Coming from a math contest background, research has been very different. I still sort of expect everything to have an elegant solution that can be found in a half hour or less, and I have to remind myself that isn't always the case. Things are often messy, but when I do find something that might be interesting or useful, the fact that it exists at all among the chaos makes it doubly beautiful.

Christina wrote:

This was my first time at research, so I did not really expect anything significant. I was actually pretty scared that I would not achieve much. However, I did discover many interesting points and collected them in my paper.

Mathematical research is such a worthwhile and valuable experience. It is very different from problem solving because it does not have the security of a known solution. Sometimes, you are worried about not obtaining anything particularly useful or interesting. However, in the end, when you do, that feeling is empowering because you have determined something nobody ever has before. During the process, you both acquire new knowledge and the experience of confronting the inevitable setbacks of such a project, which can then be applied to other subjects.

Although the PRIMES program is restricted to students who live in the Boston area, their recommended reading list is a great resource for all high school students interested in building a foundation for early research endeavors.

Photo credit: Alison Miller

Math Prize Olympiad 2011 Medalists

2011-12-18T18:55:00.000-08:00

Advantage Testing Foundation Math Prize for Girls is pleased to announce the names of our 2011 Math Prize Olympiad medalists. These 19 astonishingly accomplished young women have risen to the top of an extremely challenging series of contests, completing the final step in a remarkable mathematical odyssey that began with a math contest at their schools last February, brought them together for a longer and harder contest at MIT in September, and ultimately culminated with an "extreme math" challenge in November: our Math Prize Olympiad.

Gold Medalists:

(listed in alphabetical order)

Christina Chen
Newton North High School, Massachusetts

Julia Huang
Lynbrook High School, California

Ramya Rangan,
Harker School, California

Victoria Xia
Thomas Jefferson High School for Science & Technology, Virginia

Silver Medalists:
(listed in alphabetical order)

Sheela Devadas, Lexington High School, Massachusetts
Anupa Murali, Bishop Brady High School, New Hampshire
Mia Smith, Ithaca High School, New York
Danielle Wang, Westmont High School, California
Alicia Weng, North Hollywood High School , California

Bronze Medalists:
(listed in alphabetical order)

Monica Agrawal, Chamblee Charter High School, Georgia
Jiapei Chen, Phillips Exeter Academy, New Hampshire
Frances Ding, Ravenwood High School , Tennessee
Yun Jia (Melody) Guan, Univ. of Toronto Schools, Ontario, Canada
Sylvia Hurlimann, Newton South High School, Massachusetts
Elaine Lin, Seminole High School, Florida
Chen (Leo) Lou, Hotchkiss School, Connecticut
Elizabeth Shen, South Mecklenburg High School , North Carolina
DiYun (Susan) Sun, West Vancouver Secondary School, British Columbia, Canada
Elizabeth Yang, West Windsor-Plainsboro High School South, New Jersey

Our 19 olympiad medalists began their odyssey by joining tens of thousands of young women from all over the United States and Canada in taking the AMC10 or AMC12 contest at their high schools last February. That annual 75-minute contest sponsored by the Mathematical Association of America had 25 challenging multiple choice problems. You can find links to sample problems and more information about the AMC contest here.

Over 270 young women with very strong scores on those February AMC contests qualified to participate in the Advantage Testing Foundation Math Prize for Girls contest, held at MIT in September. The girls spent 150 minutes on the 20 challenging short answer problems, which you can find here. The problems for the September contest were written by Dr. Ravi Boppana, Advantage Testing Director of Mathematics and founding director of the Math Prize for Girls. MIT graduate student Joel Lewis, a longtime member of the New York City Math Team coaching staff, again served as contest reviewer for the problems.

Top students from the September contest held at MIT (including 2010 olympiad medalists still in high school) qualified to take a final additional challenging contest in November: a four-hour proof-based exam with four extremely challenging problems. Those olympiad problems are available here: #1, #2, #3, and #4. Problem #2 was adapted from an original problem proposed by Dr. Ken Fan, the president and founder of Girls' Angle. Dr. Boppana composed the other problems on the olympiad. Princeton graduate student Alison Miller, a Math Olympiad Summer Program instructor and member of the coaching staff of the China Girls Math Olympiad teams, again served as consultant for the selection of the olympiad problems. Oleg Kryzhanovsky, a member of the New York City Math Team coaching staff, served as a consultant in the reviewing/editing/grading of the contest problems.

The results of our November olympiad have now been graded. A completely correct and rigorously justified essay/proof-style solution to each problem was worth seven points. Partial credit for substantial progress towards a valid solution is possible, but--in the olympiad tradition--such credit is awarded very sparingly. Gold medals went to students who scored 22 or more points out of a possible 28, silver medals to students scoring 19 to 21 points, and bronze medals to students scoring 15 to 18 points.

We are grateful to the following teachers who served as lead proctors at the local administrations of the Math Prize Olympiad on November 10: Adam Brown (University of Toronto Schools), Alaina Krystek (Hercules High School), Albert Roos (Lexington High School), Alison Miller (Princeton University/Princeton Math Circle), Altair Maine (North Hollywood High School), Cyndi Howes (Ravenwood High School), Dr. Barbara Emil (C Leon King High School), Dr. Francoise Dastous (Desert Visit High School), Dr. Jessica Hunt (Chamblee Charter High School), Dr. Marta Eso (Hotchkiss School), Elaine Miller (South Mecklenburg High School), Elisse Ghitelman (Newton North High School), Gregory Roberts (Bishop Brady High School), Helen Perl (Ithaca High School), Joe Obrycki (Central Academy), Jon Creamer (Groton School), Lindsey Quinlisk (Westmont High School), Misael Fisico (Harker School), Pam Douglas (Maclean High School), Pat Gabriel (Thomas Jefferson High School for Science & Technology), Patty Cordova (Whitney High School), Philip Rash (North Carolina School of Science and Math), PJ Yim (Saratoga High School), Rita Korsunsky (Lynbrook High School), Steve Condie (Illinois Math Science Academy), Trung Vong (Seminole High School), Weilly Lin (West Vancouver Secondary School), Zuming Feng (Philips Exeter Academy).

Olympiad medalists Julia Huang, Elizabeth Shen, and Victoria Xia eagerly looking forward to the next challenge in their olympiad odyssey.

Olympiad-style exams require unusual perseverence in the face of seemingly impossible challenges, and a willingness to think more deeply, longer, harder, and more resourcefully than most conventional academic tasks ask of high school students. The apt words on our olympiad medals "To look deeper than others look" are drawn from Sonia Kovalevsky, a noted 19th century mathematician and writer whose portrait hangs in a hallway in MIT Building 2, which houses the mathematics department.

Many who have never had occasion to learn what mathematics is confuse it with arithmetic, and consider it a dry and arid science. In reality, however, it is the science which demands the utmost imagination, and one of the leading mathematicians of our century states the case quite correctly when he says that it is impossible to be a mathematician without being a poet in soul. It seems to me that the poety must perceive what others do not see, must look deeper than others look. And the mathematician must do the same thing.

Congratulations to our medalists and to all 37 olympiad students who wholeheartedly embraced the challenge of taking our Math Prize Olympiad on November 10.

All of you are outstanding examples of Sonya Kovalevsky's message in practice--you have indeed looked deeper than others look.

Math and linguistics? Yes, indeed!

2011-11-03T12:28:00.000-07:00

MIT Professor Shafi Goldwasser and Math Prize Honorable Mention Caroline Ellison

Continuing with our "Do math and you can do anything!" theme from my last post, we now present more outstanding examples of the many ways our math prize community members excel in areas beyond mathematics.

Caroline Ellison*, a senior at Newton North High School, alumna of HCSSiM, and participant in Math Prize for Girls 2009, 2010, and 2011, has also won extreme honors in an area that might surprise many: linguistics!

Caroline is one of the winners of the 2011 North American Computational Linguistics Olympiad. She represented the USA at the 2011 International Linguistics Olympiad, where she earned an Honorable Mention as well as special recognition for submitting the best solution to problem #3. The photo below shows Caroline with some of her teammates at the 2011 ILO.

Alex Wade, Caroline Ellison, Aaron Klein, Chelsea Voss, and Allen Yuan

If you are curious about what a linguistics olympiad involves, it is something like a logic puzzle, where you are given some limited information samples about an incredibly obscure language (which nobody is expected to know--including languages you have probably never heard of, e.g., Vai or Menominee) and you need to try and decode the logic of the grammar, syntax, and vocabulary based on your analysis of those samples. Here are some sample problems to get you started.

It sounds like a huge amount of fun--something I think I would have loved doing if it had been around when I was young. I still have fond memories of my dad, a chess-playing poet and polyglot librarian who loved languages, but also a person who had always thought of himself as "not good at math." When I was a young girl, my dad introduced me to language decoding. As a university librarian, he encountered many books in obscure languages that neither he nor any of his librarian colleagues at the university knew and it was a challenge to catalog some of them properly, a challenge he embraced enthusiastically. Neither of us realized at the time that the logic of what he was doing was a kind of mathematical analysis!

If you would like to pursue this further, the first step is to see if there is a nearby university site where you can take the North American Computational Linguistics Olympiad (NACLO) in February. If there is no nearby university site, you might recruit other interested students at your school and then approach a teacher or administrator about whether your school could be a site for NACLO 2012. (For anyone within easy driving distance of Schenectady, New York, Union College will host a site for the 2012 NACLO. More information about Union College's offering of NACLO is here.)

Who knows where it might lead? Maybe one summer down the road you might head off to some exotic location as part of a future US team at the International Linguistics Olympiad (ILO). Next summer's ILO will be held in Slovenia.

In any case, you have a ton of fun ahead of you as you tackle the challenges of the linguistics puzzles. And the fun can start early--you don't need a lot of advanced training in math or foreign language, just a willingness to play with puzzles and think analytically. Caroline's sister Anna (Math Prize 2011) was one of the top eighth graders on the 2011 NACLO.

Linguistics olympiads are also good preparation for other fun adventures you might enjoy down the road, such as the MIT Mystery Puzzle Hunt and the Microsoft College Puzzle Challenge.

(*If you are wondering about those yellow pigs Caroline is wearing on her shirt, check out this page.)

Do math ... and you can do anything!

2011-10-25T08:42:00.000-07:00

Math Prize girls have many talents that go beyond mathematics. Melody Guan, a senior at University of Toronto High School, is a great example with world class honors in chemistry and biology. Melody earned Honorable Mention at Math Prize 2010 and went on to receive a Bronze Medal on our inaugural Math Prize Olympiad in 2010. The photo at right shows Melody (in red) receiving congratulations from MIT President Susan Hockfield along with bronze medalist Julia Huang. Julia, Melody, and all 2010 olympiad medalists still in high school will be writing the 2011 Math Prize olympiad on November 10, along with top ranking students from the 2011 Math Prize for Girls held at MIT in September.

This past summer, Melody was a member of the Canadian team at the International Chemistry Olympiad, held in Ankara, Turkey, where she won a silver medal, contributing to the best team finish ever for the Canadian team. The photo below shows her with the other members of team Canada at the International Chemistry Olympiad 2011.

In 2010, Melody was a member of the team representing Canada at the International Biology Olympiad, where she earned a gold medal. Her individual rank was seventh in the world and contributed to Canada's best ever performance in that olympiad as well. The photo below shows her with the other members of the Canadian team at the International Biology Olympiad 2010.

President Susan Hockfield welcomes Math Prize contestants to MIT

2011-09-27T20:30:00.000-07:00

To all of theMath Prize contestants and your families: Welcome to MIT. Since I was once a math-loving girl myself, Icannot tell you how inspiring it is to see all of this ambitious mathematicaltalent in one place. I am very proud ofall of you and delighted that we have this opportunity to let you explore MIT.

This fantastic contest, like all great events, had adedicated team of people who made it happen, so I want to thank the AdvantageTesting Foundation -- including its president, Arun Alagappan -- for founding this important prizeand serving as its main sponsor. Thanksalso to the Akamai Foundation -- including its founder and MIT faculty member, ProfessorTom Leighton -- for supporting the prize. Finally, I am also very grateful to everyoneat MIT who helped make this event successful, especially Professor MichaelSipser, head of MIT’s Math Department, who was instrumental in bringing theMath Prize for Girls to our campus.

Alchemist, a sculpture by Jaume Plensa

During yourvisit to MIT, I expect you have seen the striking white, numerically sculptedfigure on the lawn between this auditorium and Massachusetts Avenue:“Alchemist,” by world-renowned sculptor Jaume Plensa. I hope you will see it as a clear sign that“Math is spoken here.” Frankly, it ishard to think of a more fitting place than our campus for today’s competition.

However, as youknow, most people are not quite as enthusiastic about math as you are, and aswe are here at MIT. I know wellthat when you are in high school, being very, very good at math can sometimesbe a kind of lonely experience – especially if you are a girl.

So I am here to tell you two things: First, you are not alone. There are many people in the world who careintensely about math and science and engineering, even if there may not be lotsof them at your high school. Here at MIT, we have about 4,300undergraduates. About 45% of them are young women. All MIT students, men andwomen, are good at math, and many of them are great at math. In fact, 85% of our undergraduates major in math,engineering or the natural sciences --85% of the men and 85% of the women,too. That contrasts sharply with thenational average: only 15% of US bachelor's degrees are awarded in these fields. If you feel lonely from time to time in highschool, remember: there are lots of usout here waiting for you to join us!

My secondpoint is even more important, because your interest in math tells me that, morethan most of your peers, you are truly ready to seize the opportunity to beleaders of your generation. Let meexplain, with this story. A friend of mine was encouraging his sonto study engineering or science in college, and his son replied, “Dad, whywould I do that? Everything’s already been invented.” If that is what so many of your peers think, it is no wonder they do not seethe value, or the fun, in studying math and science.

As educators,parents and people who appreciate the power of computation and mathematicalanalysis, we want to remind you: Think of your favorite device or application-- an iPod, or a smart phone, or a Wii, or GPS, or a video game, or Google. All have transformed our lives, and Iguarantee that the people who invented them knew a lot about math andengineering and science. If you knowanyone whose life was saved by a medical treatment – who beat cancer, or had aheart bypass, or who's now living with HIV-AIDS – the people who invented thosetreatments knew a great deal about math and engineering and science. And if you are hoping for technologies thatmight save the planet – like electric cars, or radical new ways of harvestingsolar energy, or making nuclear energy a safer option – the inventors andentrepreneurs who will bring them to life will definitely know a lot about mathand engineering and science. I do notneed to remind our contestants today that, with your skills and interests, youcan be one of those who will invent the future of our planet.

President Hockfield congratulates olympiad medalists Julia Huang, a sophomore at Lynbrook High School in California, and Melody Guan, a senior at University of Toronto High School in Ontario, Canada.

Let me close bysaying something you know very well already: That the math skills each of youis building now will allow you to live a life beyond that of spectators andconsumers. You can be the creators and inventorsand problem-solvers of our future, and I can guarantee that there is nothingmore exhilarating. I wish each of youmuch success in today’s competition, and may you find inspiring ways to useyour extraordinary skills in service to the world.

Susan Hockfield

Welcome for MathPrize for Girls

Kresge Auditorium atMIT

September 17, 2011

AS PREPARED FORDELIVERY

T-shirt mathematics and Mathematica

2011-09-24T06:37:00.000-07:00

Math Prize for Girls t-shirts were popular again this year. The photo above shows a lei-clad volunteer and a current contestant admiring the shirts, as sun streamed into MIT's Lobby 10 during check-in last week. The back of this year's shirt features a chrysanthemum surrounded by a word cloud of the first names of this year's Math Prize contestants. (The word cloud was created in Tagxedo, available here.)

A post on the Playing with Mathematica blog inspired the chrysanthemum at the center of the design. Chrysanthemums seemed especially appropriate for Math Prize t-shirt since they flourish in September, the time of our competition. Indeed, we spotted many chrysanthemums blooming in the roof garden near the space at the Meridien-Cambridge hotel where we held our Games Night event.

Here is the equation that generated our chrysanthemum:

Here is the actual Mathematica code we used to create the design:

PolarPlot[
{6 (1 + Sin[13 u/6]) - 5 Sin[(19 u/4)]^4*Sin[2 Cos[3 u] - 35 u]^8},
{u, 0, 23 Pi/2}, Axes -> False, PlotStyle -> {Yellow, Thickness[0.005]},
Background -> Blue]

Wolfram Research, the publisher of Mathematica, has kindly donated a free student license to all Math Prize for Girls contestants (a license that will remain valid as long as you are a high school or university student), so you can feel free to cut and paste this code into a Mathematica notebook, and then play with the parameters. This is what you will get from the code above:

Your free student license of Mathematica makes it easy to create your own graphs, changing the parameters so you can make a whole family of beautiful designs. You can easily modify colors, plotline thickness and many other aspects.

Using the "Manipulate" command in Mathematica makes it easy to generate a graph with sliders that you can use to adjust the parameters in your equation to find especially nice graphs. Here is a slightly modified version of our previous code that incorporates the Manipulate command:

Manipulate[
PolarPlot[{6 (1 + Sin[a* u/6]) -
5 Sin[(b* u/4)]^4*Sin[2 Cos[3 u] - c* u]^8}, {u, 0, 23 Pi/2},
Axes -> False, PlotStyle -> {Yellow, Thickness[0.005]},
Background -> Blue], {a, 1, 30}, {b, 1, 50}, {c, 1, 50}]

Pasting this code into your Mathematica notebook generates a graph with three sliders you can then slide around to easily explore a large variety of possible variations. Here is a screenshot that shows one particular variation below, but pasting the code above into your Mathematica notebook will allow you to generate a wide range of other possibilities.

Using Mathematica's Dynamic command allows for even more possibilities--you can include color slider bars, and much more. You can also use Mathematica's Animate command to animate your plot, yielding an automated continuous display showing how your graph changes as the parameters change. You can also save your work in Computable Document Format (CDF), which allows you to share it with others: anyone with a freely downloadable Mathematica Player can then explore your graph dynamically.

More beautiful inspirations for graphs to explore are available here and here. T hese families of graphs trace back to articles published by mathematician Temple Fay in MAA journals in 1989 and 1997. Full citations are available here.

The Playing with Mathematica blog which inspired our chrysanthemum design for the t-shirt is a treasure trove of other great ideas for learning to use Mathematica's power.

More fun from Games Night at Math Prize for Girls

2011-09-23T20:41:00.001-07:00

Ken Fan from Girls' Angle brought an origami "discoball" to our Games Night. A number of participants were struck by it and asked for more details about it, which Ken kindly provided here:

It's made out of 212 pieces of origami interlocked without tape or glue...just folding. There are 3 hub types and 2 triangle types. Geometrically, it's a "frequency 3" geodesic dome based on an icosahedron.

Here is a closeup Ken provided showing the details of the ball's construction:

Ken continued with more fascinating stories of origami constructions:

I also made an 8 foot diameter origami geodesic dome for the 2005 Origami USA Convention (both the 8 foot dome and the disco ball were displayed at that convention). The 8 foot dome was a huge project! I bought a few hundred dollars worth of Canford paper and cut it into large origami squares to fold the pieces. Because Canford paper is so thick, I had to wet each crease with watercolor brushes and then weigh it down under books so that the folds would hold shape. I didn't have time to test whether the dome would stay up before the convention, so drove down to NYC with all the pieces in 5 boxes. Bystanders saw us putting up the dome and joined in. Because the dome becomes more and more unstable until the capstone is placed, five of us were inside with 4 holding up the dome walls while a fifth added pieces.

I have no idea how big a dome or sphere is possible using this technique but it would be neat to make one that is about 14' in diameter so that you would be able to stand inside without having to prop it up on a table. That would take quite a huge effort though!

You can see Ken's 8 foot origami geodesic dome (under construction and complete) here.

Ken has also created a treasure-trove of many other wonderful mathematical explorations available in Girls' Angle Bulletins (downloadable here.) His blog is also full of treasures, including a great post about a cool method for figuring out the volume of a tetrahedron, which he showed to a Math Prize contestant at the party last week.

WBUR Here and Now Interviews Victoria Xia

2011-09-19T20:32:00.000-07:00

Robin Young interviewed 2011 Math Prize for Girls winner Victoria Xia on WBUR's nationally syndicated public radio show, Here and Now. You can listen to the podcast here. A transcript of the interview follows below, posted with the permission of the show.

Robin Young [RY]:
Hundreds of high schoolers gathered at MIT in Cambridge, Massachusetts this weekend for the third annual Math Prize for Girls. It's the only national all girl math contest. They have the biggest monetary award, twenty five thousand dollars. It's sponsored by the tutoring company Advantage Testing with the goal to encourage girls to become the mathematical and scientific leaders of tomorrow. So, who took home that money? Victoria Xia, a tenth grader at Thomas Jefferson High School in Alexandria, Virginia. Victoria, congratulations!

Victoria Xia [VX]:

Oh thank you so much!

[RY]: Tell us a little bit about the competition. Some of the questions involved geometry, trigonometry. What happens? We understand you were given 20 problems, and you had a couple hours to do them. Do you pick the ones you think you can do first? How did you approach it?

[VX]: They are roughly arranged in order of difficulty so it makes sense to start from the beginning, but then, yeah, towards the end, you start picking and choosing!

[RY]: Give us a sense. Can you remember one of the problems?

[VX]: I remember the last question on the test just because it's hard. I am not sure if anyone solved it in the end.

So the problem was that you have an equilateral triangle, ABC, and the sidelength of the triangle is 1. And the question is they want you to calculate the probability that if a point is chosen randomly on side AB and another is chosen independently on side AC, that the two points would be less than one over the fourth root of three apart.

[RN]: You had me up to--I mean I diagrammed an ABC triangle but that's about as far as I got. ... Why do you think you won?

[VX]: Oh gosh, that's a tough question to answer. I have been doing math for a really long time. But everyone has their good days and bad days. I feel like if you gave the same contest a week later, the rankings would have been completely different.

[RY]: Almost like a math biorhythm.

[VX]: Yeah, I guess you could say that.

[RY]: You say you have liked math for a long time. As you are well aware, girls are thought not to like math. Or they do like math, they start out first, second, third grade, they are the best in the class and then it becomes uncool. Your thoughts about that?

[VX]: I wouldn't necessarily say it's uncool, but if you look at our math teams, for example, the boy-girl ratio is certainly very high. So sometimes you might feel lonely, I guess.

[RY]: Well in fact MIT economist Glenn Ellison found that female competitive mathletes, you know people like you, are outnumbered three to one by boys.

[VX]: I just don't think it's a reason that you should quit though, especially if you like it. Sure it would be nicer if there were more girls, but most of the time I do it for the math.

[RY]: Well and even as you say that we know that it is changing. We know that work that has been done to encourage women in areas of math and science have been successful, that more and more women are taking their place in math. Are you feeling that as well?

[VX]: Yes, and I'm very glad that that's happening.

[RY]: So now you have won this prize...twenty five thousand dollars! First of all, what are you going to do with it?

[VX]: I plan to donate at least part of it, just to give back to all the teachers that I owe so much to--and the rest of it, I haven't really thought about yet.

[RY]: Well I am wondering then--have you even thought about--what do you want to do?

[VX]: Oh gosh, I don't think I want to become a pure mathematician, but I will probably do something that branches off of math.

[RY]: Well we suspect that you will do well no matter what you do. And, by the way, we have heard that this summer you have traveled to China for the China Girls Math Olympiad, a contest just for girls in China at one time, now they have invited girls from around the world...which brings us back to this all girls contest that you just won. What do you say to people who might say, "Look it's time to open it up, you should compete with boys as well?"

[VX]: Oh yes, certainly. Most of the nationwide math competitions do involve both boys and girls.

[RY]: But what do you say to people who say: “You wouldn't have won if there was a guy in there?”

[VX]: It might be true to some extent but it's not like I would have backed down if there were guys involved.

[RY]: Something tells me that it also might not be true--that they would have won....Victoria Xia, who won the Math Prize for Girls at MIT this weekend. Victoria, thanks for being with us.

[VX]: My pleasure.

Credit: Transcript posted with permission from public radio's Here & Now

More info about Math Prize for Girls 2011@MIT

2011-09-19T11:00:00.000-07:00

A complete list of the top-scoring 41 students and their schools is available here.

The first twelve problems on the contest have now been posted here. Feel free to try them and join the discussion on Art of Problem Solving's forum. The last eight problems, which are harder, will be posted later. The real learning experience comes after the contest, when you think of cooler and more awesome ways to solve the problem, and come up with extensions of your own. [Update: all 20 problems have now been posted.]

Finally, a playful and imaginative spirit is critical to success in "extreme math" problem solving events like ours. We saw lots of that spirit at our Games Night social event, held at the Hotel Meridien Cambridge-MIT on the eve of the official contest, as well as in the lunch time socializing after the contest.

Visually, the entire event was a treat for the eyes--it was like no other math contest event I have ever seen.

Mathematical origami, mathematical cake decorating, polyhedra building, topologically challenging Twister games and more were all very popular. Students decorated the cake above with fabric flowers to represent a triangle inscribed in a circle. They arranged the flowers on the cake below to make pi and sigma characters. They used the flower picks as styli to inscribe Schroedinger wave function equations on the surface of yet another cake.

More photos will be coming soon, but to give you a little bit of a flavor of our Games Night, check out the photo of a current contestant and MIT freshman Luyi Zhang, an alumna volunteer, (at right) putting their heads together inside an icosahedron they built from printer paper and yarn. (For instructions on how to make one of your own, see Luyi's blog here.) Luyi was also our alumna speaker at our awards ceremony--we'll be posting her inspiring speech on this blog later this week.)

Wearing polyhedra was very popular at the Friday evening party. Alumna volunteer Bridget McCoy, an MIT student and ROTC cadet studying mechanical engineering, smiles through her icosahedron at left. There was plenty of good cheer all around, despite (or because?) of the fact that ice water was the only beverage served at the event.

The exam rooms were bright and cheerful with the colorful polyhedra built the night before as well as the flowered leis worn by proctors and other volunteers to distinguish them from the students. The leis were a real necessity because so many of the contest volunteers were young alumnae in college (e.g., MIT freshman Luyi Zhang at top right) who otherwise looked indistinguishable from current students. We did give our volunteers lots of flexibility as to how and where they wore their leis, as long as they were prominently visible. Some leis wound up on heads, looped through belts at the waist, or threaded through backpack loops. Lead proctor in room 10-250, Elisse Ghitelman, a math teacher from Newton North High School, is pictured below wearing her lei in a fairly conventional fashion.

Students settle into their seats and get ready for the exam. Some of them brought snacks along to fortify themselves for the challenging 2.5 hour exam.

The weather was glorious, and smiles and hugs were the order of the day at lunchtime after the contest as students basked in the warm September sunshine overlooking the Charles River.

2010 Math Prize Olympiad medalists return to 2011 Math Prize

2011-09-19T06:30:00.000-07:00

Eleven of our twelve 2010 Math Prize Olympiad medalists returned to 2011 Math Prize this year, three of them as college student alumnae volunteers, and the other eight as veteran high school contestants competing again in 2011. Thanks very much to MIT Professor Tom Leighton, Yale Professor Priya Natarajan, and MIT Math Department Head Michael Sipser, who joined founding sponsor Arun Alagappan in presenting their olympiad medals. Our 2010 olympiad medalists also received personal congratulations and recognition from MIT President Susan Hockfield at our 2011 ceremonies.

2010 Math Prize Olympiad medalists pictured above from left to right are: Julia Huang, Ramya Rangan, Shijie (Joy) Zheng, Danielle Wang, Victoria Xia, Elizabeth Shen, Mariya Sardarli, Luchang Wang, Melody Guan, Sheela Devadas, and Bianca Homberg. (Not pictured, Elizabeth Synge.)

Our four graduated 2010 Math Prize Olympiad medalists now in college are a remarkably accomplished group and we are deeply honored that three of them were able to join us as volunteers this year, along with dozens of other college student volunteers, most of them Math Prize alumnae at MIT.

2010 Math Prize Olympiad gold medalist Mariya Sardarli, pictured at left, attended Strathcona Composite High School in Edmonton, Canada at the time she wrote the 2010 Math Prize olympiad last winter. She is now a freshman at Princeton University. Mariya traveled to Cambridge by bus to help at Math Prize 2011 as an alumna volunteer, working as a registration assistant, proctor, grader, and tiebreak timer. Mariya has many notable accomplishments, including winning the Canadian Math Olympiad and representing Canada on their six-person team at the International Math Olympiad.

2010 Math Prize Olympiad silver medalist Joy Zheng hails from Washington State, where she founded the Seattle Infinity Math Circle. Joy attended Phillips Exeter Academy in New Hampshire at the time she wrote the Math Prize Olympiad last winter, and she is now a freshman at Harvard University. Joy has taught in several math enrichment programs, including IdeaMath, and she helped out in running the tiebreaks at this year's Math Prize event. Joy's many other accomplishments include winning gold medals at the 2009 and 2010 China Girls Math Olympiad. In 2011, she was one of the top 12 winners of the USA Math Olympiad, a very rare honor. In the entire 28-year history of that event, only five young women have ranked among the winners.

2010 Math Prize Olympiad bronze medalist Bianca Homberg attended Westborough High School in Massachusetts at the time she wrote the olympiad. She also attended Canada/USA MathCamp during her high school year, and is now a freshman at MIT. Bianca is one of seven first year winners of the Google Anita Borg Memorial Scholarship. Bianca wore many alumna volunteer "hats" during our 2011 Math Prize olympiad, including helping with running the Games Night party on Friday, serving as deputy lead proctor in one of the exam rooms, and helping to run the tiebreaks during the afternoon award ceremony. She is shown below wearing a lei (to designate her as a volunteer) while walking backwards as she leads an informal tour and guides a group of the current high school student participants over to Kresge Auditorium for the awards ceremony.

2010 Math Prize Olympiad bronze medalist, Elizabeth Synge, who attended Boston University Academy at the time she wrote the olympiad last winter, is now a freshman at Smith College and was unable to be with us this year. Elizabeth was the Math Prize for Girls grand prize winner in 2009 and runner up in 2010. She has also won gold and silver medals as a member of the US teams at the China Girls Math Olympiad in 2010 and 2009. You can read more about Elizabeth here.

Our eight 2010 olympiad medalists still in high school and therefore eligible to compete again in 2011 are also a very accomplished group. Other posts will include more photos and describe more about them, so I will simply list their names, current grades, and schools below:

Silver medalist Danielle Wang is a freshman at Westmont High School in California.

Bronze medalists still in high school are:

Sheela Devadas, senior at Lexington High School in Massachusetts
Yun Jia (Melody) Guan, senior at University of Toronto Schools, Ontario
Julia Huang, sophomore at Lynbrook High School in California
Ramya Rangan, senior at Harker School in California
Elizabeth Shen, senior at South Mecklenberg High School in North Carolina
Luchang Wang, senior at Central Academy/Valley High School in Iowa,
Victoria Xia, a sophomore at Thomas Jefferson High School for Science and Technology in Virginia

The top 41 students at Saturday's contest held at MIT will be invited to write the 2011 Olympiad, a four hour proof-based competition, at their schools later this year. The complete list of those students is available here.

Math Prize 2011@MIT winners

2011-09-18T21:12:00.001-07:00

Congratulations to Victoria Xia, a sophomore at Thomas Jefferson High School for Science and Technology in Alexandria, Virginia, who took first place and won $25,000 at Saturday's third annual Math Prize for Girls Contest, sponsored by the Advantage Testing Foundation. This year's contest was held at MIT in Cambridge, Massachusetts.

Victoria also won a gold medal as a member of the US team at the China Girls Math Olympiad (CGMO) held last month. Two years ago, as an eighth grader, Victoria was a top-12 CountDown participant in the National MATHCOUNTS competition, one of only a small handful of girls ever to rank that high in that event's history over the past three decades.

According to an article that appeared in her hometown newspaper, the Vienna (Virginia) Connection, after she returned from the CGMO, Victoria credits her father, her teachers, and her coaches for nurturing her mathematical development.

“[My father is] the one who started me off on it when I was really little,” said Victoria, who has been in Fairfax County’s Gifted and Talented programs since the third grade. “Math, problem solving-wise, stems from logic puzzles. I think they’re what got me interested in math. They’re more interesting than computational math.”

Victoria has always been active in school math programs and owes a lot of her skills to her teachers and coaches. “Being good at it has to start from a love of math because if you’re forced into it, I don’t know how likely you are to last."

Congratulations as well to Julia Huang and Danielle Wang, who tied for second/third place at the contest, and received $7,500 each after splitting the combined total of the prizes for second and third place. After an exciting tiebreak round, Danielle brought home the second place trophy and Julia brought home the third place trophy.

Julia is a tenth grader at Lynbrook High School in San Jose, California. Danielle is a ninth grader at Westmont High School in Campbell, California. Danielle, who is a member of the San Jose Math Circle, also won the $1,000 Youth Prize for the top score by a student in ninth grade or below.

All three girls are returning veterans from last year's Math Prize 2010, in which Victoria Xia received Honorable Mention, Julia was tied for 8th place, and Danielle took first place. In addition, Victoria and Julia won bronze medals in the 2010 Math Prize Olympiad, while Danielle won a silver medal in that olympiad.

Victoria, Danielle, and Julia trained last summer at the Math Olympiad Summer Program (MOSP) as part of the eight-member team for the 2011 China Girls Math Olympiad (CGMO), funded by the Akamai Foundation, which is also a sponsor of the Math Prize for Girls. The photo below was taken of that team while they were training together at MOSP. Victoria and Danielle are in the back row at right, while Julia is second from the left in the front row. Seven out of the eight students on the US CGMO teams were at the Math Prize for Girls this weekend, along with hundreds of other outstanding young women from across the US and Canada.

All eight girls on the team developed a friendly and mutually supportive camaraderie while training at MOSP and later while competing at CGMO. My daughter Alison had the pleasure of working with them as an instructor at MOSP. You can read the students' joint blog here. Another member of the US CGMO team, Christina Chen (leftmost in front row above), was also a top-ten finisher at Math Prize for Girls 2011, coming in 7th place. You can read a great article about Christina in her local paper here. Julia, Danielle, Christina, and the entire US team came home from the CGMO with medals, as you can see in the photo below.

More results and photos from the 2011 Math Prize for Girls will appear in this blog later this week.

In my personal opinion, all 276 students at the Math Prize (and the dozens of alumnae volunteers and others who assisted in math that event excellent) were winners because of the extremely positive and awesome community they formed. I have never seen so many smiles and hugs at a math competition before!

Where to eat near Math Prize for Girls@MIT

2011-09-13T13:42:00.000-07:00

Thanks very much to Maria DeVuono-Homberg, mother of Math Prize alumna and current MIT freshman Bianca Homberg*, for creating this excellent map marked with some suggestions of places to eat near the Math Prize for Girls events at MIT. There are many other delicious choices with a variety of different ethnic dining options, some of them quite modestly priced to attract people on student budgets, near the ones highlighted here, so you can just take these as a point of a departure.

The area along Massachusetts Avenue between MIT and Central Square is an especially good choice for Friday evening dinner, because you will wind up close to our Games Night event at the Meridien Hotel, which is also conveniently marked on the map.

The weather forecast looks beautiful at the moment--I hope I am not jinxing anything by writing this! In that case, contestants and their families might want to consider a Friday evening picnic in one of the nice outdoor spaces in and near the MIT campus. It is especially worth noting that the Meridien Hotel has a full-size supermarket (with deli items, etc.) located on the second floor of their building.

*Note: the entire Homberg family is awesome! All four of them are volunteering at Math Prize 2011! Bianca's mom Maria is the math team coach at Westborough High School in the Boston area, so she will be one of our lead proctors. Bianca will also be a proctor as well as helping with check-in. Bianca's dad and younger brother will also be helping out with greeting and directing parents and contestants in Lobby 7 and later helping to set up Kresge for events there.

Eyes on the prize: the generosity of the Math Prize community

2011-09-13T04:17:00.002-07:00

The generosity of spirit of math competitors and math team coaches has long been a wonder to me. In what other competitive endeavor besides math competitions do competing students and coaches have such friendly camaraderie, such willingness to share their great mathematical ideas and problem solving tips freely, such interest in giving whatever they have learned and discovered to others?

If you don't believe me, check out the free Art of Problem Solving forums where students, teachers, and coaches generously help one another, asking for nothing in the return other than joy of sharing and the satisfaction of helping others to experience an "Aha!" moment.

And nowhere have I seen that beautiful spirit of sharing and helping others captured more than among those in our own Math Prize for Girls community.

I have already mentioned that the founding director of Math Prize for Girls, Ravi Boppana, has thousands of helpful posts on the Art of Problem Solving forums. Ravi has also done a great deal of teaching to students from disadvantaged educational backgrounds, giving them access to advanced mathematical concepts that may not be available at their schools, including Advantage Testing Foundation's LEDA Scholars program at Princeton University and the Trials program at Harvard Law School. The photo above shows Ravi teaching at the Art of Problem Solving's Summer Program in Mathematical Problem Solving (SPMPS), which reached out to students in low-income New York City public schools. You can read more about that program in the New York Times coverage here, as well as on their blog here. Advantage Testing Foundation has offered financial support to make it possible for future SPMPS alumnae who qualify for Math Prize for Girls to participate in our program.

Another member of our Math Prize for Girls community, Joel Lewis, an MIT grad student, is the all time leader in AoPS posts. As of this writing, he holds the record for most posts on AoPS, with an astounding 12,846 posts on AoPS, dating all the way back to 2003. Joel has been a volunteer problem reviewer for Math Prize all three years, and he will be leading a session on origami and math at our Games Night event for Math Prize contestants this weekend.

Joel is an award-winning instructor at MIT, and he is now the course administrator for an MIT freshman calculus class, but you don't have to enroll at MIT to learn from Joel. MIT believes in sharing knowledge freely with the entire world. Independent learners anywhere in the world can get all the course materials for free through MIT's Open CourseWare Scholar initiative. You can even watch his calculus videos for free on youtube here and here.

Younger members of our community who give their knowledge freely and generously and believe passionately in "paying it forward" include Luyi Zhang, an MIT freshman who is an alumna of Math Prize 2009 and 2010. Luyi will be our alumna speaker at Saturday's awards ceremony, and she will also be leading activities at our Games Night event.

Luyi is a teaching assistant for the Art of Problem Solving. Her boss, Richard Rusczyk says that she is one of their "all time favorite TAs." Her students heartily agree. Despite her youth, Luyi has already contributed an astounding 2,779 posts on the Art of Problem Solving forums. She has also created a blog called Geometric Delights, where she shows how to use inexpensive materials such as paper, string, beads, pipe cleaners, cheese, and brownies to create beautiful geometric objects that teach geometric principles in a very playful way. Her blog has developed an international following. Here is a video from Luyi's blog.

Even as a high school student, Luyi was already heavily involved in teaching educationally disadvantaged students in her hometown of New Haven, Connecticut. The photo below shows her teaching in the Breakthrough Collaborative program located there, where she has taught middle school students for the past two years in their afterschool and summer programs.

Our lead check-in volunteer at Math Prize this year, Meena Boppana, started up a new volunteer outreach programs for middle school student girls on the Lower East Side of Manhattan last year. Meena decided to take the initiative after attending a leadership program at Mount Holyoke College, Take the Lead, which awarded her a $500 prize she is spending for materials to support the volunteer program she started up last year for 15 fifth and sixth grade girls at Girls Prep, a public middle school for girls located on the Lower East Side of Manhattan. She was originally connected up with the school by Advantage Testing Board Member Lauren Frank. Meena got lots of great ideas from her dad, Ravi, and she recruited three of her Hunter College High School math team members to help out at the school as well. One of those Hunter teammates who helped in Meena's program last year is a Math Prize contestant this year, Jenny Nitishinskaya. Two more Math Prize contestants, Sindy Tan and Tracey Cheng, will be joining their program as new volunteers this year.

The leadership of generous volunteers such as Ravi, Joel, Luyi, Meena, Jenny, Sindy, Tracey, and others like them all over the country are an inspirational model for emulation. In my own math circle, we have many volunteer student coaches as well, and outreach to students from educationally disadvantaged backgrounds is a very important priority for me personally. I am very proud to say that many of our students in the Albany Area Math Circle have been "paying it forward" by volunteering as student coaches. This year Math Prize contestant Gili Rusak from our Albany Area Math Circle will be working as a student assistant coach to Nancy Smith, a math teacher and longtime MATHCOUNTS coach at Doyle Middle School, a school in Troy, New York where 61% of the students qualify for free or reduced price lunch.

The founders of the Math Prize for Girls

2011-09-05T18:26:00.001-07:00

The Math Prize for Girls owes its existence to leadership of two men with a shared vision, Arun Alagappan, founding sponsor and president of Advantage Testing Foundation, and Ravi Boppana, the Advantage Testing Director of Mathematics, who is the founding director of Math Prize for Girls.

If you see either of these very generous and accomplished men at the Math Prize for Girls, please be sure to thank them for making this event a reality.

Arun's story, as recounted in his biography on the Advantage Testing Foundation website, is a remarkable one.

Arun Alagappan is the President and Founder of Advantage Testing, Inc. He is a magna cum laude, Phi Beta Kappa graduate of Princeton University and a graduate of Harvard Law School. At Princeton, he won the Class of 1869 Prize in Ethics. Mr. Alagappan sat on the Board of Editors of the Harvard International Law Journal, served as Law Clerk to Judge Dorothy Nelson of the United States Court of Appeals for the Ninth Circuit, and worked briefly at the law firm of Sullivan and Cromwell in New York City. He was a Teaching Fellow in Harvard's Department of Mathematics and was awarded a Certificate of Distinction for Outstanding Teaching of Harvard Undergraduates from the Dean of the College. Mr. Alagappan serves on the Board of Trustees of Prep for Prep and as Vice President of the Board of Trustees of LEDA (Leadership Enterprise for a Diverse America). The goals of these organizations are to nurture the academic and leadership potential of exceptional students of modest means and to increase the socioeconomic diversity of students at leading colleges and universities.

Arun was recently honored by the Wall Street Journal in their Donor of the Day feature column:

Arun Alagappan is helping to find the next generation of leaders who will bring diversity, new ideas, compassion and a different kind of leadership to institutions.

Mr. Alagappan, the 51-year-old founder and president of Advantage Testing Inc., a New York-based tutoring and test preparation company, became involved with the nonprofit LEDA, Leadership Enterprise for a Diverse America, more than eight years ago.

The entire Wall Street Journal article is available here. You can hear more directly from Arun about his vision for a more diverse leadership in a CNN interview with Deepak Chopra. You can read more about his educational philosophy here.

Ravi Boppana, the founding director of Math Prize for Girls and the co-director of mathematics at Advantage Testing, holds a Ph.D. in Computer Science from the Massachusetts Institute of Technology. He is a summa cum laude graduate of the University of Maryland, with a B.S. in Mathematics and Computer Science. He was a professor of computer science at Rutgers University, where he was the recipient of the "Excellence in Teaching" award. Later he was a tenured professor of computer science at New York University, where he was the recipient of the "Golden Dozen" teaching award.

Ravi has coached the New York State team at MathCounts Nationals, where one of his students, Andrew Ardito, was the national runner-up to the champion. Another of his MATHCOUNTS students, David Bieber, was inspired to follow in Ravi's footsteps by becoming a coach himself, and was the first student coach ever to be honored as a MATHCOUNTS Coach of the Week. Yet another of his students, Alexander Iriza, went on to become a winner of the North American Computational Linguistics Olympiad and was a member of the US team at the International Linguistics Olympiad. His daughter, Meena Boppana, is also a very talented young mathematician, winning many honors of her own as well as coaching students from disadvantaged educational backgrounds; you will read more about Meena and Ravi's wife Ranu, in a later post, since since they are veteran lead volunteers for the Math Prize for Girls.

Ravi was one of the earliest members of the Art of Problem Solving forums, generously sharing his mathematical insights with students on those forums. He has contributed thousands of helpful posts on a variety of mathematical topics to that forum. He recently co-authored a textbook on prealgebra published by the Art of Problem Solving.

Ravi was a remarkable successful mathlete in his own time, qualifying for the USA Math Olympiad in high school and high honors on the Putnam Math Competition in college.

But it's worth noting that he got off to a late--and not very promising--start. He did not take his first math contest until tenth grade, and it was not until 11th grade that he first took the AHSME (the contest now known as the AMC10/12).

As he wrote here:

When I was a kid in high school, I joined the math team. At the first practice, I got the first problem wrong while everyone else got it right. I thought about quitting right then. I’m glad I didn’t. Over the next three years, I got a lot better. In retrospect, math team was the most influential part of my high school experience. Because of math team and math contests, I studied math in college and grad school. I later taught math and computer science at Rutgers and NYU.

Ravi gives a lot of credit to Mrs. Linda Agreen, the high school math teacher who coached his math team--but she deserves a post of her own, which is coming soon.

If your parents are driving you to Math Prize for Girls

2011-09-05T16:36:00.000-07:00

For parents who are driving their daughters to Math Prize for Girls on Saturday morning September 17, the best place to drop them off is the Building 7 main entrance of MIT at 77 Massachusetts Avenue, which is shown above.

Once you enter Building 7, you will see a Math Prize for Girls sign on an easel and a Math Prize for Girls volunteer who will point you down the "Infinite Corridor" towards Lobby 10 for check-in. (Even if you checked in the night before at Games Night, you should still head down the infinite corridor in the general direction of Lobby 10, but if you already have your nametag, a volunteer near Lobby 10 will direct you to your assigned classroom.)

Parking is not always easy to find near MIT so we strongly recommend that your parents drop you off before they attempt to find a parking space. Here is a link to a map PDF we have created for parents. You may want to print a copy for their reference. Our map for parents has all the information they need about events for them after they drop you off.

Our parent map also shows the nearest paid public parking lots, which are several blocks away (marked A, B, C, and D on the parent map) and are not cheap. However, early on a Saturday morning, parents might be lucky enough to score free parking even closer than the paid facilities on the map. Some friendly and highly unofficial tips are available here, courtesy of Tech Squares, the MIT square and round dancing group. A shout-out of thanks also to my Albany Area Math Circle co-advisors, Bill Babbitt and Rita Biswas, for their consultation and reality check advice about driving to MIT and parking nearby.

Remember that check-in begins at 8:45 a.m., and we expect students to be in their seats in their assigned rooms by 9:35 so that they can listen to initial instructions and the contest can start right on time at 9:45.

After dropping students for contestant checkin, parents should have plenty of time to find parking before the first parent event begins. All events for parents take place in Kresge Auditorium and the parent schedule is given on our map/schedule for parents PDF.

Questions for our panel discussion for parents and teachers?

2011-09-05T12:39:00.001-07:00

Will YOUR school be represented at MPG 2011@MIT?

2011-08-24T16:02:00.000-07:00

Acton-Boxborough High School, Massachusetts { VA }
Advanced Math and Science Academy, Massachusetts { CT }
Alabama School of Fine Arts, Alabama { LMB }
Algonquin Regional High School, Massachusetts { GT }
Amity Regional High School, Connecticut { MZ }
Anne Sobrato High School, California { TM }
American High, California { SB }
Athens High School, Michigan { DM }
Avery Coonley School, Illinois { MJ }
Bakersfield Christian High School, California { S(P)L }
Barrington High School, Rhode Island { OJ }
Beaverton High School, Oregon { MM }
Beckman Catholic High School, Iowa { CW }
Benjamin N Cardozo High School, New York { ML, XC, YD }
Bergen County Academies, New Jersey { AS, CL, CX, HL, KH(S)J, MG, YI }
Bishop Brady High School, New Hampshire { AM }
Boston Latin School { HH }
Breck School, Minnesota { Y(A)J }
Brecksville-Broadview Hts High School, Ohio { CZ }
Buchholz High School, Florida { JL }
C Leon King High School, Florida { EH }
Canyon Crest Academy, California { AK, CW, MX }
Carmel High School, Indiana { CH }
Centennial High School, Ohio { JXW,VW }
Central Academy, Iowa { MM }
Chamblee Charter { MA }
Charlotte Latin School { CZ }
Chelmsford High School, Massachusetts { Y(L)G }
Choate Rosemary Hall, Connecticut { JP }
Clements High School, Texas { A(A)R, H(T)W, LS }
Columbia High School { SE }
Commonwealth School, Massachusetts { RH }
Conestoga High School, Pennsylvania { CW, LB }
Corvallis High School, Oregon { PN }
Cranbrook Schools, Michigan { X(S)C, YY }
Danaidae Learning Studio, California { RB }
Desert Vista High School, Arizona { JW, VP }
duPont Manual High School, Kentucky { HZ }
Dutch Fork High School, South Carolina { JW }
Edina High School, Minnesota { X(L)Z }
Edwin O. Smith High School, Connecticut{ JH }
Emma Willard School, New York { Z(W)F }
Enloe High School, North Carolina { JW }
Fairview High School, Colorado { CC }
Fort Collins High School, Colorado { SN }
Fox Chapel Area High School, Pennsylvania { AW }
Fryeburg Academy, Maine { X(E)D }
Governor Livingston High School, New Jersey { AK }
Groton School { R(A)X }
Harmony Middle School, Kansas { SR }
Harper Park Middle School, Virginia { HC }
Henry M. Gunn High School, California { CL }
Hercules High School, California { I-C(J)K }
Hill School, Pennsylvania { JP }
homeschooled { BD, JJ, KB, ML }
Hopkins School, Connecticut { AM, LS, YK }
Horace Greeley High School, New York { AN, G-JL }
Hotchkiss School, Connecticut { HJ(J)L }
Hudson High School, Ohio { IS }
Hunter College High School, New York { CW, EN, LC, L(T)C, ST }
Illinois Math and Science Academy, Illinois { MC, RS }
International School { CG }
Interlake, Washington { HY, KZ }
Ithaca High School, New York { AL, MS }
Jackson Prep, Mississippi { SS }
Jasper High School, Texas { SH }
John P. Stevens High School, Texas {CW, SI }
John T. Hoggard High School, North Carolina { KL }
Kings Park High School, New York { MS }
La Jolla High School, California { ML, SH }
Ladue Horton { SS }
Lamar High School, Texas { LL }
Langley High School, Virginia {SE}
Lexington High School, Massachusetts { AB, JS, KF, SS }
Lincoln East High School, Nebraska { KS }
Little Rock Central High School, Arkansas { LZ, WG }
Livingston High School, New Jersey { JJ, SL }
Loomis Chaffee, Connecticut { J(M)H, SYJ }
Longmeadow High School, Massachusetts { HG }
Lord Byng Secondary School, British Columbia { SH(J)C }
Lynbrook High School, California { JH, M(A)C }
Magee Secondary School, Vancouver { AL }
Manalapan High School, New Jersey { IP }
Marc Garneau C.I. { Z(S)S }
Menlo School, California { KP }
Mira Loma { J(E)W }
Mission San Jose High School, California { AG, RW }
Monroe Woodbury High School, New York { Q(C)D }
Montgomery Blair High School, Maryland { GS, JS, MC, MN, SC, Y(H)H }
Montrose School, Massachusetts { GRL }
Naperville Central, Illinois { EM }
North Carolina School of Science and Math, North Carolina { LZ, PP }
New Trier High School, Illinois { AP }
Newton North High School, Massachusetts { AE, CC, CE, YG }
Newton South High School, Massachusetts { MG, SH, WM }
Niskayuna High School, New York { CH, EP }
North Allegheny Senior High School, Pennsylvania { KB }
North Central High School, Indiana { MS }
North Hollywood { AW }
Northern Highlands Regional High School, New Jersey { AK }
Oak Park and River Forest High School, Illinois { ES }
Oklahoma School of Science and Mathematics, Oklahoma { JO }
Palo Alto High School, California { H-LC }
Park Tudor School, Indiana { JW }
Phillips Academy Andover, Massachusetts { JY }
Phillips Exeter Academy, New Hampshire { CG, EW, HK, HL, JC }
Phoenix Country Day School, Arizona { LC }
Princeton High School, New Jersey { RT }
Ravenwood High School, Tennesee { FD }
Redwood Middle School, California { KZ }
Ridge High School, New Jersey { CC }
Ridgewood High School, New Jersey { SP }
Rockdale Magnet School for Science and Technology, Georgia { HK }
Sacajawea Middle School, Montana { AC }
Sage Hill School, California { CL }
Salem High School, Michigan { NC }
Saratoga High School, California { AC, AZ, PK }
Scripps Ranch High School, California { AC, AZ }
Semiahmoo Secondary, British Columbia { HNRL }
Seminole High School, Kentucky { EL }
Shaker High School, New York { GR }
Shrewsbury High School, Massachusetts { VH }
Sir Winston { HJ(S)C }
South Mecklenburg High School, North Carolina { ES }
St Clare's { RA }
St Mark's School { DW }
Stamford High School, Connecticut { DY }
Stuyvesant High School, New York { AW, DU, DY, JZ, KO, LG, MM, SC }
Taft School, Connecticut { MN }
Tenafly High School, New Jersey { JH }
The Dalton School, New York { F-TL }
The Harker School, California { CL, NM, RR }
The Hockaday School, Texas { Y(C)K }
The Lawrenceville School, New Jersey { AM }
The Nueva School, California { AS }
The Pingry School, New Jersey { TL }
Thomas Jefferson High School for Science and Technology, Virginia
{ JF, JK, JW, KH, VX, JY(S)K, PC }
Unionville High School, Ontario { X(V)D }
University High School, California { B(J)S, TW }
University of Toronto Schools, Ontario { RZ, YJ(M)G }
Valley High School and Central Academy, Iowa { LW }
Vestavia Hills High School, Alabama { BM }
Ward Melville High School, New York { GZ }
Wayland High School { Y(J)P }
West Vancouver Secondary School, British Columbia { D(S)S }
West Windsor-Plainsboro High School South, New Jersey { EY }
Westborough High School { UI }
Western Canada High School, Alberta { HJ-N }
Westminster Schools, Georgia { LC }
Westmont High School, California { DW }
Weston High School, Massachusetts { GH, SP }
White Station High School, Tennessee { T(A)Z }
Whitney High School, California { YC }
Winchester High School, Massachusetts { AP, EY, JP }
Yang Academy, Maryland { JY, JY }

Math prize contestants from the high schools shown above have completed their preregistration forms for Math Prize for Girls. If you are planning to come and your school and your initials* are not listed above, please fill out our preregistration form as soon as your travel plans are reasonably certain, so that we can make sure we have to room to accommodate all students who want to attend various special events including Games Night, as well as all accompanying parents, families, and teachers who want to attend special events open to them. The preregistration deadline is September 3. We can't guarantee that there will be space at optional special events for contestants who do not preregister by that time.

We will update this list regularly, every few days, as new pre-registrations arrive.

*Students who listed a "preferred name" that begins with a different first letter than their official name have that preferred name shown in parenthesis. So, for example, a student named "Elizabeth White" who prefers the nickname "Beth" would be listed as E(B)W, but a student named Margaret White who prefers the nickname "Maggie" would simply be listed as MW.

Traveling to MIT for Math Prize for Girls 2011

2011-08-07T19:09:00.000-07:00

MIT's official website provides helpful and detailed directions here.

The MIT website even has a unique sense of humor, giving directions for arriving by blimp as follows:

Take the blimp to the tall building with all the glass windows (that would be the Hancock tower). Head north over the Charles River and have them put you down on top of the large, convex, concrete structure on the north shore of the river (that would be the Great Dome of MIT). Watch out for police cars on the roof.

But the MIT directions website has plenty of useful advice for those who only have more conventional means of travel at their disposal.

I'd like to underscore a few of their points, and add a few more ideas of my own.

1) As the MIT website says, "Parking in Cambridge and Boston is generally not an enjoyable experience. Whenever possible, park your car at the hotel at which you are staying, and use public transportation to get to the MIT campus." There is public parking available within a ten minute walk of MIT, though it won't be particularly convenient nor will it be cheap. The good news is that Cambridge and Boston are very pedestrian friendly and public transit is excellent, with frequent, inexpensive service. (In the almost 15 years that I lived in Cambridge, I never once drove a car! Now that I'm in upstate New York, I really miss those car-free, carefree days!)

2) If you are flying, the Boston airport is really only a hop, skip and a jump from MIT, just five miles from the airport to campus, so there's little need for your parents to rent a car.

You can easily get from the airport to campus via public transit in 30 to 40 minutes, depending on the connection time between the Silver Line and Red Line. Depending on traffic and time of day, a cab might or might not be quicker. Cost for public transit is $2 (or $1.70 if you buy a Charlie Card.) The MIT website estimates the cost of a cab at $35-$40.

3) If you are on the East Coast, you may want to look into traveling by Amtrak or inter-city bus. All trains and most intercity buses stop at South Station. If you get off the bus or train at South Station, you can hop right onto the Red Line. In less than 10 minutes, you can get off at Kendall Square or Central Square, the two subway stops within easy walking distance of MIT (and the hotels near MIT.)

Those of you who are staying at the Hotel Meridien Cambridge-MIT will definitely want to get off at Central Square. It is a 5 minute walk from the Central Square stop to the Meridien.

More good news: if you are a junior or senior in high school traveling with a parent, Amtrak has a special campus visit deal which will cut the cost of the second person's ticket by 50%.

No matter what grade you are in, you and your parents may want to look into other discounts. If your parents are American Automobile Association members, both Amtrak and many bus lines will offer discounts on tickets.

Note: Please note that we will NOT be able to pick contestants up at the airport, due to the wide variety of times at which contestants will be arriving.

However, since we expect that a large number of contestants and their families will depart for Logan Airport shortly after the Saturday afternoon awards ceremony end, a complimentary airport shuttle service will pick up contestants and their families near Kresge Auditorium late Saturday afternoon. We will also provide a complimentary shuttle service from the Hotel Meridien-Cambridge (about a 10 minute walk from MIT) on Sunday morning.

To request the Saturday afternoon airport shuttle service leaving from Kresge Auditorium after the ceremony, please use this form as soon as you have booked your airline tickets, but no later than September 3.

To request the Sunday morning airport shuttle service leaving from the Hotel Meridien, please use this form as soon as you have booked your airline tickets, but no later than September 3.

We will NOT be able to honor requests made after the September 3 deadline.

Panel discussion for parents and teachers accompanying Math Prize for Girls contestants

2011-06-23T17:38:00.001-07:00

We are again planning a special event for accompanying parents and teachers to take place during the morning portion of the Math Prize for Girls event while your students are taking the two and a half hour long written contest.

This year, our special event for parents and teachers will be a panel discussion on mathematical enrichment opportunities for young mathematicians that go beyond contest mathematics, especially those that introduce students to the exciting and empowering possibilities of mathematical exploration and research.

Our panelists will include Ken Fan, who has established and leads a model mathematical community for young women now entering its fifth year, Girls' Angle. Although the program meets in Cambridge, Girls' Angle also has a significant national outreach program, publishing a bimonthly magazine (available free in PDF here and in print form by subscription) and videos that bring young women everywhere into contact with mathematical role models doing cutting edge research in mathematics. The Girls' Angle Bulletin and videos are a treasure trove of model ideas and inspiration for others looking to start up similar mathematical communities in their own areas. The Girls' Angle list of mentors includes several members of the Math Prize for Girls community.

This year's panel for parents and teachers will also include representatives from some of the outstanding national summer mathematics programs for high school students that have been highly recommended by past Math Prize for Girls participants. Those programs include Canada/USA MathCamp and Hampshire College Summer Studies in Mathematics.

We will have more information about our 2011 panel for parents and teachers later this summer. In the meantime, parents may want to look over the information and links below from past years' speakers.

In 2009, Richard Rusczyk, founder and president of the Art of Problem Solving spoke to parents and teachers about opportunities and resources available to gifted students in mathematics while students took the contest. You can see a video of his presentation here. His slides are here.

In 2010, Mark Saul from the Center for Mathematical Talent at Courant Institute of Mathematical Sciences moderated a panel discussion with the title "Encouraging Your Problem Solvers." The panelists included Zuming Feng, Glenn Ellison and myself.

Zuming Feng is coach of the US teams for the International Math Olympiad and China Girls Math Olympiad. He is also the Academic Director of the Math Olympiad Summer Program as well as a mathematics teacher at Philips Exeter Academy, where he holds the Stephen G. Kurtz Endowed Teaching Chair. In addition, he is founder and director of IdeaMath. Zuming spoke about the thriving mathematical community in the Exeter Math Club. He particularly emphasized the many and varied benefits that his math club students get from organizing and leading an annual math contest that Exeter students offer to middle school students, EMC², the Exeter Math Club Competition. The two student lead organizers of that competition were seniors Shijie Joy Zheng and In Young Cho, who are both members of the Math Prize for Girls community, as are a number of other students in the Exeter Math Club. As Zuming mentioned, there are even more benefits to students from composing original problems for others than from solving other people's problems. Exeter students also gained many valuable non-mathematical skills from organizing the competition, e.g., learning how to deal with the many logistical issues such as negotiating deals with local hotels, communicating with coaches of teams bringing students to the competition, etc.

Glenn Ellison is Gregory Palm Professor of Economics at MIT. He is a former member of Harvard's first place math team on the Putnam Mathematics Competition. He has earned many honors for his research and graduate teaching in economics, but he is also a very successful volunteer coach of his daughters' math teams. In several years, he wound up with all girls teams (including an all girls MATHCOUNTS team that placed third in the state.) He was struck by how different his MATHCOUNTS teams looked from the other teams at these competitions, and that inspired research in which he and co-author Ashley Swanson brought their econometric skills to the analysis of AMC contest data. They discovered some fascinating evidence that suggests that mathematical communities may be very valuable for all students, but especially so for girls. In his words, "Differences in school quality are a potentially much more important issue (even to girls) than differences in the gender gap." The slides of his talk are available here.

One of Glenn's observations is that the girls he has coached were much more willing to read the handouts that he prepared for his middle school math teams than the boys were. He decided to develop and compile those handouts into an inexpensive book, Hard Math for Middle School, which a number of other middle school math team coaches have found extremely helpful.

My own presentation at the panel is available here. Unlike the other speakers, I myself had never participated in math competitions as a student. Indeed, I never even heard about math competitions until I got to graduate school, at which point it was too late. But I have learned a tremendous amount of mathematics and gotten a tremendous amount of enjoyment out of coaching others for math competitions. A main theme of my part of the panel is that students can learn a huge amount by teaching others, by starting little math circles of their own in their communities, as my own daughters and other students in my math circle have done. Many students finding coaching and mentoring others even more enjoyable and educational than competing themselves. The best way to really understand something is to teach it to someone else, because answering their questions forces you to deepen your own understanding. The summer is a great time for students to launch their own little informal math circles. A website I created in conjunction with my presentation lists resources that student coaches may find helpful in starting up their own math circles.

Congrats and best wishes to the US teams for CGMO

2011-06-16T09:59:00.001-07:00

Congratulations and best wishes to the eight girls who will represent the United States at the China Girls Math Olympiad in August.

From left to right, they are:

Christina Chen, Newton North High School, Massachusetts
Sarah Hermann, La Jolla High School, California
Julia Huang, Lynbrook High School, California
Rebecca Burks, BASIC Homeschool, California
Elaine Hou, Leon King High School, Florida
Victoria Xia, Thomas Jefferson High School, Virginia
Tiffany Wu, William P Clements High School, Texas
Danielle Wang, California Virtual Academy/EPGY, California

Christina, Sarah, Julia, Elaine, Victoria, Tiffany, and Danielle are alumnae of last year's Math Prize for Girls, and we are hoping that all eight will join us at Math Prize 2011 in September.

You can read more about their adventures this summer preparing for the CGMO in their on-line travel diary here.

Where to stay in Boston/Cambridge? Options to discuss with your parents

2011-06-15T05:52:00.000-07:00

Today is the deadline to apply to the Math Prize for Girls 2011.

Within five days, we will be sending out email invitations to the top 300 applicants. Since the competition will take place on September 17, earlier than in the past, invited students and their parents will want to investigate travel and accommodation options promptly.

So I'll launch the discussion here.

As a parent of two former mathletes myself, and as a founding advisor of Albany Area Math Circle, which has sent students to the Harvard-MIT Math Tournament in Cambridge every year since 2001, I have some friendly advice and suggestions to offer to parents of Math Prize for Girls contestants. My advice is based on the experiences of scores of our students over the years, as well as my own family's experiences with almost 15 years of living in Cambridge, followed by numerous trips to the area for business and educational purposes over the past two decades.

Here are some of the possibilities:

1) Hotels near the MIT campus: These are particularly good choices if you and a parent are traveling by air or train, since the MIT campus is quite close to Boston's Logan Airport and Amtrak's South Station. MIT provides a handy list here. The Math Prize for Girls has negotiated a special rate of $199 per night for a block of rooms at Le Meridien Cambridge-MIT Hotel. To make a reservation at the discounted rate, use this link before August 22. Our Games Night social event for all interested contestants (regardless of where they are staying) will be held Friday evening from 7 to 9 p.m. at the Hunsaker Ballroom in this hotel.

2) Hotels and motels on the outskirts of Boston: These can be a very practical alternative for those who are traveling by car, especially if you want to avoid Boston rush hour traffic early Friday evening. Our math circle parents driving to Cambridge have generally found early Saturday morning traffic to be a breeze compared to Friday rush hour.

One thrifty possibility is to stay at a hotel located near one of the outlying MBTA stops. Hotel rates are likely to be lower in the suburban hotels, especially since suburban hotels rarely charge for parking, and you can take the MBTA into town. My mother did this when she came up from Virginia for her granddaughter's graduation a few years ago. She stayed in a hotel in Braintree, at the southern end of the Red Line, for less than half the rate that Cambridge hotels were charging--and they provided free breakfast and a free shuttle van service to the subway station. It's a 33 minute ride from Braintree to Kendall Square (the closest T-stop to MIT.)

Some of our math circle parents (who are driving in from points west of Boston), have found it practical and inexpensive to stay in hotels along the Mass Pike as far away as Worcester (which is about an hour's drive from MIT.) Those hotels are not especially near an MBTA, but those who wish to minimize Boston driving and cut down on parking fees could drive from their hotels to the parking lot at the western end of the Red Line, Alewife Station, a 16-minute ride to Kendall Square. Or, as I mentioned before, driving into Cambridge early Saturday morning is a relative breeze compared to a rush-hour Friday evening.

3) Staying with relatives or family friends who live in the Boston/Cambridge area, a great option if you are lucky enough to have them!

4) MIT dorm as guest of a student hostess: Some contestants may have a hometown or summer program friend, or an older sister attending MIT who is willing to host the student overnight in her dorm room. This can be a fun as well as a thrifty option, if your parents agree that you are ready for this kind of college dorm preview experience. Many of our math circle students have greatly enjoyed this aspect of their travels during past trips to HMMT.

Perhaps you are interested in staying as a guest of a current MIT student, but you don't actually know anyone at MIT who is able to host you. In that case, we are happy to say that we have an awesome volunteer, Mark Velednitsky, who may be able to link you up with a current MIT student hostess willing to accommodate you. Mark is an MIT sophomore who did such a great job as housing coordinator for HMMT 2011 that he has been promoted to tournament director for HMMT 2012, and we are thrilled and delighted that he also has time to bring his experience and expertise to help us out with Math Prize for Girls 2011.

If you would like to be matched up with an MIT student hostess, please use the form at this link to request a student hostess, and Mark will pursue his best efforts to find you one. The deadline for requesting a student hostess is July 31.

A few things for you and your parents to bear in mind if you choose this option:

A) This is an entirely unofficial hosting arrangement. This arrangement is NOT made through MIT housing auspices. Mark is a student official of Harvard-MIT Math Tournament, a registered student group sponsored by the MIT math department, not the MIT housing department. You would be the personal guest of your MIT student hostess, so you and your parents will want to have discussions as to whether you are ready for this kind of unchaperoned overnight college dorm visit. (It is an arrangement similar to that which many students arrange when visiting prospective colleges in their junior or senior years.)

B) Because you will be the personal guest of your MIT student hostess, you will not get a key or keycard access to the building. Instead, you should plan to bring a cellphone, so you can easily connect up with your hostess and make arrangements to get into her building or room.

C) You should plan to bring a sleeping bag! A few hostesses may have a couch or spare bed, but most will only be able to offer you floor space.

D) College dorms have been known to be noisy, especially on Friday nights, so it may not be the best place to get a good night's sleep if you are a light sleeper. (Then again, some parents--as my daughters will be the first to tell you!--have been known to SNORE loudly in shared hotel rooms.)

My own daughters, as well as many of our math circle students have had excellent experiences as guests of student hostesses at MIT and other college campuses over the past decade, either at HMMT or for admissions preview visits, so I would say that, if you are interested in this option, it is worth considering and discussing with your parents.

When invitation emails go out in a few days, students will get more information about how you can discuss concerns that you or your parents may have as you plan for Math Prize for Girls 2011.

Math Prize Girls bring home honors on the USA Math Olympiad and USA Junior Math Olympiad

2011-05-15T13:38:00.000-07:00

Shijie Joy Zheng (MPG 2009, 2010) is a winner of the 2011 USA Math Olympiad. Joy and the other winners will be honored in a formal ceremony in Washington, DC next month. They will then go to Lincoln Nebraska for the Math Olympiad Summer Program, to take the Team Selection Test for the US team for the International Math Olympiad to be held in the Netherlands in July.

A partial list of Joy's many previous honors include include Honorable Mention at the 2011 Romanian Master's in Math and Science, a Gold Medal at the 2010 China Girls Math Olympiad, Third Place nationally in the 2010-11 Madelbrot Competition, a Silver Medal in the 2010 Math Prize for Girls Olympiad, First Place in Combinatorics at the 2010 Harvard-MIT Math Tournament, Second Place at the 2009 Math Prize for Girls, and 2nd Place Individual in the A Division of the Princeton University Math Contest (PUMaC), and a Gold Medal at the 2009 China Girls Math Olympiad.

Joy hails from Bellevue Washington, where she was a founder of the Seattle Infinity Math Circle. Joy is now a senior at Phillip Exeter Academy in New Hampshire, where she and In Young Cho (MPG 2009, 2010) have been co-directors of a very successful new initiative. They have led Exeter students in running EMC², a math contest for middle schoolers, successfully adapting the HMMT model for a younger audience. In its second year, the contest had already grown to attract over a hundred teams, including some from places as far flung as China and Indiana. Thanks to their leadership, many of their fellow students have discovered that composing problems can be a fun, rewarding, and challenging way to develop their own mathematical problem solving skills, while providing excitement and encouragement for younger students.

Congratulations as well to Julia Huang (MPG 2010), who received Honorable Mention on the USA Junior Math Olympiad. Julia is a ninth grade student at Lynbrook High School in California. She was tied for eighth place at last year's Math Prize for Girls, and won a Bronze Medal in the 2010 Math Prize for Girls Olympiad.

Math Prize Girls take top honors in 2011 Canadian Math Olympiad

2011-05-04T21:00:00.000-07:00

The Canadian Math Olympiad results are out--and two members of the 2010 Math Prize for Girls community are among the top scorers this year, among a very distinguished and worthy group of competitors, who include a number of IMO medalists.

Mariya Sardarli from Strathcona High School in Edmonton, Alberta took first place on the Canadian Math Olympiad with a score of 33 out of a possible 35 points. Mariya was also the Gold Medal Medal winner in the first Math Prize for Girls Olympiad last December. She also won a silver prize in the 2010 Asian Pacific Math Olympiad.

Susan Sun from British Columbia came in fourth place, just behind Mariya, Calvin Deng, and Alex Song, to take home Honorable Mention on the Canadian Math Olympiad. Susan also received Honorable Mention honors at the Math Prize for Girls last November.

STUDENTS RECEIVE TOP HONOURS IN NATIONAL MATH OLYMPIAD
Sun Life Financial CMO Results
OTTAWA, Ontario — The Canadian Mathematical Society (CMS) is pleased to announce the winners of the 2011 Sun Life Financial Canadian Mathematical Olympiad (CMO), now in its 43rd year.

The three top winners are:

1st Prize: Mariya Sardarli, Strathcona High School, Edmonton, AB
2nd Prize: Calvin Deng, William G. Enloe High School, Raleigh, NC (Canadian citizen)
3rd Prize: Alex Song, Detroit Country Day Middle School, Beverly Hills, MI (Canadian citizen)

In addition, six students have received honourable mentions: Susan Sun, West Vancouver Secondary School, West Vancouver, BC; Yuzhou Chen, Sir John A. Macdonald Collegiate Institute, Agincourt, ON; Hunter Spink, Western Canada High School, Calgary, AB; James Rickards, Colonel By Secondary School, Gloucester, ON; Matthew Brennan, Upper Canada College, Toronto, ON; and Yi Liu, York Mills Collegiate Institute, Toronto, ON.

“I am pleased to congratulate the CMO winners on their outstanding performance,” said Jacques Hurtubise, President of the Canadian Mathematical Society. “To achieve these high results on an advanced national competition requires a great level of dedication, hard work, and talent.”

In addition, earlier this year, both Mariya and Susan were among the top 5 students among the 8,800 who participated in the Canadian Open Mathematics Challenge.

Words to live by ... and other good mathematical ideas

2011-05-02T17:22:00.001-07:00

The excellent advice above comes from UConn Professor Erin Terwilleger Mullen in an interview in the current issue of the Girls Angle Bulletin. It's good advice whether you are working on a math contest problem or an actual research problem. Don't be afraid to try things just because you are not sure they will not work.

The Girls' Angle website is full of more good advice and mathematically inspiring activities, including many used by the Girls' Angle mentors in Cambridge, Massachusetts. Girls' Angle mentors include Math Prize for Girls alumna Kate Rudolph as well other MIT and Harvard undergraduates, graduate students, and faculty. Math Prize for Girls community members all over the country can adapt many of the ideas described in the Girls Angle bulletins and videos for use in their own local mathematical communities.

I especially enjoyed this short Girls Angle video of MIT Professor Vera Vertesi presenting a graphic proof of a deep and fundamentally important classic theorem in graph theory.

Math Prize Girls lead a mathematical uprising in Central New York

2011-04-25T09:42:00.002-07:00

Anying Li and Mia Smith are not content with individual honors--they are mathematical leaders who have worked together with others to launch one of the most exciting new math circle initiatives in the country. A little over a year ago, Anying and Mia were among the students who founded the Ithaca Math Circle, which has already achieved many impressive successes in a very short time.

A few years ago, before their math circle started up, their high school sent a math team to compete at the state math tournament and finished last in the B-division. This year at that same tournament, Ithaca finished first in the B division, and they will be in the A-division next year. Ithaca also took fourth place team honors in their division at the Princeton University Math Contest (PUMaC) and second place on their division team round at the Harvard MIT Math Tournament this year.

What sets the Ithaca Math Circle apart from most other math circles is the fact that Anying, Mia, and a few other fellow students have taken responsibility for leading the weekly meetings. The model they use is one that motivated students everywhere can emulate. Here is how Mia described the workings of their circle:

Our Math Circle started because we wanted more challenging math than what was offered in math club. We also wanted more say in what we were being taught. Our circle is entirely student run, so we get to choose what competitions we do and what topics we explore at our meetings. How our meetings run is that one of us learns a topic in depth and then presents it to the group. The leader is also in charge of finding problems to make a problem set. I really enjoy it because it means that if I find some cool math and can sign up to present one week and share it with the Math Circle. It also forces you to know the material really really well, because you have to teach it to someone else.

At our first meetings we had usually 6 members, but now it has grown to 11 (not quite double...). Right now all of our members come from the same school, since so far we've only been recruiting by word of mouth. However, we are hoping to get some new members by spreading the word to homeschoolers and other schools in the area. Recently we had a couple articles in the newspaper about how our members did at PUMaC and Math Prize For Girls, so that should raise our profile. We meet once a week for an hour and a half.

You can see the problem set handouts that Anying, Mia, and their fellow math circle members have put together for their weekly meetings in their archives.

Both Anying and Mia are also enthusiastic alumnae of Canada/USA MathCamp and they give MathCamp a lot of credit for their mathematical development as well. Mia particularly appreciated the way it exposed her to mathematics outside of contest math:

I went to MathCamp last summer, and it was the best summer of my life. It's a great opportunity to do something outside the realm of contest math; for example, I did I project on knot theory, something I'd never even heard of before Mathcamp. There is also a very strong sense of community and people are always willing to chat, play games or engage in crazy projects.

Both Anying and Mia also have lots of other interests beyond math to balance out their lives. Anying plays piano and violin and was selected for the All-State Conference String Orchestra. Mia plays soccer and is on the track team. She also loves to cook and says:

My friends and I have our own version of Top Chef, which is a blast. My advice for other girls is that you don't just have to do math, explore your other passions. If you only do math it becomes work; and the point is that it's supposed to be fun.

In the spirit of that fun, Mia described her favorite problem on the 2010 Math Prize for Girls contest, #13:

For every positive integer n, define S_n to be the sum

As n goes to infinity, what value does S_n approach?

As Mia put it: "At first it looked really gnarly and intimidating, but if you played with it for a bit, it came out beautifully."

For a discussion of the solution to that problem, see here.

Remarkable reflections of a mathematical star

2011-04-14T17:15:00.000-07:00

Over time, I have realized that what I really like most about math isn't the achievement and self-advancement, but rather, it is the process of sharing – of not only creative and insightful problem-solving approaches, but also memorable moments filled with camaraderie, generosity, and incomparable joy.

True stars do not just shine and sparkle. They enlighten and inspire us and help to orient us in a sometimes topsy-turvy world, as do the words above from Luyi Zhang (Math Prize alumna, 2009, 2010). The words come from Luyi's deeply moving essay reflecting on her mathematical odyssey, Math reflection: on true deep sincerity.

Luyi also created the star in the photo above. To make your own star, read her instructions here or watch her video below.

MIT Admissions says: "Math Women Rock!"

2011-03-08T12:30:00.000-08:00

MIT Admissions is excited about MIT hosting Math Prize 2011:

The next Math Prize for Girls competition will be held here, at MIT, on September 17th 2011! Our office worked hard in order to help bring MPG here, in no small part because math is awesome and math girls are awesome and MPG is awesome and we like to have as much awesome as possible here on campus.

Get the full story on the MIT Admissions blog.

Congratulations again, Danielle!

2011-03-02T19:32:00.000-08:00

Danielle Wang (MPG 2009, 2010), this year's winner of the Math Prize for Girls and Silver Medalist in the Math Prize Invitational Olympiad, has added yet another stellar accomplishment to her already extraordinary string.

Although Danielle is only an eighth grader, she tied with senior David Wise for top score in the country on the USA Mathematical Talent Search (USAMTS), scoring 59 out of a possible 60 points. The outstanding pool of competitors in that event included many veteran USA Math Olympiad qualifiers.

For the problems and solutions to this year's USAMTS, see here. For more about the USA Math Talent Search, see here.

UPDATE March 8: USAMTS officials have rescored some contests--congratulations as well to two additional contestants who are now tied with Danielle and David at 59 points: Calvin Deng from North Carolina and Evan Chen from California. They are certainly very worthy competitors: Calvin was a USA Math Olympiad winner last year and won a silver medal at the International Math Olympiad, while Evan was a USA Junior Math Olympiad winner last year.

PBS Need to Know covers Math Prize for Girls 2010

2011-02-11T16:16:00.000-08:00

Watch the full episode. See more Need To Know.

Check out the PBS Need to Know coverage of the November 2010 Math Prize for Girls in the video above. There's more text coverage in their blog here.

Be prepared for the 2011 AMC10/12 Contest!

2011-01-08T04:54:00.000-08:00

The AMC10 and AMC12 contests are the gateway to many exciting mathematical adventures, including the Math Prize for Girls 2011, so it's a good time to make sure your school is signed up to administer the contests. The A-date contest is one month away--on Tuesday February 8. The B-date contest is on Wednesday February 23. You can take either or both contests if your school signs up to offer them. The special early registration discount is still available through January 15 if your school uses the on-line registration form. Many schools will be on February break during the B-date, so you may also want to check with the math department at a nearby college to see if they would be willing to offer the B-date contest. Here is a list of colleges and universities that currently plan to offer the contest.

Here's a sample problem. It was among the harder problems from the 2005 AMC10:

The figure shown is called a trefoil and is constructed by drawing circular sectors about sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length 2?

Note: this problem might look like an ugly tedious slog at first, but there is a beautiful "Aha!" way to look at the problem that makes it so much nicer!

For a hint, click here. For the full solution, click here.

You can find a great free database of hundreds more old problems like this here. Clicking on the links in the database will give you the problem statements, hints, and detailed solutions to hundreds of AMC10 and AMC12 problems from previous years' exams.

The AMC also has a nice problem blog to which they post an old problem with solution links on a regular basis. Enjoy!

Geometric Delights blog

2010-12-29T22:00:00.000-08:00

Check out Geometric Delights, a new blog from Luyi Zhang (MPG 2009, 2010).

Math Prize Olympiad Medalists

2010-12-27T20:56:00.000-08:00

Congratulations to the winners of the Math Prize Invitational Olympiad!

Gold Medalist:
Mariya Sardarli

Strathcona Composite High School in Edmonton, Canada

Grade 11

Silver Medalists:

(in alphabetical order)

Danielle Wang

California Virtual Academy

California

Grade 8

Joy Zheng

Phillips Exeter Academy

New Hampshire

Grade 12

Bronze Medalists:

(in alphabetical order)

Sheela Devadas (10th grade, Lexington HS, MA)
Melody Guan (11th grade, University of Toronto Schools, Ontario)
Bianca Homberg (12th grade, Westborough HS, MA)
Julia Huang (9th grade, Lynbrook HS, CA)
Ramya Rangan (11th grade, Harker, CA)
Elizabeth Shen (11th grade, South Mecklenburg HS, NC)
Elizabeth Synge (12th grade, Boston University Academy, MA)
Luchang Wang (11th grade, Central Academy/Valley HS, IA)
Victoria Xia (9th grade, TJHSST, VA)

Photo credit: Photo of Danielle Wang courtesy of PBS Need to Know

Happy Holidays! Five gifts for you... and a wish for 2011

2010-12-21T15:39:00.000-08:00

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 (whose members include MPG participants Mia Smith and Anying Li) 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.

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!

USA Math Talent Search: a different kind of math contest...new problems available now

2010-12-11T17:11:00.000-08:00

For practical reasons, most problem-solving contests are more like sprints than marathons, but real math research problems--as well as many real world problems-- take far longer than a few minutes or even a few hours to solve. Most contests also tend to limit the tools you can use to pencil and paper, or, in some cases, perhaps a few drawing instruments (e.g., compass, straight edge) or maybe a calculator. Real world problem solvers and mathematical researchers clearly have access to a much broader set of tools than are allowed on most math contests.

One math contest stands out as an exception to that general rule: the USA Mathematical Talent Search (USAMTS) gives participants the luxury of time to reflect, to play with a problem, to try many different approaches.

The current round of USAMTS problems just became available this weekend and participants can continue to work on the problems until the January 24 submission deadline. The USAMTS is free and open to all students who are US citizens or residents. (And, of course, anyone anywhere in the world is free to work on the problems, though they should not be discussed with others until after the submission deadline.)

As for the tools you can use on the USAMTS: the sky is the limit, as long as you do not seek help from other human beings and you cite your sources. You can build physical models of the problem, research books and other reference works, or write a computer program to help you explore the problem. Math Prize for Girls contestants can even use their new copies of Mathematica 8 for Students (contributed to all MPG participants by Wolfram Research) to investigate some of the problems. If you do that, you should keep Rule #7 in mind: you will need to explain what your program did and prove that it solves the problem. Thus, the software is really a tool for preliminary investigation--you won't get any credit if you submit a solution that says "I typed this input into the software and got this result back."

If you look at the USAMTS archives, you can see some familiar Math Prize for Girls names on the listings for the past few years: Valeria Fedyk (MPG 2009), Kate Rudolph (MPG 2009), Lilly Shen (MPG 2009, 2010), Danielle Wang (MPG 2009, 2010), Luna Zhang (MPG 2009), and Luyi Zhang (MPG 2009, 2010) are all names listed on the USAMTS Leaderboard over the course of the past three or four years. (Please let me know if there are any more MPG names I overlooked.)

If you want to see what an exemplary solution writeup looks like, check out the archives of problems from past rounds of the USAMTS.

In particular, check out Problem #5 in Round 2 from 2007-2008.

USAMTS contest officials selected a solution submitted by Luyi Zhang (Math Prize for Girls 2009 and 2010 alumna) as their published exemplary solution to the problem. I can see why they selected Luyi's solution for commendation: it has crystal clear exposition and beautiful diagrams that help the reader follow the logic of her approach.

I asked Luyi how she came up with her solution: her essential insight was surprising and certainly did not jump off the page at me when I initially looked at the original problem statement. Here is her response:

I actually did build a 3-d model! Several, in fact. First, I made the full icosahedron, using toothpicks as the edges and joining them together with spheres of clay as the vertices. Then I made a second model, this time just the truncated icosahedron in question. I looked down on it from a bird's eye view and realized that I could see a hexagon... and decided to extend some lines and create a full hexagonal prism, which would be easier to work with. The solution followed from there :) This is a prime example of why geometry is so fascinating to me: there are so many ways to visualize a given formation.

Luyi, now a senior at Hopkins School in Connecticut, who has participated--and earned recognition--in many other contests, including ARML, the Harvard-MIT Math Tournament, and the USA Math Olympiad, enthusiastically recommends the USAMTS Contests to other students:

USAMTS is such an well-organized contest; it's incredible how it encourages perseverance and creativity while being interesting and challenging. Everyone should totally go for it.

Luyi also says that she enjoys using a variety of different media to build and visualize geometric objects, including beads and pipe cleaners. She and I are both big fans of the websites of Vi Hart and Vi's father George Hart, which illustrate many other cool and beautiful ways to construct beautiful geometric models.

Here's Luyi's latest creation, an icosahedron--any guesses what is made out of? I thought it was PVC tubing, and was really surprised when Luyi told me how she'd made it. (See below.)

Luyi wrote:

I was doing some really cool problems thus creating lots of scratch paper in the process. And I thought OH WOW I can roll this paper up and create a tube that looks like a really long bead. Then I can use it to create an icosahedron! So that's what I did. I used tape to secure the paper rolls, and then used some cotton string to string it all together. So much fun. And the best part is that it's accessible to anyone... all you need is some paper, tape and a few feet of string!

Below is a rhombicuboctahedron Luyi and her little brother recently constructed together from pipe cleaners. Her brother created the squares and then she connected them to form the Archimedean solid. I loved her description of the color scheme she chose for their creation: "Koala that discovered a bright pink highlighter."

I also liked the composition of Luyi's photograph--that's Hamlet's eye peering through the square faces of the polyhedron. One wonders if he is thinking, "...I could be bounded in a nutshell and count myself the king of infinite space..." (Act II Scene ii)

Math Prize Olympiad 2010

2010-12-10T08:46:00.000-08:00

The four olympiad problems for yesterday's 2010 Math Prize Olympiad are now available here.

We encourage all students to use the problems as a resource for learning and exploration. They are great practice for students planning to take the Putnam math contest in college or any of the high school olympiad-style contests (USAMO/USAJMO/CGMO/USAMTS.) There are discussion threads for the Math Prize Olympiad problems on the Art of Problem Solving website so that students can discuss solution approaches.

The problems were written by Ravi Boppana, the director of the Math Prize for Girls contest and the co-director of mathematics at Advantage Testing, who earned honors of his own as a student on college and high school olympiad contests, the Putnams and USAMO. Ravi is a summa cum laude graduate of the University of Maryland, with a B.S. in Mathematics and Computer Science. He holds a Ph.D. in Computer Science from MIT. He was a professor of computer science at Rutgers University, where he was the recipient of the "Excellence in Teaching" award. Later he was a tenured professor of computer science at New York University, where he was the recipient of the "Golden Dozen" teaching award. He has coached the New York State team at MathCounts Nationals.

Alison Miller, a math graduate student at Princeton who has helped to coach the US teams for the China Girls Math Olympiad and International Math Olympiad as a member of the instructional staff at the Math Olympiad Summer Program, assisted Ravi with a review and analysis of the Math Prize Olympiad problems. (Alison has also been a mentor at Canada/USA MathCamp, where this photo was taken by Kelly Griffith of Closed Circle Photography.)

Official solutions to the Math Prize Olympiad problems will be posted later.

Grading olympiad problems is a demanding and time-intensive project, so it will be a while before results will be available. For example, the Putnam Math Competition (discussed in my last post) is given on the first Saturday in December and results are generally posted in late March.

The Math Prize Olympiad results should be available well before the Putnam results (late December or early January), and we will post the names and photographs of the gold, silver, and bronze medal winners in this blog.

Math Prize Olympiad, the Putnam Math Contest, and other olympiad problem solving opportunities

2010-12-09T09:25:00.001-08:00

Our thirty five highest scoring students on the November 13 Math Prize for Girls written contest, i.e., those ranked at Honorable Mention or above, were invited to take today's Math Prize Olympiad.

We send our best wishes to all those taking that contest today and hope you will enjoy an exciting problem-solving adventure.

We will post those problems to the web after the conclusion of the official contest administration time has ended, so that everyone can enjoy thinking about them and discussing them.

We also send our best wishes as well to those of our 2009 Math Prize for Girls alumnae who are now in college and took the William Lowell Putnam Math Competition last Saturday. We hope many of our 2010 Math Prize for Girls alumnae will be joining you at the Putnam next year!

Some of you reading this are probably wondering, "What is the Putnam?" Those who have heard about it have probably heard scary things about it.

The Putnam is an annual olympiad-style math contest open to all college students in North America, so it is something that all members of the Math Prize for Girls community can look forward to taking in the future.

The Putnam is notoriously difficult, but over 3,000 strong college math students attempt the challenge every year. It's the Mount Everest of problem solving, and many colleges (including the one where I teach) sponsor friendly and informal Putnam problem solving group sessions that have fun preparing by working on the problems and talking them over together. Although women constitute more than 50% of math majors these days, it is unfortunate that, at most colleges, women are a small minority of the students who choose to take advantage of these fun opportunities to develop their problem solving abilities, either by attending the informal practice sessions and/or by taking the Putnam contest itself.

I hope this post will demystify the Putnam a little bit, so that more young women can enjoy taking part in the Putnam experience in the future.

Here is a great description from the University of Oklahoma's Putnam preparation website:

The Putnam Mathematical Competition is a math contest held every year on the first Saturday of December for undergraduate students in the U.S. and Canada. The problems range across the undergraduate mathematics curriculum, but most do not require specialized knowledge of mathematics beyond calculus.

Over the years the exam has built up a good reputation for containing nice, interesting problems - the kind you find it hard to stop thinking about, whether you've managed to solve it or not. The best problems reveal attractive and intricate bits of mathematics lurking in seemingly simple situations.

The best way to learn to solve Putnam problems is to start trying to solve some. Although no two Putnam problems are alike, as you start to see more of them, you insensibly build up a store of intuition and ideas that help you with the next one. Even if you don't succeed in getting very far on many problems, you will find that the mere process of grappling with them strengthens your ability. For this reason, we hold a problem seminar at OU each fall to give students the chance to attempt to solve Putnam problems.

Everybody is welcome at the seminar, whether they're thinking of participating in the competition or not. Working on difficult, but interesting, mathematical problems is a good way to improve your mathematical abilities and have fun at the same time. You'll not only be better at mathematics proper, you'll be able to work better in any field of science or engineering that uses mathematics!

Harvey Mudd College has an especially large and enthusiastic Putnam practice group--ten percent of their student body takes the Putnam contest every year, by far the highest participation rate in the country. The Harvey Mudd weekly practice sessions offer a "lab in polar geometry and fair division" (click here to see what that involves!). The Harvey Mudd Putnam problem solving webpage has lots of helpful links to resources for anyone looking to prepare for the Putnam. Professors Andrew Burnoff and Francis Su, who run the Harvey Mudd problem solving sessions, have written a great article for Math Horizons magazine describing how their group works, full of excellent ideas for math prize alumnae or anyone who wants to start a similar group at their college. One of my favorite ideas: Harvey Mudd creates a commemorative mug with a graphic representing a problem from each year's Putnam contest. Every Harvey Mudd student who competes on the Putnam gets a mug for that year as a souvenir of their "extreme math" problem solving adventure.

The Putnam gives students six hours to solve twelve very challenging problems, each worth 10 points. (Partial credit is possible, but the Putnam graders are notoriously stingy, so it's important for students to make sure their solution writeups are rigorous and consider all possible special cases of the problem.] The median score on the Putnam exam in a typical year is 1 point out of a possible 120 points!

If you do well on the Putnam, you can bring fame and fortune to your college. (Math Prize for Girls Director Ravi Boppana was a star on the University of Maryland's Putnam team, helping it finish third place in the country in 1980 and fifth place in 1981. Another U of Maryland Putnam star, Sergey Brin, went on to found Google!)

Several members of the Math Prize for Girls advisory panel were also stars on the Putnam contest when they were in college. As a sophomore at NYU in 1997, panel member Professor Ioana Dumitriu was the first woman to be named a "Putnam Fellow" (as the top five Putnam winners--who are not otherwise ranked among themselves--are called). The New York Times covered that landmark event in an article you can read here. Professor Dumitriu now teaches at the University of Washington, where--among many other things--she coaches the Putnam problem group. Thanks in part to her efforts, University of Washington had its first Putnam Fellow ever in 2008.

Math Prize for Girls advisory panel member Professor Melanie Wood, now at Stanford, was the second woman in history to win Putnam Fellow honors, back in 2003 when she was an undergraduate at Duke. She was also the first woman to win the Morgan Prize, the top national award for undergraduate research in mathematics. You can read more about Melanie here and here. During her graduate studies, she led a problem solving seminar for Princeton undergraduates preparing for the Putnam, and she also coached students at the Math Olympiad Summer Programs for the teams that represented our country at the International Math Olympiads. As a graduate student, Melanie wrote the successful grant proposals to obtain sponsorship for the United States to send teams to the China Girls Math Olympiad (CGMO) and she accompanied the first American CGMO team to China as a coach in 2007.

Although intended for college students, some of the Putnam problems are accessible even to high school students who have not yet taken calculus. Here are a couple of the problems from this year's Putnam Contest that Schuyler Smith, a student leader in my local math circle, recommends for high school students interested in exploring Putnam challenges before they get to college:

2010 Putnam A1: Given a positive integer n, what is the largest k such that the numbers 1,2,...,n can be put into k boxes so that the sum of the numbers in each box is the same? [When n = 8, the example {1,2,3,6},{4,8},{5,7} shows that the largest k is at least 3.]

2010 Putnam B3: There are 2010 boxes labeled B₁, B₂,...,B₂₀₁₀, and 2010n balls have been distributed among them, for some positive integer n. You may redistribute the balls by a sequence of moves, each of which consists of choosing an i and moving exactly i balls from box B_i into any other box. For which values of n is it possible to reach the distribution with exactly n balls in each box, regardless of the initial distribution of balls?

Students in our math circle will be working on these problems together tomorrow night. I hope some other members of the Math Prize for Girls community around the country will also enjoy playing with these problems--don't be scared by the Putnam's reputation for impossibility!

Be playful when messing around with these problems, savor the problem solving opportunities they represent--when you are working informally, you have no time constraints, no rules against talking it over with others, and you should feel free to get some manipulatives (index cards with numbers on them for A1, boxes and marbles for B3), try some simpler cases and see what insights they yield. First, see what you can discover about the problems. Then, later, you can think about how you can prove it rigorously to the satisfaction of those (notoriously stingy!) Putnam graders.

The true prize of the Putnam is not the fame or fortune that can accrue to the winners, it is the learning and discovery and development of problem solving skills and the satisfaction of working one's way up a mathematical mountain (or at least a foothill!)

One of the quotes in the New York Times article about Math Prize for Girls advisory panelist Ioana Dumitriu that I mentioned above really struck home for me:

[NYU] Prof. Joel Spencer, who was a Putnam winner himself, said her work for his class in problem solving last year was remarkable. ''What really got me was her fearlessness,'' he said. ''To be good at math, you have to go right at it and start playing around with it, and she had that from the start.''

Working on Putnam problems is a good way to learn to be fearless. Everybody "knows" they are impossible, but don't be scared off by that--try them anyway. Take comfort from the fact they are supposed to be "impossible." Nobody expects you to solve them, especially for those of you who are not yet in college, so you have nothing to lose by trying them!

Follow this excellent advice from Stanford Professor (and four-time Putnam Fellow) Ravi Vakil:

The Hints: Work in groups. Try small cases. Plug in smaller numbers. Do examples. Look for patterns. Draw pictures. Use lots of paper. Talk it over. Choose effective notation. Look for symmetry. Divide into cases. Work backwards. Argue by contradiction. Consider extreme cases. Eat pizza. Modify the problem. Generalize. Don't give up after five minutes. Don't be afraid of a little algebra. Sleep on it if need be. Ask.

And, above all, follow the advice I give my own students: Have a good time! Enjoy the problems! Be fearless! Be playful!

More Putnam resources:

The complete archive of past Putnam problems and solutions is available here.

Harvard University offers a Putnam preparation "Problem of the Day" website here.

MIT Putnam Problem Seminar website

Stanford University Polya Problem Solving Seminar and Putnam website

University of Illinois Putnam training site

St. Mary's College of Maryland, a public honors college in Maryland, had an awesome pep rally before the Putnam this year--check out their video below. They have 30 students a year taking the Putnam, phenomenal for a college their size--and it's nice to see an unusually high proportion of women taking the Putnam there. No matter where you wind up in college, you could take the initiative to help organize a pep rally and community like theirs!

If you don't want to wait until college before taking an olympiad-style contest, take note--in my next post, I will talk about the USA Mathematical Talent Search (USAMTS), a great olympiad style contest available (free!) to all students in high school or below. And--one of the best things about the USAMTS is that you will have six weeks to work on it! And the time for the next one runs December 10 to January 24, so you will have the luxury of using some of your time over the winter break on it.

Tiebreak Round #1

2010-12-07T16:26:00.001-08:00

Corinne Madsen (Illinois Math & Science Academy), Jessie Duan (North Carolina School for Science & Math), and In Young Cho (Phillips Exeter Academy) prepare for the ARML-style tiebreak rounds, as their timekeepers, Caroline Taylor (a 2009 Math Prize alumna now studying at Columbia University) and Erica Hopkins (Haverford College) stand behind them.

The round #1 problem resolved the three-way tie for third place and two-way tie for sixth place. Here is the problem those five students raced to solve.

Let m and n be integers such that 4m - 3n + mn = 155.
Of all possible values of m+n, which is closest to zero?

You can find a discussion of solution approaches here.

(Note: tiebreak rounds were only used to determine the distribution of place-winner trophies. Cash prizes were divided equally among all contestants with the same scores on the written competition given in the morning.)

Tiebreak Round #2

2010-12-07T15:33:00.000-08:00

With trophies sparkling in the background, Elizabeth Yang from West Windsor Plainsboro High School in New Jersey and Harlin Lee from Phillips Exeter Academy in New Hampshire smile as they prepare for the tiebreak round 2 problem to help break the ten way tie for eighth place:

If a, b, and c are integers such that the cubic polynomial
x³ + ax² + bx + c = 0 has as a root, compute
the ordered triple (a,b,c).

You can find a discussion of solution approaches to this problem here.

Tie Break Round #3

2010-12-07T15:09:00.000-08:00

Moya Chen, from Vernon Hills High School in Illinois, was the first to solve this tiebreak round problem:

One of the angles of a triangle has measure x^o.
If cos(3x^o) + cos(x^o) = 0, what is the largest possible value of x?

You can find a discussion of solution approaches to this problem here.

First place winner - Danielle Wang

2010-12-04T21:57:00.001-08:00

Danielle Wang
California Virtual Academy
California

$25,000 Grand Prize Winner
$1,000 Youth Prize Winner

This year's grand prize $25,000 winner, Danielle Wang, successfully solved problems #1 through #18 as well as #20 for a total score of 19, the highest score among all 210 contestants. She was the only one of the contestants to solve #20.

20. What is the value of the sum

where z ranges over all 7 solutions (real and nonreal) of the equation

.

Express your answer as a fraction in simplest form.

You can find a discussion of the solution to this problem here.

Because Danielle is an eighth grader, she also won the $1,000 prize for the highest scoring student in 9th grade or below.

Danielle comes from the San Francisco Bay Area, which has a vibrant mathematical community, including a number of math circles as well as the Bay Area Math Olympiad (BAMO) and a great American Regions Math League (ARML) team. Danielle attends a math circle almost every week, and has participated in both BAMO and ARML.

Two years ago, Danielle won a first place award in the BAMO. You can find the archives of past BAMO problems and solutions here--they are a terrific resource for students who would like to improve their problem-solving skills. The BAMO has olympiad-style problems designed to challenge and inspire both middle school and high school students.

Danielle has also participated in the USA Mathematical Talent Search (USAMTS), a very challenging national math contest designed for high school students, in which students must submit clearly written justifications for their solutions. As a seventh grader in 2009-2010, she won a gold prize with a score of 92 out of a possible 100 points. Her score was among the top 25 high school students in the country on that contest.

Danielle also recommends the following books: The Art of Problem Solving (Volume 1 and Volume 2) as well as Paul Zeitz' The Art and Craft of Problem Solving.

Photo credit: Top photo courtesy of PBS Need to Know

Second place winner - Elizabeth Synge

2010-12-04T21:47:00.001-08:00

Elizabeth Synge

Boston University Academy

Massachusetts

2010 Second Place $10,000 Prize Winner
2009 First Place $20,000 Prize Winner

Our second place finisher, Elizabeth Synge, a senior at Boston University Academy, successfully solved 18 out of the 20 problems.

She was the only one of our 210 contestants to solve Problem #19:

19. Let S be the set of 81 points (x,y) such that x and y are integers from -4 through 4. Let A, B, and C be random points chosen independently from S, with each of the 81 points being equally likely. (The points A, B, and C do not have to be different.) Let K be the area of the (possibly degenerate) triangle ABC.

What is the expected value (average value) of K²?

You can find a discussion of the solution to this problem here.

Elizabeth comes the Boston area, which also has a vibrant mathematical community including several math circles. She has worked with mentor Jim Tanton at the Boston Math Circle and studied in the summer at the Hampshire College Summer Studies in Mathematics (HCSSiM) program in central Massachusetts. Elizabeth clearly enjoys giving as well as receiving: she has taught in workshop programs for younger students.

Elizabeth's passion for problem solving has also taken her on many farflung adventures--around the country and around the world.

During her middle school years, Elizabeth was a member of a MATHCOUNTS team sponsored by the (aptly named) Voyagers Home School Cooperative. Elizabeth won two trips to National MATHCOUNTS as a member of the four-person Massachusetts team, travelling to Arlington, Virginia in 2006 and Fort Worth, Texas in 2007. Several years earlier, she had enjoyed watching the top twelve mathletes in the country compete on the ESPN broadcast of the MATHCOUNTS National CountDown Round in the middle of the National Spelling Bee. At MATHCOUNTS Nationals in 2007, Elizabeth herself reached that National CountDown Round, ranking among the 12 highest scoring students in the country.

Elizabeth has qualified for the USA Math Olympiad (USAMO) every year since eighth grade. Beginning in ninth grade, she has scored high enough on the USAMO to win trips to train at the Math Olympiad Summer Program, held each summer at the University of Nebraska-Lincoln.

Along with seven other American girls, Elizabeth also won trips to represent our country at the China Girls Math Olympiad (CGMO) in each of the past two years. She returned home from China with a silver medal in 2009, and a gold medal in 2010. The US teams have done a terrific job among the world-class competition at the CGMO each year since they began participating in 2007. You can read a travelogue from Elizabeth and her CGMO teammates here. The problems on the 2010 CGMO test are available here. All of Elizabeth's CGMO 2009 and 2010 teammates who are still in high school (and therefore eligible to participate) were also contestants at this year's Math Prize for Girls. You'll be reading more about them in future posts to this blog.

After the 2010 CGMO, the Public Radio International show The World interviewed Elizabeth and her CGMO teammate Lynnelle Ye. Here's an excerpt from that interview:

Public Radio International The World (PRI TW): Hi, Elizabeth, give us a sense of the competition, help people understand what the math is like, what it's like to do it over there.

Elizabeth Synge: It's difficult math, but it's so much fun. When I sit down to take the competition, it just feels very good, [I'm] at home, it doesn't really matter where I am. I enjoy solving problems and it's always great to have solved the problem.

PRI TW: And how would you describe those problems to someone whose not especially good at math?

ES: It's like figuring out why something happens. Like figuring out for yourself why something happens, then being able to show it to others.

PRI TW: What do you think will be your strongest memory that you'll take back?

ES: Walking around the school campus with some of the volunteers. We just played around on the seaside and stuff like that. And, I was speaking a bit of Chinese. I had taken a Chinese class during the year. I actually spoke some Chinese, that was so much fun!

You can read more about Elizabeth in these two delightful articles from her hometown newspapers:

"Am I smarter than a tenth grader?" and

"Math problems hurt your head? To this whiz kid, they are play."

Third, Fourth, and Fifth Place Winners

2010-12-04T21:26:00.000-08:00

In Young Cho
Phillips Exeter Academy
New Hampshire
Third place:
(after tiebreak)
$2,700

Jae Shin
Phillips Academy Andover, Massachusetts
Fourth Place
(after tiebreak)
$2,700

Alissa Zhang
Saratoga High School
California
Fifth Place
(after tiebreak)
$2,700

Sixth and Seventh Place Winners

2010-12-04T21:14:00.000-08:00

Corinne Madsen
Illinois Science & Math Academy
Illinois
Sixth Place
(after tiebreak)
$1,000

Jessie Duan
North Carolina School of Science & Mathematics
North Carolina
Seventh Place
(after tiebreak)
$1,000

Tied for eighth place

2010-12-04T20:17:00.000-08:00

Harlin Lee
(8th place trophy after tiebreak)
Phillips Exeter Academy
New Hampshire

Elizabeth Shen
(9th place trophy after tiebreak)
South Mecklenburg High School
North Carolina

Moya Chen
(10th place trophy after tiebreak)
Vernon Hills High School
Illinois

Grace Huckins
Weston High School
MA

Ramya Rangan
Harker School
California

Pei Tao
Newport High School
Washington

Elizabeth Yang
West-Windsor Plainsboro South
New Jersey

Julia Huang
Lynbrook High School
California

Mihika Prabhu
West Lafayette High School
Indiana

Emily Zhang
Newport High School
Washington

All students tied for eighth place received $300 prizes.

Honorable Mentions

2010-12-04T18:38:00.000-08:00

Monica Agrawal

Chamblee Charter High School
Georgia

Megan Chen
Illinois Mathematics & Science Academy
Illinois

Ashley Cho
Emma Willard School
Albany Area Math Circle
New York

Bianca Homberg
Westborough High School
Massachusetts

Anying Li
Ithaca High School
Ithaca Math Circle
New York

Mariya Sardarli
Strathcona Composite High School
Alberta

Mia Smith
Ithaca High School
Ithaca Math Circle
New York

Marissa Stephens
North Central High School
Indiana

Susan Sun
West Vancouver Secondary School
British Columbia

Luchang Wang
Central Academy/Valley High School
Iowa

Victoria Xia
Thomas Jefferson High School for Science & Technology
Virginia

Shuxin Zhan
Hempfield High School
Pennsylvania

Joy Zheng
Phillips Exeter Academy
New Hampshire

Sheela Devadas
Lexington High School
Massachusetts

Jao-ke Chin-Lee
Stuyvesant High School
New York

Melody Guan
University of Toronto Schools
Ontario

Kathleen Zhou
Interlake High School
Washington

Additional photos of Winners and Honorable Mention recipients will be posted after we receive photographic releases signed by the students and their parents.

A Thanksgiving toast to all who made the Math Prize for Girls a great experience!

2010-11-25T06:47:00.000-08:00

Thanks to all 210 Math Prize Contestants from all over the United States and Canada who came together so exuberantly to share a very challenging "extreme math" experience together! I am in awe of all the collective talent, mathematical enthusiasm and problem-solving promise that assembled at NYU's Courant Institute of Mathematics on November 13. And thanks to your parents for encouraging and supporting you in embracing problem-solving challenges.

Thanks to Arun Alagappan of Advantage Testing Foundation for his vision, leadership, and generosity in sponsoring this event to encourage young women everywhere--not just those who came to the competition in New York City, but all those whose lives will be touched by the 210 enthusiastic contestants who are bringing back the spirit of mathematical camaraderie to their communities and inspiring other girls to follow in their footsteps.

Thanks to Dr. Ravi Boppana for all his work in creating and organizing the contest, for staying unflappably positive while juggling an unbelievable number of logistical details. Special thanks as well to his wife Dr. Ranu Boppana and their daughter Meena, who were ubiquitous in volunteering to manage where they were needed throughout the day--and who provided an awesome demonstration of harmonious family teamwork at its best.

Thanks to the distinguished mathematicians who serve on the Board of Advisors to Ravi: Professor Ioana Dumitriu (University of Washington), President Maria Klawe (Harvey Mudd College), Richard Rusczyk (Art of Problem Solving), Professor Michael Sipser (MIT), Professor Gigliola Staffilani (MIT), Professor Lauren Williams (University of California-Berkeley), Dr. Joseph Woo, and Professor Melanie Matchett Wood (Stanford University).

Thanks to the world-class team of problem reviewers who test-solved the problems and assisted in making the problems sparkle even more with clarity and brilliance: Professor Ioana Dumitriu, a former Putnam Fellow who now coaches the Putnam team at the University of Washington, which had its first Putnam Fellow this year, Jennifer Iglesias (Harvey Mudd undergrad, and coach of the 2009 China Girls Math Olympiad (CGMO) team as well as a member of the CGMO 2007 and 2008 teams), Joel Lewis (MIT grad student, who has helped to lead and/or coach the NYC Math Team for the past decade), and Kate Rudolph (Math Prize 2009 alumna and speaker).

The problem writing/reviewing team all exemplify the very best of what I love about working with the math competition community--they all delight in sharing what they have learned from their own problem-solving experiences to encourage and help others to develop their own mathematical understanding and insights.

Thanks to the speakers whose work has highlighted some of the many ways that mathematical skills can be put to use in the world. MIT undergraduate Kate Rudolph's research on hypersphere packing has applications in chemistry and cryptology. Akamai's Gene Meyer spoke of how Akamai uses mathematics to optimize the performance of the Internet, while Dr. Tal Rabin spoke of the importance of mathematics in computer science research at IBM.

Yale University cosmologist Priya Natarajan shared the fundamental equations she uses in her theoretical astrophysics work, along with the fascinating evidence suggesting that the vast majority of what surrounds us is actually "dark energy" and "dark matter."

Thanks to Akamai Foundation for joining in to help sponsor this event, making travel assistance possible for USA Math Olympiad (USAMO) qualifiers. Thanks as well to the Akamai Foundation for all it has done to sponsor other great opportunities for girls at the Math Olympiad Summer Program and China Girls Math Olympiad. This year's field at the Math Prize for Girls was exceptionally impressive, even stronger than last year, in part thanks to the olympiad training opportunities Akamai has helped to finance. All seven eligible members of past China Girls Math Olympiad teams as well as over 80% of the eligible female 2010 USAMO and USAJMO qualifiers participated in this year's Math Prize for Girls.

Thanks to all the volunteers who worked behind the scenes in planning and preparation, helping with the essential tasks of registration, proctoring, scoring, and more of the countless frequently thankless but unnoticed tasks that make an event like this one a great experience for everyone involved. The collective experience and expertise of the New York math teachers and NYC Math Team coaches as well as the Advantage Testing staff volunteers were once again a tremendous resource. This year's volunteers were: Deanna Abramowitz, Brigitte Bentele, Meena Boppana, Dr. Ranu Boppana, Elizabeth Cohan, Rebecca Damas, Eve Drucker, Tim Evans, Heidi Fisher, Erica Hopkins, Ashvin Jaishankar, Ruozhou Jia, Oleg Kryzhanovsky, Eliza Kuberska, Priya Kumar, Alex Lee, Reed LaFleche, Tina Lesem, Charles Loxton, Marie Parham, Ming Jack Po, Gabe Perez-Giz, Jed Schwartz, Caroline Taylor, Rani Vedanthan, and Ruyin Xue.

But once more, thanks to the 210 girls who embraced the challenging problems at the 2010 Math Prize for Girls.

Your willingness to rise to challenges like these has shown me that you are bright shining stars that give hope for our country's future, so I've created a star for you in Tagxedo. (Click on the image below for a higher resolution picture.)

'Twas the night before the Math Prize for Girls, and ...

2010-11-24T18:53:00.000-08:00

'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.

Words as well as numbers are important!

2010-11-24T17:46:00.000-08:00

Math Prize alumna Kate Rudolph's excellent delivery of her speech at this year's Math Prize for Girls surely drew on her high school experiences in theater and as captain of the speech team.

Being able to communicate your ideas effectively in words as well as formulas is an asset to mathematicians and scientists--it is often said that the test of truly understanding your work is whether you can explain it to someone else. That's one of the reasons I always encourage our math circle students to coach younger students. They will deepen their own understanding by sharing their work with others.

Here is a video of Kate explaining her work on four-dimensional sphere-packing to an audience of young girls at the 2010 Intel Science Talent Search.

There's more from Kate here:

In the interview video above, Kate discussed the excitement of learning to write proofs in olympiad-style exams and college classes. It's important for mathematicians to be able to communicate via the written as well as the spoken word.

Good ways to get that kind of mathematical expository writing experience include participating in the USA Mathematical Talent Search (free and open to any student who has not yet graduated from high school) and team Power Round contests such as the ARML Power Contest. Some summer programs such as Canada/USA MathCamp and HCSSiM have excellent proof-based admission quizzes that can provide some great experiences in proof-writing as well.

An easy, informal way to get started on expository mathematical writing is to participate in the free Art of Problem Solving forums. 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.

Wise and heartfelt words from a veteran

2010-11-24T15:05:00.000-08:00

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 speech into which she had 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."

Building friendly bridges across the US and Canada at Math Prize 2010: where do Math Prize girls come from?

2010-11-24T13:42:00.000-08:00

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. Thanks as well to generous local sponsors like the Colorado Math Circle, which offered a travel subsidy to make it easier for girls from their math circle to accept invitations to participate.

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)

2009 Math Prize for Girls highlights

2009-11-15T10:45:00.000-08:00

A century ago, suffragettes gathered in Cooper Union's Great Hall, agitating for the right to vote for women. I believe they would have been bursting with pride if they could have seen the first annual Math Prize for Girls awards ceremony held in that hallowed and historic hall yesterday afternoon.

The winner was Elizabeth Synge from Massachusetts, taking home a prize check for $20,000 for top honors on a very challenging set of problems during yesterday's written test held at NYU's Courant Institute of Mathematics. This prize was yet another impressive accomplishment for Elizabeth, shown above in a photo taken last summer at an international competition in China, where she also won high honors. You can read more about Elizabeth's background here.

Joy Zheng of Washington, Lynnelle Ye of California, and Jane Wang of New Jersey all tied for second place in the contest and took home checks for $6,000 each.

Albany Area Math Circle's own Ashley Cho from Emma Willard School, who tied for 25th place, brought home a beautiful sparkling crystal engraved trophy for Honorable Mention. Complete results for the top 31 students are listed here. All 220 students took home Mathematica software donated by Wolfram as well as new friendships forged with kindred spirits talking over the problems after the competition.

It was an honor just to qualify for an invitation to such an event, and Albany Area Math Circle was also proud to be represented by Ashley's schoolmate Heidi Chen from Emma Willard as well as Anagha Tolpadi from Niskayuna High School. Younger Albany Area Math Circle students have already been inspired to work hard in hopes of qualifying in future years.

As advisor to the Albany Area Math Circle, I have attended scores of math contests but never have I attended one quite as unusual--or as visually spectacular--or as well-organized!--as this one.

I have some brief notes and observations below--more will follow when I have time.

#1) To my knowledge, never have so many young women with so much mathematical promise come together in a single place before. The gathering provided an opportunity for a girl who might have few kindred spirits sharing her passion in a small hometown to make friends and form bonds with a community of young women sharing her interests from all over the country. The students attending the event have been exchanging email addresses, cell phone numbers, and Facebook friend invitations.

To give some idea of the strength of the field at the Math Prize for Girls, the 220 contestants from around the country included numerous USA Math Olympiad qualifiers as well as members of recent US China Girls Math Olympiad (CGMO) teams who are still in high school, including gold, silver, and bronze medalists from that prestigious international competition.

#2) There were 20 excellent and very challenging problems for the girls to tackle during the 2.5 hour morning written exam, mostly created by the contest's extraordinary director, the highly talented Ravi Boppana. He was assisted by a stellar advisory board, including mathematicians from Berkeley, Harvey Mudd, MIT, Princeton, and Stanford. I hope the Math Prize for Girls will publish their problems on the website, because they will be a great problem-solving resource and learning opportunity* for all students to work on, no matter what their gender, where they live, or whether they were able to take part in person.

#3) While students were taking the written test, Richard Rusczyk, from Art of Problem Solving, gave an outstanding talk to parents with excellent and eminently sensible advice about opportunities and resources for encouraging students to develop their problem-solving abilities. I agreed with pretty much everything he said, except there were things I wanted to add and underscore. After the slides from his talk are posted to the contest website, I'll create a post adding my own thoughts.

#4) Mathematician Cathy O'Neil gave a superb keynote speech, which struck exactly the perfect chord. It's not easy to give a talk that engages a large group of high school students you've never met before who are mathematically exhausted after a morning of working on very hard math problems and who are nervous and excited about the upcoming announcement of awards and a possible tie-break round, but she delivered a sparkling talk on a fascinating topic she'd first encountered on an old HCSSiM "Interesting Test." Her discussion focused on an application of directed graph theory problems known as "chicken pecking order" problems. There are many related explorations math circle students can explore, and you can find some good related problems in Sam Vandervelde's list here.

#5) The other shorter talks were great as well. I enjoyed them all. I have sat through scores of tedious awards ceremony speeches over the past ten years--these were the best ever.

#6) The newly renovated historic Cooper Union Great Hall provided an awe-inspiring and highly appropriate setting for the awards ceremony. Presidents from Lincoln through Obama have spoken here. Many important social movements, including women's suffrage, took root here. What a terrific place to promote a new movement to encourage even more young women across the country to embrace mathematical challenges.

#7) There was a superb team of volunteers assisting with the contest, including many familiar faces and names I knew from the New York City Math Teachers' Circle or NYSML. Volunteers I recognized included Deanna Abramowitz, Tim Evans, Maggie Feurtado, Sheila Krilov, Marie Parham, Ming Jack Po, Amy Prager, and others whose faces were familiar but whose names escape me. Many of the volunteers were highly dedicated New York City math teachers, going above and beyond their usual duties after a hard week of work in the classroom.

Thanks to so much able and highly experienced help, proctoring and scoring went extremely well. I was sitting very close to the side of the stage and found myself extremely impressed by the exceptionally smooth and graceful execution of the simultaneous and complex tie-breaking round to break ties for second, fifth, and eighth place. It's volunteers like these who make such contests possible.

#8) One highly talented young woman, Meena Boppana, was present at the event, but notably absent from the competition. Meena is a Hunter College High School sophomore and already has established an outstanding record as a New York mathematical rock-star. Since her dad was the director of the Math Prize for Girls event, she was of course not eligible to compete, but she and her mother, Dr. Ranu Boppana, were both enthusiastic and very helpful volunteers.

As a seventh grader, Meena made mathematical history by winning the Manhattan Chapter MATHCOUNTS written contest, almost surely the first girl to do so. As an eighth grader, Meena ranked 2nd in the statewide MATHCOUNTS competition and represented the great state of New York as a member of the state team at Nationals in Denver. As a ninth grade freshman, Meena made the citywide A-division high school team which won the New York State Math League championship.

#9) I felt an overwhelming sense of "grandmotherly" maternal pride at this event. I don't have any actual biological grandchildren so you might be wondering how this could be possible.

So many of the participants were students that my daughter Alison had mentored through her work as a mentor or coach or instructor in programs such as China Girls Math Olympiad, MathCamp, Girls' Angle, MATHCOUNTS, and the Math Olympiad Summer Program, that I realized that I was in some sense a "mathematical grandmother" of many of these girls. In fact, some of the girls may even have been been mentored and coached by still other students whom Alison had mentored, which makes me their "mathematical great-grandmother" (or who knows, maybe even a mathematical great-great-grandmother....)

It makes me feel a little old....but I don't mind! And I also didn't mind the long lines in the women's restrooms at the end....it was nice to see all the networking among the girls going on in the lines (and waiting in the long lines gave me a chance to dispense a few more tips to other mothers interested in starting up math circles in their hometowns.) Women's restrooms are usually relatively deserted places during typical math contests--it was nice to be in a busy one for a change.

*In my opinion, the learning opportunity is a great one for adults as well as students. I plan to work on the contest problems myself. I also have a few ideas for some who could learn a lot from working on these problems, but I'll reserve those for a separate post.

NOTE: Updated 11/18/2009--thanks to Contest Director Ravi Boppana for providing information to set the record straight and correct a few errors in the earlier version of my post. The most significant error is that his daughter Meena actually attends Hunter College High School, rather than Stuyvesant as I had previously stated incorrectly.