tag:blogger.com,1999:blog-44796901109752676632017-10-13T01:48:08.642-07:00Albany Area Math CircleNYSML 2010 Host Team UAlbany 4/10/10
Thanks to UAlbany College of Nanoscale Science & Engineering for sponsorship!Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.comBlogger209125tag:blogger.com,1999:blog-4479690110975267663.post-8444614169659206822017-03-25T14:12:00.006-07:002017-03-25T14:14:01.299-07:00MATHCOUNTS Congratulations!<br />I am delighted to share the exciting news that two Albany Area Math Circle members placed among the top four individuals at last week's New York State MATHCOUNTS championship contest, earning the right to represent our state at the National MATHCOUNTS Competition in Orlando Florida in May. David Li from Utica was the New York State champion and Rowechen Zhong from Iroquois was the fourth highest scoring individual, and his school team (pictured below) was second place in the state.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-Vg8sJRkfE-4/WNbXrGX9LKI/AAAAAAAAGxA/c-a7xowG6oE9nXCeikxfmqxHr_RMChbogCLcB/s1600/IMG_1603.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="285" src="https://2.bp.blogspot.com/-Vg8sJRkfE-4/WNbXrGX9LKI/AAAAAAAAGxA/c-a7xowG6oE9nXCeikxfmqxHr_RMChbogCLcB/s400/IMG_1603.JPG" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><br />Iroquois Middle School team<br /><span class="il" style="background-color: white; color: #222222; font-family: "arial" , sans-serif; font-size: 12.8px;">Steve Schmidt (coach), Stephanie</span><span style="background-color: white; color: #222222; font-family: "arial" , sans-serif; font-size: 12.8px;"> Vernooy (coach), <br />Harini Prabaharan, Jeffrey Huang, Christine Lee, Sarah Vernooy, Rowechen Zhong</span></td></tr></tbody></table><br />Congratulations to the entire Iroquois Middle School's team and coaches for their outstanding second place finish at the state contest last weekend. Veteran head coach Professor Steve Schmidt is my colleague in the economics department at Union College as well as the husband of AAMC advisor Ms. Alexandra Schmidt. Steve headed a strong coaching team that included Professor Stephanie Vernooy (from Siena College's Biology Department) and AAMC student coaches Gabriel Kammer and Ian Vernooy. AAMC alumni Gideon Schmidt and Patrick Chi served as student coaches in prior years helping veterans on the Iroquois team build a firm foundation in their earlier years of middle school, as did prior adult coach Ambady Suresh.<br /><br />Professor Schmidt will coach the New York State team at the National MATHCOUNTS Competition in May and will accompany David, Rowechen, and their two teammates to Orlando.<br /><br />Congratulations again and best wishes to all!<br /><br /><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com4tag:blogger.com,1999:blog-4479690110975267663.post-49928712590328276642015-05-13T02:54:00.000-07:002015-05-13T14:24:05.664-07:00Intriguing guest speaker: Professor Ivana AlexandrovaThis spring, our math circle was fortunate to have a special treat: Professor <a href="http://www.albany.edu/ialexandrova/">Ivana Alexandrova</a> from UAlbany gave our high school students a guest presentation full of fascinating problems in trigonometry. Professor Alexandrova grew up in Vratsa, Bulgaria, which has a rich and venerable tradition of math circles, and she herself participated in math circles as a student before coming to this country for college and graduate studies. As a graduate student at UC-Berkeley, she met another mathematician from Bulgaria, Professor Zvezdelina Stankova, who leads the Berkeley Math Circle, and she was happy to learn that math circles have started to establish themselves in this country as well.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-oLCJqGE4iH0/VVMUgHIodrI/AAAAAAAAGP4/rgw6l5iMbY8/s1600/IMG_0068.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="275" src="http://2.bp.blogspot.com/-oLCJqGE4iH0/VVMUgHIodrI/AAAAAAAAGP4/rgw6l5iMbY8/s400/IMG_0068.JPG" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Professor Ivana Alexandrova with math circle student leaders Gili Rusak and Phil Sun after her intriguing talk. Gili and Phil are graduating seniors and longtime members of Albany Area Math Circle. Like Professor Alexandrova, they have grown up as members of a math circle that helped to develop their passion for problem solving and they have been sharing their passions and talents with younger students. Next year Gili will be studying at Stanford and Phil will be studying at MIT.</td></tr></tbody></table><br /><br />Professor Alexandrova, whose research focuses on partial differential equations and mathematical physics, chose to discuss trigonometry in her presentation, because it is a beautiful, highly useful, and often misunderstood subject which is unfortunately somewhat neglected in conventional American mathematics education. Many college professors share her wish that their students had stronger backgrounds in trig. Under her guidance scary looking trig problems that might initially make your eyes glaze over sparkled and came to life as she developed beautiful ways to approach them. Her trig problems were indeed very in<b>trig</b>uing!<br /><br />You can see some of her presentation in the whiteboard shots below. She has also created a very nice website for high school students with weekly problems designed to draw less experienced students into the world of intriguing math, with a few algebra problems mixed in among the trig problems. You can find her <a href="http://www.albany.edu/ialexandrova/HS.html">problems and solutions here.</a> The current problem is very nice: Solve 1 + sin x + cos x < 0.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-X1FfvURNqKI/VVMeIPtiSAI/AAAAAAAAGQI/PPHrF4rn10g/s1600/IMG_0065.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="http://1.bp.blogspot.com/-X1FfvURNqKI/VVMeIPtiSAI/AAAAAAAAGQI/PPHrF4rn10g/s400/IMG_0065.JPG" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-fF4jvAcbwCQ/VVMegdsIpRI/AAAAAAAAGQQ/YT9h9vD_ic4/s1600/IMG_0064.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="http://1.bp.blogspot.com/-fF4jvAcbwCQ/VVMegdsIpRI/AAAAAAAAGQQ/YT9h9vD_ic4/s400/IMG_0064.JPG" width="400" /></a></div><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com5tag:blogger.com,1999:blog-4479690110975267663.post-33301186287896032112013-10-20T08:44:00.000-07:002013-10-20T08:45:20.558-07:00Math Circle plans for the 2013-2014 school year: new time/day/location Albany Area Math Circle will be starting up its 13th year!<br /><br />Our high school group will start meeting soon. We welcome new students in grades 9 to 12 to join us. To stay informed with all the information you need about place/day/time, please sign up for our email list by sending an email to AlbanyAreaMathCircle-subscribe@yahoogroups.com.<br /><br />Students in middle school (grades 8 and below), we have not forgotten about you. Our high school students will be making plans for fun events to welcome you into our mathematical community later this year. Your parents are also welcome to sign up for our email list (using the same address as above) so your families can stay informed about those plans.<br /><br /><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-74806178660009111602013-05-29T15:08:00.000-07:002013-05-29T15:29:31.767-07:00Recommended summer reading for young students (and their parents!) aspiring to climb mathematical mountains together this summer<br /><div style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img height="200" src="http://ecx.images-amazon.com/images/I/41VH2uaiBQL._SY300_.jpg" width="160" /></div>Does math class make your child feel like a hamster in a cage stuck in a wheel of an endlessly repetitive "spiral curriculum" with little to challenge or inspire her? If you answered yes, then <a href="http://www.amazon.com/Hard-Elementary-School-Glenn-Ellison/dp/1489507175/ref=la_B00447TN8K_1_3?ie=UTF8&qid=1369864868&sr=1-3">this book</a> could provide a much-needed breath of fresh air.<br /><br />Imagine if one of your daughter's classmates had an MIT professor dad who loved the fun of mathematical problem solving in his spare time. Dream on and imagine that he volunteered to share his enthusiasm and talents as a mentor with a small group of students including your child, busting them out of the conventional curriculum hamster wheel to take them on challenging mathematical rock-climbing adventures with inspiring views of beautiful mathematical mountain vistas. <br /><br />Glenn Ellison's daughters are fortunate to have just such a dad and this engaging book is the result of his very successful mathematical excursions with his daughters and their schoolmates. Some of the students with whom he has worked for a number of years have now grown into world-class problem solvers.<br /><br />Written in a good-natured conversational style, <i><a href="http://www.amazon.com/Hard-Elementary-School-Glenn-Ellison/dp/1489507175/ref=la_B00447TN8K_1_3?ie=UTF8&qid=1369864868&sr=1-3">Hard Math for Elementary School</a> </i>lays the foundation for elementary school students to develop the tools and habits of confident, capable, and curious problem solvers. The text provides well-organized explanations and the accompanying workbook poses thoughtfully composed practice problems designed to inspire children to tackle tough problems that exceed the expectations of conventional textbooks. <span style="font-family: inherit;">This book and its earlier counterpart for somewhat older students,</span><span style="font-family: inherit;"> </span><a href="http://www.amazon.com/Hard-Math-Middle-School-IMLEM/dp/1453814450/ref=la_B00447TN8K_1_1?ie=UTF8&qid=1369864868&sr=1-1" style="font-family: inherit;">Hard Math for Middle School</a><span style="font-family: inherit;">,</span><span style="font-family: inherit;"> are great solutions to questions frequently posed by parents of young students looking for summer reading for their mathematically voracious students.</span><br /><span style="font-family: inherit;"><i><br /></i></span><br /><div style="text-align: center;"><i style="font-family: inherit;"><a href="http://en.wikipedia.org/wiki/Sumer_Is_Icumen_In">S</a><span style="background-color: white; line-height: 19.197919845581055px;"><a href="http://en.wikipedia.org/wiki/Sumer_Is_Icumen_In">umer is icumen in</a>,</span></i><br /><i style="font-family: inherit;"><span style="background-color: white; line-height: 19.197919845581055px;"><br /></span></i><i style="font-family: inherit;">Lhude sing cuccu!</i></div><span style="font-family: inherit;"></span><br /><div style="text-align: center;"><span style="font-family: inherit;"><i style="font-family: inherit;">Groweth sed and bloweth med</i></span></div><span style="font-family: inherit;"></span><br /><div style="text-align: center;"><span style="font-family: inherit;"><i style="font-family: inherit;">And springth the wude nu,</i></span></div><span style="font-family: inherit;"></span><br /><div style="text-align: center;"><span style="font-family: inherit;"><i style="font-family: inherit; line-height: 19.197919845581055px;">Sing cuccu!</i></span></div><span style="font-family: inherit;"></span><br /><div style="text-align: center;"><br /></div><span style="font-weight: normal;">Enjoy your summer! Parents may find they too enjoy learning some new mathematical insights if they talk about these problems with their children. It is great for students to discover that sometimes they can figure out answers to problems that stump grownups! As I have discovered myself, time and time again, when working with my own children as well as other people's children in my math outreach activities, while it may be humbling for me, it is empowering and exciting for children when a flash of insight enables them to climb a mathematical mountain before I do. </span><br /><span style="font-weight: normal;"><br /></span><br /><div><span style="font-weight: normal;">(Disclosure: thanks to <a href="http://economics.mit.edu/faculty/gellison">Professor Ellison</a> for sharing a prepublication review copy of the manuscript with me.)</span></div>Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-71151776596150339342013-04-04T21:40:00.000-07:002013-04-05T12:07:31.265-07:00Doing justice to describing the work of other math circles that have inspired usLast week, Sol Lederman interviewed <a href="http://albanyareamathcircle.blogspot.com/2013/02/gili-rusak-mathematical-community.html">Gili Rusak</a> and myself for a podcast now featured on his blog, <a href="http://wildaboutmath.com/">Wild About Math</a>. Thanks to Catherine Miller for typing up a transcript of that conversation, which will soon be available in a link on <a href="http://wildaboutmath.com/2013/03/31/gili-rusak-mary-okeeffe-inspired-by-math-27/">Sol's blogpost</a>. Reading that transcript of an informal live unrehearsed and unscripted conversation was certainly humbling and subsequent reflection made me realize that there are things I need to clarify. There were so many things that I wish I had said, inspiring people who have massively contributed to our math circle I wish I had named or things I had said a bit more clearly. In one case, what came out of my mouth (when I was talking about "ends and means") was totally the opposite of what I intended to say and changed the meaning entirely. So I have added annotation in brackets to the transcript, and I have also provided links. <br /><br />It was a fun experience talking to Sol, who is clearly a kindred spirit, an amateur math-lover like the two of us who shares our passion for promoting math communities where people enjoy celebrating mistakes and sharing Aha! experiences as they explore challenging problems together. We touched on many subjects and definitely did not have time to do justice to all of them in an hour-long informal conversation.<br /><br />I want to acknowledge here in this blog an important distinction which we did not make in the podcast and which I have also neglected to make in the past in this blog, and which Ken Fan, the mathematician who directs <a href="http://www.girlsangle.org/">Girls' Angle</a>, and invented the treasure hunt concept, has called to our attention and asked that we clarify. There is a good deal of difference between SUMiT, the original treasure hunt created by Girls' Angle and the small local treasure hunts in Schenectady inspired by it. We have not described the extremely rich complexity of the far more elaborate original <a href="http://www.girlsangle.org/page/SUMiT.html">SUMiT</a> event Gili attended. Although Ken has asked that SUMiT participants not disclose the full details of that experience (in order not to spoil the story line for future participants), he would like to clarify that the original event is far more complex with several stages, and the crossword element described by Gili in the podcast was only one of those stages. Ken has told me that thousands of hours of work have gone into creating and developing the SUMiT event. Prizes given to all participants included stereo speakers, a backpack, a set of Zometools, a Tetraxis puzzle from KO Sticks, candy, and a copy of Maria Dzielska's book <i>Hypatia of Alexandra</i>.<br /><br />In the podcast, we also talked about some of the other mathematical circle communities which have inspired us and which are run by full-time professional mathematicians who dedicate their lives to creating mathematics and mathematical communities, but again I feel I did not do them adequate justice in giving them the credit they deserve for the inspiration they have provided to our math circle. I am in awe of them and have long and fervently wished that our own local community had such dedicated fulltime professional mathematicians leading a local math circle as <a href="http://math2.uncc.edu/~hbreiter/">Harold Reiter</a> from the <a href="http://www.davidson.edu/math/davis/CMCMath/index.html">Charlotte Math Club</a>, <a href="http://www.themathcircle.org/thefounders.php">Bob and Ellen Kaplan</a> from the <a href="http://www.themathcircle.org/index.php">Boston Math Circle</a>, <a href="http://www.mills.edu/academics/faculty/math/stankova/stankova.php">Zvezda Stankova</a> from the <a href="http://mathcircle.berkeley.edu/">Berkeley Math Circle</a>, <a href="http://www.sjsu.edu/math/people/faculty/shubin/">Tatiana Shubin</a> from the <a href="http://www.sanjosemathcircle.org/">San Jose Math Circle</a>, <a href="http://www.usfca.edu/facultydetails.aspx?id=4294969541">Paul Zeitz</a> and <a href="http://www.msri.org/people/staff/brandy/professional.php">Brandy Weigers</a> from the <a href="http://www.usfca.edu/facultydetails.aspx?id=4294969541">San Francisco Math Circle</a>, <a href="http://www.linkedin.com/pub/joshua-zucker/4/2b4/962">Joshua Zucker </a>from the <a href="https://www.msri.org/web/msri/static-pages/-/node/194">MSRI Julia Robinson Math Festivals</a>, <a href="http://riverbendmath.org/about/people/AmandaSerenevy">Amanda Serenevy</a> from the <a href="http://riverbendmath.org/">Riverbend Community Math Center</a>, <a href="http://www.linkedin.com/pub/ken-fan/7/4b4/7a0">Ken Fan</a> from <a href="http://www.girlsangle.org/">Girls' Angle</a>, or <a href="http://www.linkedin.com/in/japhethwood">Japheth Wood</a> from the<a href="https://www.nymathcircle.org/"> NYC Math Circle</a> and <a href="http://bardmathcircle.blogspot.com/">Bard Math Circle</a>.<br /><br />I also wish that I had encountered such people and communities when I was a student myself. I missed out on a lot of joy as a result when I was young. I never dreamed that math would be fun to do as a student or that it would be fun to do with other people rather than as a solitary pursuit. Indeed, when I was Gili's age, math was my weakest subject and I remember feeling quite lost and confused in my 10th grade geometry class (a much less advanced math class than she is taking. Like a number of our math circle students, Gili is already taking advanced college math courses.) It was only later when my younger brother and sister--out of desperation and having nobody else to turn to as they were entering a new high school where they did not want to be behind the other students--started asking for my help in learning mathematics that I began to get an inkling that it could actually be fun to figure out how to work together with them to try to find answers for their questions and to share my own (generally half-baked) insights. In some sense, we are still doing that in our math circle all these years later.<br /><br />I also want to make clear that--in default of such folks living in our midst--our Albany Area Math Circle activities are all led by adult and student volunteers, amateurs who do not have the mathematical sophistication of full-time professional mathematicians who have spent their lives immersed in mathematics. While we have benefited from the countless wonderful ideas generously shared by professional mathematician math circle leaders and especially the facilitation of <a href="http://www.mathcircles.org/">MSRI National Association of Math Circles</a> in providing opportunities for them to share their ideas with us, we have no illusions that the depth of our mathematical understanding of all the nuances of the problems we investigate is anything like theirs or that we are able to describe them fully, but we do encourage others not to give up altogether if they also find themselves in a community lacking such dedicated professionals.<br /><br />I encourage all our members as well as readers of this blog thinking about starting their own local math communities to go directly to the source--and also to support the math circles led by professionals whose work you admire by considering purchasing some of <a href="http://www.ams.org/bookstore/mclseries">the MSRI Math Circle book series</a>, <a href="http://www.themathcircle.org/thefounders.php">Bob and Ellen Kaplan's books</a>, subscribing to the <i><a href="http://www.girlsangle.org/page/bulletin.php">Girls' Angle Bulletin</a>, </i>participating in a future<a href="http://www.themathcircle.org/thefounders.php"> SUMiT</a>, and/or just making a donation directly to any of <a href="http://www.mathcircles.org/Wiki_ExistingMathCirclePrograms">these circles</a> that has provided ideas you have especially enjoyed. These worthy organizations typically operate on very fragile financing and deserve your support. The end of the school year will soon be upon us, and I know that many math teachers would be delighted to receive such a book, a subscription, and/or a thoughtful donation made in their honor rather than the usual end-of-year thank you teacher gifts like candy or toiletries. It's a gift that will keep on giving for many years to come as your teachers' future students will benefit in many ways. You can also help support these generous professional math circle leaders by suggesting to your friendly local librarian that the library consider purchasing or subscribing to their publications.<br /><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com2tag:blogger.com,1999:blog-4479690110975267663.post-51319608133186638862013-03-27T21:55:00.001-07:002013-04-08T05:28:30.327-07:00Math Circle student research honorsMath Circle students Gili Rusak, Matthew Babbitt, and Zubin Mukerjee have won honors this year for their original math research projects. They will be presenting their research in separate sessions at the 20th annual <a href="https://apps.skidmore.edu/pls/apex/f?p=115:8:1755761185994283::NO:::">Hudson Undergraduate Math Research Conference</a>, which will be held at Williams College on Saturday April 6.<br /><br />Gili's applied mathematics project, <i><a href="https://apps.skidmore.edu/pls/apex/XX_APEX02.download_my_file?p_file=20011008997768070">An Analysis of Teenage Twitter Communities</a></i>, which draws on graph theory, probability, and sociology, won top honors at Capital Regional Science and Engineering Fair at RPI last week. This means that Gili will represent our region at the <a href="http://www.societyforscience.org/isef/">Intel International Science and Engineering Fair (ISEF)</a> to be held in Phoenix, Arizona. This is the world's largest international science fair, where over 1,500 students from over 70 countries around the world gather to present their work. Over $3 million in prizes will be awarded. Gili is a sophomore at Shaker High School who has been taking advanced college classes at Siena College. You can read more about Gili's awesome work as a mathematical community builder <a href="http://albanyareamathcircle.blogspot.com/2013/02/gili-rusak-mathematical-community.html">here</a>.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://www.societyforscience.org/view.image?Id=580" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="http://www.societyforscience.org/view.image?Id=580" width="400" /></a></div>Matt Babbitt's graph theory research project, <i style="background-color: white;"><span style="font-family: inherit;"><a href="https://apps.skidmore.edu/pls/apex/XX_APEX02.download_my_file?p_file=20104217546974538">Counting number of edges, thickness, and chromatic number of k-visibility graphs</a>, </span></i>won semifinalist honors in this year's <a href="http://www.societyforscience.org/STS">Intel Science Talent Search</a>. Matt's research benefits from advice from his MIT Research Science Institute mentor, Jesse Geneson, and Dr. Tanya Khovanova, the head mathematics mentor at RSI. Matt, a homeschooled senior from Fort Edward who has taken advanced math classes at Union College, has been named a <a href="http://www.jkcf.org/scholarships/college-scholarship-program/">Jack Kent Cooke Scholar</a> and plans to attend MIT next year.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-IHg7xU0Vy-g/UVPQs-0mHOI/AAAAAAAAFm8/n4Z0N80Zj78/s1600/intel.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="http://3.bp.blogspot.com/-IHg7xU0Vy-g/UVPQs-0mHOI/AAAAAAAAFm8/n4Z0N80Zj78/s200/intel.png" width="131" /></a></div><img alt="Siemens Foundation - Iselin, NJ" height="200" src="https://fbcdn-profile-a.akamaihd.net/hprofile-ak-ash4/s160x160/196280_10150120532158462_1666047_a.jpg" width="200" /><br /><br /><br />Zubin Mukerjee's number theory research project, <i><a href="https://apps.skidmore.edu/pls/apex/XX_APEX02.download_my_file?p_file=20106201335149650">Random Involutions and the Number of Prime Factors</a></i>, is based on his joint work with a fellow student, Uthsav Chitra, at <a href="http://www.promys.org/">PROMYS</a> last summer. Their research mentor was Dr. Kristen Wickelgren, a research fellow at Harvard. The project won semifinalist honors in the <i><a href="http://www.siemens-foundation.org/en/competition.htm">Siemens Competition in Math Science and Technology</a></i>. Zubin, a senior at Guilderland High School, who has been taking advanced math classes at SUNY Albany, has also won a number of honors in history and music. You can read more about <a href="http://albanyareamathcircle.blogspot.com/2012/10/congratulations-zubin.html">Zubin here</a>.Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com3tag:blogger.com,1999:blog-4479690110975267663.post-19726287140583022802013-02-08T18:03:00.001-08:002013-02-09T12:56:28.872-08:00Gili Rusak, mathematical community builder<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-26C8ZQVXbbM/URWAP3fHkxI/AAAAAAAAFkY/GZku5Lm2yWg/s1600/gili.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="307" src="http://4.bp.blogspot.com/-26C8ZQVXbbM/URWAP3fHkxI/AAAAAAAAFkY/GZku5Lm2yWg/s400/gili.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gili Rusak launches students on investigations of Archimedean solids.</td></tr></tbody></table><br />Gili Rusak, a tenth grader at Shaker High School who also takes advanced math classes at Siena College, has been building deep, rich, and inclusive mathematical communities all around the Capital District and even beyond. For the past two years, she has been helping Doyle Middle School teacher Nancy Smith with coaching Doyle's MATHCOUNTS team in Troy. <br /><br />Last winter, she participated in the first annual <a href="http://www.girlsangle.org/page/SUMiT.html">SUMiT</a>, a "fully collaborative, math intensive event" organized by <a href="http://www.girlsangle.org/">Girls' Angle</a> and the <a href="http://mit-uswim.blogspot.com/">Undergraduate Society for Women in Mathematics</a> at MIT and returned home efferverscent with enthusiasm about the wonderful experiences she had had as a participant in that event. She came back inspired with a missionary zeal to create a similar math event here in the Capital District, to bring that same mathematical joyful collaboration to students in the Capital District.<br /><br />After months of thoughtful planning and brainstorming, Gili designed, organized, and led a completely marvelous math treasure hunt inspired by the SUMiT model. Gili's local event took place at Union College's Kenney Community Center last summer. Watching Gili and the two AAMC veterans she had recruited to help, Cecilia Holodak and Elizabeth Parizh, orchestrate this event was the single most epic math experience of my entire career as a math outreach volunteer! (And I have had many awesome ones, so that is saying a lot!) The photo below shows Gili and Elizabeth with some of their happy treasure hunters and you can learn much more about that treasure hunt in the writeup and photos on <a href="http://messormath.wordpress.com/2012/09/05/puzzle-hunt-with-pictures/">Gili's blog</a> <a href="http://messormath.wordpress.com/2012/09/05/puzzle-hunt-with-pictures/">here</a>. <br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-mHLQslLzxS4/UFndcDQ-B8I/AAAAAAAAFXM/GhqPEU3CGPw/s1600/Gili+at+treasure+hunt.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="290" src="http://1.bp.blogspot.com/-mHLQslLzxS4/UFndcDQ-B8I/AAAAAAAAFXM/GhqPEU3CGPw/s400/Gili+at+treasure+hunt.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gili leading a Math Treasure Hunt she designed and organized for younger girls at the Kenney Community Center at Union College late last summer .</td></tr></tbody></table><br />After hearing about Gili's very successful local treasure hunt, Ken Fan at <a href="http://www.girlsangle.org/">Girls' Angle</a> invited Gili to help him lead a much larger treasure hunt at Microsoft New England Research & Development Center as part of a social event ("Games Night") at the Math Prize for Girls at MIT last fall. It was a *huge* hit engaging scores of girls from all over the United States and Canada. <br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-rkQzGjAe-rA/URWkqWCcHoI/AAAAAAAAFlc/VDlHPfJcwVQ/s1600/girls.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="302" src="http://4.bp.blogspot.com/-rkQzGjAe-rA/URWkqWCcHoI/AAAAAAAAFlc/VDlHPfJcwVQ/s400/girls.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Math Prize for Girls @MIT participants enjoy the extremely fun yet challenging math treasure hunt Kan Fan and Gili ran at a "Games Night" social event at Microsoft New England Research and Development (NERD) Center.</td></tr></tbody></table><br />Gili's account of that night is <a href="http://messormath.wordpress.com/2012/10/03/math-treasure-hunt-at-math-prize-games-night/">here</a>. Ken describes one fun part of their treasure hunt, Mental Madness, <a href="http://girlsangle.wordpress.com/2012/09/22/mental-madness-at-math-prize-for-girls/">here</a>. In another event, called "Robo-Ape", Gili and Ken asked the girls to compose algorithms to instruct a robotic ape about how to eat a banana. Gili then read their algorithms aloud while Ken played the role of the robotic ape, executing their algorithmic instructions quite literally to great amusement. (You can see a <a href="http://www.youtube.com/watch?feature=player_embedded&v=LEJEApYEJcY">video clip of RoboApe here</a>.)<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-rKVG29bKJJw/URWl0YZVW1I/AAAAAAAAFlk/s95BNia_xcA/s1600/roboape.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="260" src="http://4.bp.blogspot.com/-rKVG29bKJJw/URWl0YZVW1I/AAAAAAAAFlk/s95BNia_xcA/s400/roboape.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Ken Fan from Girls' Angle and Gili in the Robo-Ape event</td></tr></tbody></table><br /><br />Attendees at the Math Prize social event included <a href="http://www.stephenwolfram.com/">Stephen Wolfram</a> and his 15-year-old daughter Catherine, who was intrigued by the treasure hunt idea that Ken and Gili were leading. Afterwards, Gili and Catherine stayed in touch and worked together to create yet another local treasure hunt back in Schenectady at Union College's Kenney Center in early November, this one with a Halloween theme. You can see a little bit of their treasure hunt in <a href="https://www.youtube.com/watch?v=vksUaRjKG18">this video (starting at 3:27)</a>. Gili described some of their activities in <a href="http://messormath.wordpress.com/2012/11/22/halloween-treasure-hunt/">her blog here</a>. <br /><br />Gili is an outstanding role model, a trail blazer who is creating wonderful road maps that other students can follow as well to create their own mathematical community building events! She is only a tenth grader, but her work thus far exceeds my wildest dreams of what I would have thought possible. And she started out in a small satellite middle school math circle led by Zagreb Mukerjee at a table in the Clifton Park library back in when she was a fifth grader.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-jlxGESmpcis/SSpOA4_rNrI/AAAAAAAAAdQ/eU9DXa8gP6k/s1600/Zagreb+leading+ms+math+circle.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="188" src="http://1.bp.blogspot.com/-jlxGESmpcis/SSpOA4_rNrI/AAAAAAAAAdQ/eU9DXa8gP6k/s320/Zagreb+leading+ms+math+circle.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Where it all began years ago: a younger Gili (center, back to camera) participating in a small satellite middle school math circle led by Zagreb Mukerjee (standing) at the Clifton Park Library.</td></tr></tbody></table><br /> Zagreb is now off in <a href="http://albanyareamathcircle.blogspot.com/2011/09/math-circle-alum-wins-harvard-social.html">college</a>, but Gili is indeed doing her utmost to "pay it forward" and share the magic of creating vibrant local mathematical communities with younger people in new and innovative ways. And who knows what wondrous activities Gili will--in her turn--inspire the young students with whom SHE is working to do a few years down the road, when it is THEIR turn to pay it forward!<br /><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com1tag:blogger.com,1999:blog-4479690110975267663.post-76578123254733186592013-01-24T05:37:00.002-08:002013-02-04T05:54:17.187-08:00Sign up for AMC10B or AMC12B at Siena College!<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-3fBTtdCTgus/UQFXekQQPQI/AAAAAAAAFgA/W_Z0vN4sAAQ/s1600/affiliate.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="35" src="http://4.bp.blogspot.com/-3fBTtdCTgus/UQFXekQQPQI/AAAAAAAAFgA/W_Z0vN4sAAQ/s400/affiliate.png" width="400" /></a></div>Thanks to <a href="http://www.siena.edu/pages/2072.asp">Siena College Math Department </a>and especially to Professor Mohammad Javaheri (<a href="http://www.imocompendium.com/database/index.php?mod=20&imetakm=Mohammad%20Javaheri">a silver medalist at the 1995 International Math Olympiad</a>) for sponsoring this exciting math contest for high school students in the Capital District. The AMC10/12 is the <a href="http://www.artofproblemsolving.com/Wiki/index.php/AMC_10">first in a series</a> of challenging "extreme math problem solving" events that ultimately leads to selection to the US team for the International Math Olympiad! It also opens many other doors as well, including the American Invitational Math Exam, the USA Math Olympiad and USA Junior Math Olympiad. If you are a girl, it is also the entry point to the <a href="http://mathprize.atfoundation.org/index">Math Prize for Girls at MIT</a> next September!<br /><br /> We especially encourage participation from students who enjoy math challenges but who have never even heard of this contest before. High school students interested in joining Albany Area Math Circle sessions to help prepare you to have an enjoyable extreme math experience should contact AAMC advisor Mary O'Keeffe at mathcircle@gmail.com for more information about how to prepare. Please use the form below to sign up to take the contest at Siena on February 20.<br /><br /> <iframe frameborder="0" height="1900" marginheight="0" marginwidth="0" src="https://docs.google.com/spreadsheet/embeddedform?formkey=dGJJS1FKUmluMzZqWnJkY05MMlZ2MUE6MA" width="760">Loading...</iframe>Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com1tag:blogger.com,1999:blog-4479690110975267663.post-28262500218614632312012-10-21T14:16:00.002-07:002013-01-09T14:28:15.835-08:00Congratulations, Zubin!<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-fGnOL_HrE-g/UIRQuMywHSI/AAAAAAAAFZ4/948TPSwBUyw/s1600/zubin.png" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="400" src="http://2.bp.blogspot.com/-fGnOL_HrE-g/UIRQuMywHSI/AAAAAAAAFZ4/948TPSwBUyw/s400/zubin.png" width="341" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Zubin Mukerjee, at right, with other members of the Upstate New York All-Star Math Team at the national high school math tournament, ARML, in June</td></tr></tbody></table><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Zubin Mukerjee, a veteran leader of Albany Area Math Circle who has also organized and led a satellite math circle of his own for younger students, has blazed yet another a new trail for others to follow. <br /><br />Zubin, a Guilderland High School senior, who is taking advanced classes in math and economics at SUNY Albany, and his co-author, Uthsav Chitra from Delaware, have won semifinalist honors in a prestigious national research contest for high school students. Zubin and Uthsav worked on an original research project in number theory, "Random Involutions and the Number of Prime Factors of an Integer,"under the guidance of a mentor at <a href="http://www.promys.org/research/">PROMYS</a> in Boston last summer. <br /><br />Research presents new challenges as well as new rewards compared to the contest problems with which many math circle students are familiar. When you work on a contest problem, it may be very hard, but you KNOW that you are working on a problem that somebody else has already solved and that there must be a clever elegant solution to the problem. It is indeed exciting to have the Aha! moment when you find the solution to a contest problem, but such moments pale compared to those you can experience in math research, the thrill of discovering an answer to a problem nobody else has ever found before. Sometimes the results are negatives ones, not exactly the ones you were hoping for originally, but even those disappointing results can provide important clues to promising new lines for exploration.<br /><br />It takes passion, perseverance, and luck to find original new research results, far moreso than in contests. When doing original research, there are no guarantees at the outset that the problem will even have a solution at all, let alone that it will yield interesting results worth sharing with others. Even once the problem is solved, it takes excellent writing skills to write up your research results in a way that will allow others to appreciate the importance and validity of what you have discovered. Zubin's years of helping to write power round solutions for our math circle teams as well as his prize-winning entries in history day competitions have certainly polished his expository writing skills.<br /><br />Here are the abstract and executive summary for Zubin and Uthsav's research project.<br /><br /><b>Abstract: </b><i> For hundreds of years, mathematicians have tried to find good approximations for the function d(n), which counts the number of prime factors of an integer n. In this paper, we examine </i><i>using random involutions to approximate d(n) by comparing the number of fixed points of a </i><i>random involution on F<sub>2</sub><sup>2g(n)</sup> to the number of fixed points of a specific involution, <span style="background-color: white; font-family: 'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size: 15.333333015441895px; line-height: 19.19999885559082px; white-space: nowrap;">τ</span>(n). We find and prove that the expected number of fixed points of a random involution converges, so that d(n) cannot be approximated using this method; moreover, we use this to show that the involution <span style="background-color: white; font-family: 'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size: 15.333333015441895px; line-height: 19.19999885559082px; white-space: nowrap;">τ</span>(n) is not random, as it has more fixed points than a random involution.</i><br /><br /><b>Executive summary:</b> <i>The natural numbers are perhaps the most familiar to humans. They are the counting numbers: 1, </i><i>2, 3, etc. A divisor of a number is something that divides evenly into that number. For example, 3 </i><i>and 14 are divisors of 42, but 42 is not a divisor of 3 or 14. A prime number is a natural number </i><i>whose only positive divisors are 1 and itself. The first few primes are 2, 3, 5, 7 ... there are also </i><i>infinitely many of these. There is a well-known function that returns the number of prime divisors </i><i>of a number n, given that number. We denote this function d(n). Our goal in this project is to </i><i>further research on modeling d(n).</i><br /><i><br /></i><i>Our mentor proposed a possible method of modeling d(n) by looking at special functions called </i><i>involutions that act on the surface of modular curves. In particular, we studied the involution</i><i> </i><span style="background-color: white; font-family: 'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size: 15.333333015441895px; line-height: 19.19999885559082px; white-space: nowrap;">τ</span><i>(n), which is related to d(n), by comparing it to random involutions. We were able to conclude,</i><i>through a series of proofs and derivations as well as some graphical analysis using Mathematica, </i><i>that d(n) cannot be modeled by </i><span style="background-color: white; font-family: 'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size: 15.333333015441895px; line-height: 19.19999885559082px; white-space: nowrap;">τ</span><i>(n) and that, as a result, </i><span style="background-color: white; font-family: 'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size: 15.333333015441895px; line-height: 19.19999885559082px; white-space: nowrap;">τ</span><i>(n) is not random. In other words, </i><i>there is something special about </i><span style="background-color: white; font-family: 'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size: 15.333333015441895px; line-height: 19.19999885559082px; white-space: nowrap;">τ</span><i>(n) that makes it so we can’t model d(n).</i><br /><i><br /></i><i>The consequences of this result are not yet fully clear. Nevertheless, this result can lead the way to </i><i>studying other types of involutions, some of which may be able to model d(n). An accurate model </i><i>for d(n) would be incredible, as it would make finding the prime factorization of large numbers </i><i>much easier; this would have many applications in cryptography and computer science. Much </i><i>research remains to be done on involutions though; perhaps one day, a closed-form expression for </i><i>d(n) will be found through random involutions.</i><br /><br />Zubin and Uthsav's research mentor was Dr. Kirsten Wickelgren, an American Institute of Mathematics fellow at Harvard University. Here is a <a href="https://docs.google.com/viewer?url=http%3A%2F%2Fwww.math.harvard.edu%2F~kwickelg%2FRandom_modules.pdf">link to a copy of the background document </a>including the problems she suggested they investigate as well as definitions of some key concepts and a helpful list of the supplementary references with which she initially launched them on their way. If you are interested in understanding more about their work, you may want to take a look at those references yourself. Students who have not yet studied much number theory will also find the <i>Art of Problem Solving'</i>s <a href="http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:nt">textbook on introductory number theory</a> very helpful. [Added later: Zubin also passed along another recommendation of a classic number theory book, Hardy & Wright's <i>Introduction to the Theory of Numbers, </i>endorsed by PROMYS Director Glenn Stevens as "clear and concise." Zubin also notes that Hardy & Wright cover many topics in number theory in their book, some relevant to their project and some not.]<br /><br />You will also note that Zubin and Uthsav used Wolfram <i>Mathematica </i>computer software to help create graphs to give them insights into their problem analysis. Thanks to Wolfram's sponsorship of contests such as American Regions Math League (ARML), Harvard-MIT Math Tournament (HMMT), and Princeton University Math Contest (PUMaC), Zubin and all our veteran math circle students who have participated in one or more of those contests have received free student licenses to use this very powerful software. Those licenses will remain valid as long as they are students, including college and graduate school years ahead.Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com3tag:blogger.com,1999:blog-4479690110975267663.post-90921241530713527812012-09-29T20:02:00.002-07:002012-09-29T20:02:46.281-07:00Math Circle travel contest dates this yearMath contests are a fun (but entirely OPTIONAL) part of our Albany Area Math Circle experience. <br /><br />To help our members plan ahead, I will describe the entire calendar of contests in which members can participate below. I have broken them down into two categories: travel contests and locally administered contests. This post describes the travel contests we plan for this coming year. My next post will describe the locally administered contests we plan.<br /><br /><br /><b><span style="font-size: large;">Harvard-MIT November Tournament (HMNT): </span></b><br /><b>Saturday November 10 at Harvard University in Cambridge, MA </b><br />This is an ideal travel contest for our younger veterans who have done at least NYSML in the past, but who have not yet done much proof-writing. Note that participating in this contest rules out participating in PUMaC the following weekend. It also rules out participating in the (much harder) February 2013 HMMT. If you are seriously considering this contest but not yet sure of your schedule, please email Mr. Babbitt ASAP to let him know of your tentative (or definite) interest. <br /><b>HMNT November Cost per student: </b> $10 registration fee plus modest costs for lunch. AAMC can put parents in touch with one another to arrange carpools so that parents can share gas and tolls. Math contests at Harvard and MIT have been done as a daytrip by AAMC mathletes who were comfortable getting up early and sleeping in the car. If your parents agree, it may also be possible for students to arrange to stay overnight in a Harvard or MIT dorm with a college student host or hostess. (You would need to bring a sleeping bag, and you will probably be sleeping on the floor. Note that dorms can be noisy on Friday nights!) Parent drivers may want to work out arrangements to share hotel rooms (unless they are driving as a day trip.) Although we will put parents in touch with each other to facilitate whatever arrangements seem most suitable to them, it is entirely up to the parents involved to work out mutually satisfactory travel arrangements.<br /><br /><br /><b><span style="font-size: large;">Princeton University Math Contest (PUMaC): </span> </b><br /><b>Saturday November 17 at Princeton University in Princeton, NJ </b><br />This is a very challenging contest which includes a collaborative team round. Only experienced veteran students should consider this contest. It is considerably harder than the AIME, so students who have not yet taken the AIME should not consider it. But even the AIME is not sufficient preparation, because the team round requires mathematical expository skills. The team round is proof-based and essay style. Students need to be prepared to work collaboratively (and remotely) on a google document from Nov 10 through November 16. In addition, there will be mandatory on-line practice in October for all team members on our AoPS forum. Non-team members are also welcome to join the on-line practice forum. Our Math Circle veteran leaders, Matt Babbitt and Zubin Mukerjee, will provide further information about what is expected of team members on the AoPS forum. If you are seriously considering this contest but not yet sure of your schedule, please email Mr. Babbitt ASAP to let him know of your tentative (or definite) interest. <br /><b>Cost per student: </b> $12.50 registration fee (which includes lunch). AAMC can put parents in touch with one another to arrange carpools so that parents can share gas and tolls. Parent drivers will probably want to work out arrangements to share hotel rooms. Due to the distance involved as well as the need to finalize the power round with a final team meeting in Princeton on Friday evening, this event is NOT doable as a day trip. Although we will put parents in touch with each other to facilitate whatever arrangements seem most suitable to them, it is entirely up to the parents involved to work out mutually satisfactory travel arrangements.<br /><br /><b><span style="font-size: large;">Harvard-MIT Math Tournament (HMMT)</span></b><br /><b>Saturday February 16, 2013 at MIT in Cambridge, MA</b><br />This contest has always been extremely hard, and we expect that trend to continue to unprecedented epic levels of difficulty this year. Only those with extreme tolerance for mathematical endurance should consider this event. However, mathematical strength is not enough to be selected for this team, since collaboration with other team members will be very important. It is very important that all members of our HMMT team know one another's strengths and weaknesses so that the "whole can be more than the sum of the parts." It is also important that all team members encourage one another when the going gets tough, because--believe me!--it will get tough!<br /><br />Our advanced veteran students who wholeheartedly participate in fall math circle activities including our PUMaC on-line practices on the AoPS forum and regularly attend (most of) our Friday meetings with an extremely positive and supportive spirit that encourages others not to give up when the going seems hopeless will be given first preference in team selection. All other factors being equal, seniors will be given preference over younger students. For younger students, participation in previous years' HMMT on-line events or travel events will be a plus factor. All other factors being equal, younger students who have done well in prior year on-line HMMT events will be given preference over those who attended the travel event and did equally well.<br /><br /><b>Cost per student for Feb HMMT: </b> $10 registration fee plus modest costs for lunch. AAMC can put parents in touch with one another to arrange carpools so that parents can share gas and tolls. The event can be done as a daytrip if your mathletes are comfortable getting up early and sleeping in the car. If your parents agree, it may also be possible for students to arrange to stay overnight in a Harvard or MIT dorm with a college student host or hostess. (You would need to bring a sleeping bag, and you will probably be sleeping on the floor. Note that dorms can be noisy on Friday nights!) Parent drivers may want to work out arrangements to share hotel rooms (unless they are driving as a day trip.) Although we will put parents in touch with each other to facilitate whatever arrangements seem most suitable to them, it is entirely up to the parents involved to work out mutually satisfactory travel arrangements.<br /><br /><b><span style="font-size: large;">New York State Math League (NYSML)</span></b><br /><b>Saturday April 13, 2013 at <a href="https://maps.google.com/maps?ie=UTF-8&gl=us&daddr=12+Tripp+Lane,+Armonk,+NY+10504&panel=1&f=d&fb=1&dirflg=d&geocode=0,41.134785,-73.689174&cid=0,0,6182272259823446317&hq=byram+hills+high&ei=5l5nUJCdA-Tr0gGWqoCQCQ&ved=0CJkBEPUX">Biram Hills High School</a> in Westchester County</b><br />NYSML is an ideal "first" travel competition for our students. It is the statewide math championship for high school students. It is held in a different place each year. We (Albany Area Math Circle) were the host league in 2010, Suffolk County in eastern Long Island hosted in 2011, Southern Tier was the host league in 2012. The 2013 host will be the Westchester-Putnam Math League. All high school students who attend meetings regularly and demonstrate mathematical and behavioral maturity as well as enthusiasm and persistence are welcome to join our NYSML teams. Unlike the other travel tournaments, we expect to be able to take as many 15-person teams as we would like to NYSML. (In 2010, we had three teams with almost 45 students. If a team is a bit short of 15 students, we can use alternates from other teams and vice versa at NYSML.)<br /><br /><b>Cost per student for NYSML: </b> Unknown at this time, but probably around $20 per student (including lunch). It is a potential day trip (for mathletes who don't mind getting up early and sleeping in the car.) Some parents and mathletes may prefer to stay in a hotel. As with all travel contests, we will facilitate parents getting in touch with each other to make their own carpool/travel arrangements. Although we will put parents in touch with each other to facilitate whatever arrangements seem most suitable to them, it is entirely up to the parents involved to work out mutually satisfactory travel arrangements.<br /><br /><b><span style="font-size: large;">American Regions Math League (ARML)</span></b><br /><b>Saturday June 1, 2013 at Penn State (depart Albany morning of 5/30 and practice with team on 5/31 at Penn State, so students need to miss several days of school for this.)</b><br />ARML is the national high school championship event. It has a format similar to NYSML but the problems are harder. Albany Area Math Circle students can apply to be on the Upstate NY ARML team. You will want to wait until you have your AMC, and (if applicable) AIME and NYSML scores before you apply to the team. NYSML experience and performance will also be a big plus for ARML team selection. <br /><br /><b>Important info about conflict with SAT testing date:</b> if you are thinking of doing ARML, please plan ahead for the SAT conflict. June 1 is an SAT administration date. It is expensive and time-consuming and may not be possible to arrange a makeup date. It is MUCH better if you plan to take your SAT subject tests in May rather than June, and/or your SAT reasoning tests in January or March rather than June. The SAT schedule for this coming year is <a href="http://professionals.collegeboard.com/testing/sat-reasoning/register/test-dates">here</a>.<br /><br /><b>Cost per student for ARML: </b> Unknown at this time, but in recent years the cost has been around $300 to $325. That included a chartered bus from Binghamton to Penn State and back as well as two night's housing in Penn State dorms and some, but not all, meals. Students also needed about $25 to buy additional meals on their own. Thanks to Cecilia and Gili's moms efforts in fundraising the NYSSPE donated funds that helped to offset about $100 of the costs per student.<br /><br />In the next post, I will describe the contests that we expect to be offered locally, without the need to travel.<br /><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com1tag:blogger.com,1999:blog-4479690110975267663.post-27073374773101733352012-06-12T21:07:00.001-07:002012-06-12T21:09:07.860-07:00Upstate NY All Stars!<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-vAGyox8qJQ8/T9gDVkXT6hI/AAAAAAAAFHw/idXfzV-0xXI/s1600/nys+allstars.png" imageanchor="1"><img border="0" height="135" src="http://1.bp.blogspot.com/-vAGyox8qJQ8/T9gDVkXT6hI/AAAAAAAAFHw/idXfzV-0xXI/s400/nys+allstars.png" width="400" /></a></div><span style="font-size: large;">Albany Area Math Circle members of the New York State All Star Math Team thank the New York State Society of Professional Engineers for their support: </span><br /><span style="font-size: large;">Yujun (Etheal) Chen, Emma Willard School</span><br /><span style="font-size: large;">Sherry He, Emma Willard School</span><br /><span style="font-size: large;">Gili Rusak, Shaker High School</span><br /><span style="font-size: large;">Jien Ogawa, South Colonie High School</span><br /><span style="font-size: large;">Cecilia Holodak, Niskayuna High School</span><br /><span style="font-size: large;">Matt Babbitt, heeg</span><br /><span style="font-size: large;">Zubin Mukerjee, Guilderland High School</span><br /><span style="font-size: large;">Ziqing (Bill) Dong. Farnsworth Middle School</span><br /><span style="font-size: large;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-urpHQ3UHFYo/T9gR1bVY0kI/AAAAAAAAFIc/tZHIpTwmnvE/s1600/arml+2012+team+entire.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="135" src="http://4.bp.blogspot.com/-urpHQ3UHFYo/T9gR1bVY0kI/AAAAAAAAFIc/tZHIpTwmnvE/s400/arml+2012+team+entire.png" width="400" /></a></div>Complete 2012 Upstate NY AllStar Math team roster for 2012 ARML, including students from all over Upstate New York (defined as New York State minus {New York City, Nassau County, Suffolk Count})<br /><br /><br /><table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 345px;"> <colgroup><col style="width: 48pt;" width="64"></col> <col style="mso-width-alt: 3766; mso-width-source: userset; width: 77pt;" width="103"></col> <col style="mso-width-alt: 6509; mso-width-source: userset; width: 134pt;" width="178"></col> </colgroup><tbody><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt; width: 48pt;" width="64">Matthew</td> <td style="width: 77pt;" width="103">Babbitt</td> <td style="width: 134pt;" width="178">heeg</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Jemmin</td> <td>Chang</td> <td>Somers</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Yujun</td> <td>Chen</td> <td>Emma Willard</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Yiqun</td> <td>Cui</td> <td>Brighton</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Matt</td> <td>DeCross</td> <td>Pittsford-Sutherland</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Pranav</td> <td>Devarakonda</td> <td>Brighton</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Matt</td> <td>Dobbins</td> <td>Corning West</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Ziqing</td> <td>Dong</td> <td>Farnsworth</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Ryan</td> <td>Gao</td> <td>Brighton</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Huajun</td> <td>Gu</td> <td>Corning West</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Jeff</td> <td>Guo</td> <td>Penfield</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Sherry</td> <td>He</td> <td>Emma Willard</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Cecilia</td> <td>Holodak</td> <td>Niskayuna</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Doug</td> <td>Knowles</td> <td>Churchville-Chili</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Jeremy</td> <td>Koob</td> <td>Corning West</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Benjamin</td> <td>Lei</td> <td>Arlington</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Devin</td> <td>Li</td> <td>Corning West</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Allen</td> <td>Liu</td> <td>Penfield</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Ben</td> <td>Lowenstein</td> <td>Pittsford-Sutherland</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Dongze</td> <td>Lu</td> <td>Harley-Allendale-Columbia</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Evan</td> <td>Lustick</td> <td>Canandaigua</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Zubin</td> <td>Mukerjee</td> <td>Guilderland</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Jien</td> <td>Ogawa</td> <td>South Colonie</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Jordan</td> <td>Roeder</td> <td>Canandaigua</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Gili</td> <td>Rusak</td> <td>Shaker</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Perry</td> <td>Wang</td> <td>Corning West</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Felix</td> <td>Weilacher</td> <td>Penfield</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Yunmei</td> <td>Zhang</td> <td>Harley-Allendale-Columbia</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Simon</td> <td>Zheng</td> <td>Somers</td> </tr></tbody></table><br /><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-76633498917520637572012-06-12T10:30:00.001-07:002012-06-12T10:32:24.374-07:00Guerrilla Math venues?<br /><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;">Schenectady--and more broadly, the Capital District, have many wonderful free outdoor activities. They are fun family places to go and enjoy our beautiful summers. And they are great places for you and your families to do Guerrilla Math! Just bring some sidewalk chalk or a portable whiteboard and markers, and your ideas for fun math explorations to share with families waiting for the event to begin or during intermissions, afterwards. </div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><br /></div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;">Here are few links I got from a colleague at Union College. If you can suggest other links, please post in the comments below.</div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><br /></div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><a href="http://www.saratogian.com/articles/2012/06/10/entertainment/doc4fcfef2b1fc51469705464.txt?viewmode=fullstory">Central Park (Music Haven) Schenectady summer concerts</a></div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><br /></div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><a href="http://www.albany.com/event/jazz-on-jay-48780/">Jazz on Jay Street</a></div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><br /></div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><a href="http://www.freedomparkscotia.org/schedule.html">Freedom park summer concerts (Scotia)</a></div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><br /></div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><a href="http://www.schenectadyparking.com/events.php">Other Schenectady events</a></div><div class="MsoNormal" style="font-family: Calibri, sans-serif; font-size: 11pt; margin: 0in 0in 0.0001pt;"><br /></div>Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-53702201047173860832012-06-10T05:45:00.002-07:002012-06-10T05:57:10.558-07:00Guerrilla Math Circle at the Youth Peace RallyIt is a beautiful day for more sidewalk chalk Guerrilla Math Circles. I will be doing it at today's Youth Peace Rally at Jerry Burrell Park in Schenectady.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-HJ4TUuB-8bE/T9SVJ4TO5AI/AAAAAAAAFHE/5E2oJzvt7eQ/s1600/peace+rally+flyer.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="http://1.bp.blogspot.com/-HJ4TUuB-8bE/T9SVJ4TO5AI/AAAAAAAAFHE/5E2oJzvt7eQ/s400/peace+rally+flyer.png" width="365" /></a></div><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />As I wrote in my last post:<br /><br /><blockquote class="tr_bq"><span style="background-color: white; color: #333333; font-family: Georgia, serif; font-size: 13px; line-height: 20px; text-align: left;">Jerry Burrell Park is a place that is near and dear to my heart, because one of my former students at Union College, </span><a href="http://www.union.edu/N/DS/s.php?s=8955" style="background-color: white; color: #999999; font-family: Georgia, serif; font-size: 13px; line-height: 20px; text-align: left; text-decoration: none;">Jeremy Taglieri</a><span style="background-color: white; color: #333333; font-family: Georgia, serif; font-size: 13px; line-height: 20px; text-align: left;">, spent a year working along with two friends to raise $84,000 in funds and recruiting 140 volunteers to renovate the park. They called their project </span><a href="http://www.sicm.us/SKIP/ProjectSkip.html" style="background-color: white; color: #999999; font-family: Georgia, serif; font-size: 13px; line-height: 20px; text-align: left; text-decoration: none;">Project SKIP</a><span style="background-color: white; color: #333333; font-family: Georgia, serif; font-size: 13px; line-height: 20px; text-align: left;">, where SKIP = "Schenectady Kids Imagine and Play." Jerry Burrell Park is also the site of a SICM free lunch site, and in fact, volunteers from my own church will take a turn serving lunch for a week there later this summer. </span></blockquote><br />All math circle families, siblings, friends, and neighbors are cordially welcome to join us. But--as I also wrote in my last post--I am mindful that not all parents will be comfortable with their families coming to this neighborhood. It is a decision that should be made with full information--this is one of the highest crime neighborhoods in our area, and in 2010, just a few weeks after the playground's renovation, a <a href="http://www.dailygazette.net/standard/ShowStoryTemplate.asp?Path=SCH/2012/05/15&ID=Ar00901&Section=Local_News">17-year-old shot and seriously wounded an 11-year-old boy and his 18-year-old older brother</a>. Each family needs to make a choice they are comfortable with.<br /><br />But today, I choose to join those who hope to bring and keep peace in this community. And I will bring what I have to share--the beauty and excitement of creating and discovering mathematical patterns.<br /><br /><b>Directions: </b> Jerry Burrell Park is located at the corner of Hamilton and Schenectady Streets in the Hamilton Hill neighborhood of Schenectady.Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com1tag:blogger.com,1999:blog-4479690110975267663.post-52845333839302008082012-06-08T10:57:00.003-07:002012-06-08T11:08:59.207-07:00Pascal's triangle in sidewalk chalk<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-U4z_6J_9q04/T9IzJaY931I/AAAAAAAAFG8/Jzj6FbSlW74/s1600/pascal+triangle+sidewalk+chalk.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="http://2.bp.blogspot.com/-U4z_6J_9q04/T9IzJaY931I/AAAAAAAAFG8/Jzj6FbSlW74/s640/pascal+triangle+sidewalk+chalk.jpg" width="406" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">First 15 rows of Pascal's triangle (mod 2) in sidewalk chalk</td></tr></tbody></table><br />Imagine that you throw a dart at <a href="http://www.mathsisfun.com/pascals-triangle.html">Pascal's triangle.</a> What are the odds you will hit an even number?<br /><br />Paul Zeitz raised this fascinating question at the <a href="http://www.msri.org/web/msri/scientific/show/-/event/Wm511">MSRI Great Circle's workshop </a>three years ago.<br /><br />It's a fun one to explore in sidewalk chalk--perfect for Guerrilla Math Circles. <br /><br />A good way to start thinking about this problem is simply to begin coloring in the triangle--and what could be more fun that the idea of creating a really large one with sidewalk chalk? And engaging any curious passersby in helping you. How big can we make it if we get lots of folks helping us? (And of course, we could also start some people on exploring Pascal's triangles with multiples of other prime numbers colored in.)<br /><br />I started one the other day in Schenectady's Central Park and I will be back there this evening (Friday June 8) to do more. There is a nice large stretch of blacktop that is blocked off from automobile access. It is adjacent to Tiny Totland and not far from the Music Haven (site of many wonderful free concerts) and also near the picnic pavillion area where <a href="http://www.sicm.us/Summer_Ministries.html">Schenectady Inner City Mission serves free lunches</a> in the summer. Central Park is the "crown jewel" of Schenectady's park system, designed by Frederick Olmsted and with a world class <a href="http://www.schenectadyrose.com/">rose garden</a>. To get to where I will be tonight, enter Central Park via the main entrance off Central Parkway and then turn to the left when you get to the lake. Park in the parking lot near Tiny Totland and look for me in the blacktop area between Tiny Totland and the lake.<br /><br />On Sunday afternoon, from 1 to 5 p.m. I will be doing more Guerrilla Math Circles at a different park in Schenectady, Jerry Burrell Park. Jerry Burrell Park is a place that is near and dear to my heart, because one of my former students at Union College,<a href="http://www.union.edu/N/DS/s.php?s=8955"> Jeremy Taglieri</a>, spent a year working along with two friends to raise $84,000 in funds and recruiting 140 volunteers to renovate the park. They called their project <a href="http://www.sicm.us/SKIP/ProjectSkip.html">Project SKIP</a>, where SKIP = "Schenectady Kids Imagine and Play." Jerry Burrell Park is also the site of a SICM free lunch site, and in fact, volunteers from my own church will take a turn serving lunch for a week there later this summer. <br /><br />I invite Albany Area Math Circle families (students, parents, siblings) to join me in sharing the fun, beauty, and awesomeness of mathematics with a wider world, a world of folks who have yet to discover how much delight can be had in exploring the wilds of mathematics. <br /><br />All of you can do these activities wherever your parents feel comfortable with your doing them. I grew up in a city myself, and have always been comfortable having my children play in Schenectady parks when they were growing up, with--of course--sensible precautions taken about when and where to go. Personally, I am comfortable being in city parks when SICM volunteers from churches all over the area are serving free lunches, but not when they are mostly deserted. And this Sunday's event at Jerry Burrell Park is part of a larger event organized by city officials. <br /><br />Nothing is ever 100% safe--and there are risks to just sitting in your own living room (<a href="http://abcnews.go.com/GMA/story?id=128087&page=1">a car might come crashing through the wall</a>), but I recognize that these are decisions that math circle parents needs to make for their own children. I feel compelled to point out that--sadly--just a few weeks after the renovation of the Jerry Burrell Park in 2010, a 17-year-old boy <a href="http://www.dailygazette.net/standard/ShowStoryTemplate.asp?Path=SCH/2012/05/15&ID=Ar00901&Section=Local_News">shot and seriously wounded </a>an 11-year-old and an 18-year-old boy who were walking to the park from just a block away.<br /><br />But--remember that you and your sons and daughters can also do these same activities WHEREVER you happen to be--on the sidewalk in front of your own home or the park just down the street from you in your own neighborhood. <br /><br />No matter where you are comfortable with participating in our outreach activities, you can work with us to brainstorm ideas and post links to photos in the comments below. Albany Area Math Circle members can also post about their experiences in our <a href="http://www.artofproblemsolving.com/Forum/viewforum.php?f=380">private discussion forum</a> on the Art of Problem Solving.<br /><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com3tag:blogger.com,1999:blog-4479690110975267663.post-58720995781525641532012-06-07T14:13:00.002-07:002012-06-08T08:02:00.401-07:00Home of the math champions: Upstate New York!<span id="goog_722163379"></span><span id="goog_722163380"></span><a href="http://www.blogger.com/"></a><br /><div class="separator" style="clear: both; text-align: center;"></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-PMVDidB3N7M/T9C1gfFdCcI/AAAAAAAAFGM/V-yDmlV8yug/s1600/allen+arml+2012+1+copy.png" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="259" src="http://2.bp.blogspot.com/-PMVDidB3N7M/T9C1gfFdCcI/AAAAAAAAFGM/V-yDmlV8yug/s400/allen+arml+2012+1+copy.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="text-align: -webkit-auto;"><span style="font-size: small;">Upstate NY All-Star Math Team celebrates the announcement that <b>Allen Liu</b> is the national high school math champion!</span></span></td></tr></tbody></table><br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-aZte34R4cDg/T9C5p4q7g3I/AAAAAAAAFGc/Kw8KqLUoo2o/s1600/allen+arml+2012+3+copy.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="http://3.bp.blogspot.com/-aZte34R4cDg/T9C5p4q7g3I/AAAAAAAAFGc/Kw8KqLUoo2o/s400/allen+arml+2012+3+copy.png" width="396" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><div style="text-align: left;"><span style="font-size: small;">Hundreds of mathletes and coaches applaud Allen as he walks down to center court at Penn State's Bryce Jordan Center. Allen's victory is all the more impressive because he is only an eighth grader. He attends Bay Trails Middle School in Penfield, New York, but he has already been excelling in math classes at the University of Rochester. He is currently attending the<a href="http://amc.maa.org/a-activities/a6-mosp/mosp.shtml"> Math Olympiad Summer Program</a>, along with high school students on this year's International Math Olympiad team and others considered strong prospects for future year teams. As a USA Math Olympiad qualifier every year since the fifth grade and a top-10 finisher at ARML since sixth grade, Allen has already compiled an extraordinary track record, yet he is an outstanding example of modesty and a generous spirit always willing to share what he knows with others.</span></div></td></tr></tbody></table><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: left;"><tbody><tr><td style="text-align: center;"><img border="0" height="203" src="http://4.bp.blogspot.com/-jvx7qX87aLQ/T9EG6v6zzXI/AAAAAAAAFG0/VzcPhfN3INQ/s400/arml+2012+coaches+copy.png" width="400" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><div style="text-align: left;"><span style="font-size: small;">Upstate NY All-Star Coaches Jen Vibber, Brenda Munch, and Tom Zink beam with pride as Allen becomes the newest member of their Upstate NY dynasty of national champions. </span><span style="font-size: small;">No other ARML team anywhere in the country (or world!) can boast about so many national champions. ARML went national in 1984. Since that time, 26 distinct<a href="http://arml.com/major_awards_tab/individual_winners.php"> individuals</a> have won ARML. </span><span style="font-size: small;"> </span><span style="font-size: small;"> Of those 26 champions, four are from the Upstate NY team:</span><span style="text-align: center;"></span></div><span style="font-size: small;"><br />Robert Kleimberg (1992)<br />Jeremy Bem (1993)<br />Aaron Pixton (2004)<br />Allen Liu (2012)</span></td></tr></tbody></table><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-UAV538MjWtc/T9DiiU4WD8I/AAAAAAAAFGs/XiAk7DaPfk4/s1600/allen+arml+2012+5+copy.png" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="400" src="http://2.bp.blogspot.com/-UAV538MjWtc/T9DiiU4WD8I/AAAAAAAAFGs/XiAk7DaPfk4/s400/allen+arml+2012+5+copy.png" width="387" /></a></td></tr><tr><td class="tr-caption" style="text-align: left;"><span style="font-size: small;">Coach Jen Vibber has been Allen's local coach throughout his middle school years, as well as a member of the Upstate NY Math Team coaching staff. She is also the incoming head coach for the Upstate NY Math Team. </span><span style="font-size: small;">That's outgoing Upstate NY head coach George Reuter looking over her shoulder in the photo! With the foundation built by George, Jen, and the other dedicated veteran coaches on the Upstate NY staff, we all know the Upstate NY team is in great hands going forward. </span><span style="font-size: small;">Thanks to all the tremendously dedicated coaches for the many hours of tireless work they put into creating an awesome community experience for mathematically passionate kindred spirit students all over Upstate NY. It is obviously a labor of love for each and every one of them, as they are all volunteers. They are outstanding teachers who inspire their mathletes with their character as well as their knowledge of problem-solving methods.</span><br /><br /><div style="text-align: center;"><span style="font-size: large;">2012 Upstate NY Math Team Coaching Staff:</span></div><br /><div style="text-align: center;"><br /><span style="font-size: small;">George Reuter (<a href="http://teachersites.schoolworld.com/webpages/MCML/">MCML</a>/Canandaigua Academy) </span><br /><span style="font-size: small;">Doug Becker (MCML/Gates-Chili HS), Treasurer</span><br /><span style="font-size: small;">Brenda Munch (MCML/Brighton High School)</span><br /><span style="font-size: small;">Patty Pragel (MCML/Greece Arcadia High School)</span><br /><span style="font-size: small;">Jen Vibber (MCML/Penfield High School)</span><br /><span style="font-size: small;">Glen Stephenson (Corning West High School)</span><br /><span style="font-size: small;">Tom Zink (AAMC/MicroStrategy)</span><br /><span style="font-size: small;">Bill Babbitt (AAMC/RPI)</span><br /><span style="font-size: small;">Rita Biswas (AAMC/UAlbany)</span></div><span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;"></span></span></span></span><br /><div style="text-align: center;"><span style="font-size: small; text-align: left;"><br /></span></div><span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;"></span></span></span><br /><div style="text-align: left;"><span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;">(If you would like to learn more about the "Parent Function" cited on the Upstate NY team t-shirts, check out <a href="http://pballew.blogspot.com/2009/05/functions-parents-and-parent-functions.html">Pat Ballew's blog post describing the fascinating history of the term's usage</a>.)</span></span></span></div><span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;"></span></span></span></td></tr></tbody></table><div><br /></div><div class="separator" style="clear: both; text-align: center;"></div>Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com4tag:blogger.com,1999:blog-4479690110975267663.post-64167666498668192312012-05-21T20:10:00.001-07:002012-05-26T06:33:12.136-07:00NY team scales new heights at MATHCOUNTS Nationals<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-WjJhU4Q_bQk/T7r5uGmeogI/AAAAAAAAFCg/zR__fyhiWCo/s1600/roller+coaster.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="http://3.bp.blogspot.com/-WjJhU4Q_bQk/T7r5uGmeogI/AAAAAAAAFCg/zR__fyhiWCo/s400/roller+coaster.png" width="330" /></a></div><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />The New York State MATHCOUNTS team raised the bar to the highest heights in recent memory with a fourth place finish at the National MATHCOUNTS competition held in Orlando, Florida last week. The photo above shows the team celebrating on <a href="http://disneyworld.disney.go.com/parks/animal-kingdom/attractions/expedition-everest/">Expedition Everest</a> at Disney World after the contest.<br /><br />Three-year team veteran <b>Allen Liu</b> from the Rochester area reached the National Countdown for the third consecutive year, the first New Yorker ever to accomplish this feat, and reached the semifinals for a top four individual finish. <br /><br />Albany Area Math Circle's own <b>Alex Wei</b> had one of the best finishes ever for an Albany Area mathlete, coming in a very impressive 18th place among the 224 national finalists. Alex's first MATHCOUNTS coach, who launched him on his way back when he was in sixth grade, was another former national mathlete from the Albany Area, <a href="http://albanyareamathcircle.blogspot.com/2010/02/dave-bieber-heart-of-albany-area-math.html">Dave Bieber</a>. (Dave, in turn, had been coached by yet another former national mathlete from the Albany Area, founding AAMC member Alison Miller, when he was in sixth grade!)<br /><br />For the first time anyone can recall, all four members of the team, which also included two-time veteran <b>Peter Mizes</b> from the Rochester area and <b>Calvin Lee</b>, the Manhattan MATHCOUNTS chapter champion, all earned top 56 recognition. Most impressively of all, they were able to come in very strong on the collaborative team round, allowing their team to rank higher than the traditional powerhouse states of California and Texas. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-ngvHLXeq7OQ/T7sBZEd2KNI/AAAAAAAAFCo/mnZ0kbznglA/s1600/ny+team+mathcounts+2012.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="193" src="http://3.bp.blogspot.com/-ngvHLXeq7OQ/T7sBZEd2KNI/AAAAAAAAFCo/mnZ0kbznglA/s400/ny+team+mathcounts+2012.png" width="400" /></a></div><br />Because of the very large distances separating the mathletes and the fact that there is no travel budget to enable the team to practice together as a team prior to nationals, the students seized the initiative, took ownership of their learning, and organized their own on-line collaborative practices prior to nationals, without requiring adult assistance. Essentially, they coached themselves. The team clearly made New York State proud in many ways--their friendly collaborative work together carried on a fine tradition to new heights and surely will inspire future mathletes from our state to new heights, as they stand on the shoulders of these mathematically collaborative and resourceful giants.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-0D5iygbYPXU/T7sCaM0e0eI/AAAAAAAAFCw/Z7v0qETY_Oo/s1600/team+at+dinner.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="127" src="http://1.bp.blogspot.com/-0D5iygbYPXU/T7sCaM0e0eI/AAAAAAAAFCw/Z7v0qETY_Oo/s400/team+at+dinner.png" width="400" /></a></div><br /><br /><br /><br /><br /><br /><br /><br />If you would like to see the problems they tackled, you can find them posted on the Art of Problem Solving discussion forum <a href="http://www.artofproblemsolving.com/Forum/viewforum.php?f=132">here</a>. One of my favorite problems from this year's national contest is <a href="http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=479988">here</a>--it is a beautiful illustration of how probability problems can often be solved by viewing them as geometry problems.Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-1615434538061494062012-05-06T09:14:00.003-07:002012-05-06T21:10:53.452-07:00Guerrilla Math Circles brainstormingDan Zaharapol, the founding director of the extremely awesome <a href="http://www.artofproblemsolving.org/spmps/">Summer Program in Mathematical Problem Solving</a> (SPMPS), has been blogging about <a href="http://considerlearning.com/2012/05/04/low-cost-high-impact-ways-to-spread-math-opportunity/">low-cost high impact ideas to spread math opportunity</a>. <br /><br />Now, if you don't already know about Dan's program, you should definitely <a href="http://www.artofproblemsolving.org/spmps/">check it out</a>, especially the link to the nice <i>New York Times</i> article covering the program, <i><a href="http://www.nytimes.com/2011/07/28/nyregion/a-sleepaway-camp-for-low-income-ny-math-whizzes.html">A Sleepaway Camp where Math is the Main Sport</a></i>.<br /><br />But, as Dan acknowledges in his post, although the program is terrific and serves a historically very underserved population (inner city middle school students), its reach is very small due to the expense and logistics involved in running a residential summer program. The program started with 20 students last summer and--after a major fundraising effort led by its sponsors at Art of Problem Solving, the program will double in size to 40 students this summer.<br /><br />And even if there were funds to serve every middle schooler, the problem is that we need outreach to children long before they reach middle school age, long before they are ready to head off to a residential summer program.<br /><br />And, as Dan writes:<br /><br /><blockquote><i>Too many students are ready to do more mathematics but </i></blockquote><blockquote><ul><li><i>do not know where to do it, and</i></li><li><i>do not even know that such opportunities exist or that they should be doing it. </i></li></ul></blockquote><blockquote><i>The students don’t know; their parents don’t know; their teachers don’t know. They have no way to discover that their peers, successful math students from other communities, do more than just what they see in school. </i></blockquote><blockquote><i>It’s not just that they need to be told about it; it needs to be part of their culture. It’s not just that they must know that such programs exist and that successful people do them; they should feel it is expected of them, that lots of people they’ve known and admired do math beyond school. </i></blockquote><blockquote><i>How can we possibly create this culture and community where it does not already exist?</i></blockquote>This is exactly the same problem that I have been thinking about for years, but <a href="http://albanyareamathcircle.blogspot.com/2012/04/guerrilla-math-circles-math-super.html">three weeks ago at the Julia Robinson Math Festival</a>, a brainstorm hit me, which I have been calling Guerrilla Math Circles.<br /><br />What do I mean by Guerrilla Math Circles? The idea for the name comes from <a href="http://en.wikipedia.org/wiki/Guerrilla_marketing">guerrilla marketing</a>, which in turn originated with guerrilla warfare. It is all about low-cost, informal, unconventional, low overhead, and non-bureaucratic approaches. It is all done on a shoestring, small scale, but very easy to replicate, emulate, and improve by trial and error and sharing on blogs, videos, and social media.<br /><br /><b><span style="font-size: large;">How</span></b> do Guerrilla Math Circles happen?<br /><br />Guerrilla Math Circles do not involve signing kids up for anything. They do not involve any kind of custodial responsibility for the children--because they happen in places and times where and when children are already with their parents or caretakers. They do not require parents to take their children to any particular special places where they would not already be going.<br /><br />Basically, the guiding principal of Guerrilla Math Circles is we bring the same kind of fun engaging low-cost activities done at Julia Robinson Math Festivals to places where the children who need them most already are. And we do it on a shoestring, including elements of math as performance art on the street and math as theatrical improv or maybe even flashmobs. They are low-tech and high touch, person-to-person and interactive. <br /><br />Remember <a href="http://www.pbs.org/marktwain/learnmore/writings_tom.html">Tom Sawyer whitewashing the fence</a> and how he convinced all his friends that this would be a fun thing to do? That's kind of the spirit of Guerrilla Math Circles. Start doing some interesting math in a highly visible public place in a way that invites others to join in.<br /><br />Another inspiration for Guerrilla Math Circles comes from the long-time example of chess outreach programs in public parks and other public spaces. In our area, the local chess club sponsors a "<a href="http://blog.timesunion.com/yourday/chess-under-the-marquee-returns-monday-in-schenectady/3074/">Chess under the Marquee</a>" program under the marquee of Proctor's Theater in downtown Schenectady. The marquee provides shelter from sun and rain and the broad sidewalk provides space to set up tables for drop-in folks to engage in pickup chess games. Why not ask Proctor's if we can have "Math under the Marquee" at another time or day?<br /><br />My head is virtually exploding with ideas--they come to me faster than I have had time to organize them all, so I will just use this post to add them as I have time to do so.<br /><br /><b><span style="font-size: large;">Where</span> </b>can Guerrilla Math Circles happen?<br /><br />urban playgrounds<br />urban parks, especially those that serve free lunches in the summer<br />urban swimming pools<br />urban street festivals<br />urban farmer's markets<br /><br />urban daycare programs<br />urban libraries<br /><br />waiting rooms at social services agencies (where parents often may have bored children in tow, and would be happy to have them entertained while they wait)<br /><br />urban bus stops (where parents may also be stuck waiting with bored children in tow)<br /><br />Places where children are with their parents are especially good, because we have the opportunity to get parents as well as children engaged!<br /><br /><b><span style="font-size: large;">What </span></b>can happen at a Guerrilla Math Circle?<br /><br />Use simple materials (paper, yarn, beads) to make beautiful polyhedra using the ideas from <a href="http://geometricdelights.com/">Geometric Delights</a>. Or use balloons and <a href="http://vihart.com/balloons/">these ideas</a> from Vi Hart's blog.<br /><br />Introduce kids to the unsolved "Million Dollar Math Problems" at <a href="http://mathpickle.com/">mathpickle.com</a>--again, these typically require only simple materials like sidewalk chalk or dice. (Two of the million dollar math problems have special local resonance for our neck of the woods. A <a href="http://www.mathpickle.com/K-12/MathPickle_Podcast/Entries/2010/8/19_Grade_3_$1,000,000_Unsolved_Problem.html">mathpickle problem</a> accessible to 7 or 8-year olds introduces the ideas behind the Graceful Tree Conjecture, which is related to our own <a href="http://albanyareamathcircle.blogspot.com/2008/10/congratulations-professor-moorthy.html">Professor Krishnamoorthy</a>'s research. I'll be blogging about this soon. <a href="http://www.mathpickle.com/K-12/MathPickle_Podcast/Entries/2011/1/12_Grade_6_$1,000,000_Unsolved_Problem.html">Another mathpickle game</a> accessible to slightly older children introduces them to the ideas behind the RSA algorithm. Ron Rivest, the "R" in RSA, attended a local high school, located in the affluent and highly educated suburban town where our math circle holds its weekly meetings. A number of our current math circle students come from that town, and other students in our math circle come from affluent and highly educated towns up to 45 minutes or an hour away at rush hour. But just ten minutes away from our regular meeting place at Ron Rivest's old high school are desperately poor neighborhoods, filled with children whose parents have limited and largely negative experiences with formal education, neighborhoods which have never sent a single student to our math circle--and those are the students who most need our outreach efforts!)<br /><br />Share/read aloud mathematical picture books like <a href="http://books.google.com/books?id=Qp0iQwAACAAJ&dq=inauthor:%22Masaichiro+Anno%22&hl=en&sa=X&ei=QeKmT-iZLOaV6AHrmZGcBA&ved=0CD0Q6AEwAA">Anno's Mysterious Multiplying Jar</a> or <a href="http://marysmath.blogspot.com/2008/10/power-of-books.html">Melisande</a> or The King's Chessboard or <a href="http://books.google.com/books?id=TxOGHAAACAAJ&dq=powers+of+ten&hl=en&sa=X&ei=Z-2mT46LOsb56QGd7bSwBA&ved=0CEAQ6AEwAQ">Powers of Ten</a>. Use simple props to draw kids into acting out the roles.<br /><br />Tell stories about famous mathematicians (like Archimedes and the bathtub or Gauss and the evil Prussian schoolmaster--admit they might be aprocryphal but there is math involved!) or read mathematical poetry (Theoni Pappas' <a href="http://books.google.com/books/about/Math_Talk.html?id=4QLRqp41qrgC">Math Talk: mathematical ideas in poems for two voices</a> is great fun!) or sing mathematical songs (like <a href="http://divisbyzero.com/2009/09/05/tom-lehrers-math-songs/">these</a> from Tom Lehrer) or get children acting out little skits involving logic problems like <a href="http://www.mathcircles.org/content/island-blue-and-brown-eyes">this</a>.<br /><br />Give a child a large sheet of newspaper and challenge the child to see how many times they can fold it in half--then talk about powers of two and why it is so hard to fold with regular paper. (Until ten years ago, it was thought to be impossible to fold more than seven times, but then a high school student in California managed to surprise everyone by getting to 12 folds, and just last year a group of Massachusetts high school students and their advisor set <a href="http://www.newscientist.com/blogs/nstv/2012/01/paper-folding-limits-pushed.html">a new record at 13 folds</a>, but they had to use over half a mile of very thin toilet paper.) Then, get them thinking about an allowance that starts at a penny a week--and doubles every week. Supposing their dad is Bill Gates or Warren Buffett, how long before their allowance bankrupts him? (Give them a long strip of adding machine tape and a pencil and get them to start doubling. This is also fun to do with sidewalk chalk.)<br /><br />Speaking of pennies, you could start a kid flipping pennies and charting strings of heads and tails and finding patterns. Or casting dice and charting totals and discovering that not all totals come up equally often (and figuring out why that's true--and some of the implications for which properties are the best investments in Monopoly, along the <a href="http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml">lines here</a>.) You could also teach kids how to play a fun game called <a href="http://albanyareamathcircle.blogspot.com/2009/11/prime-number-monopoly.html">Prime Number Monopoly</a> or <a href="http://albanyareamathcircle.blogspot.com/2009/07/hangmath.html">HangMath</a>. (Hmm, and we could actually talk about the mathematics of lottery probabilities right in the shadow of the New York State lottery headquarters, which are located in downtown Schenectady!)<br /><br /><b><span style="font-size: large;">Who</span></b> can make guerrilla math circles happen?<br /><br />anyone with a love of recreational mathematics and a willingness to share it! That would be all kinds of folks--for starters, the students in formal math circle programs like ours, college and high school math clubs, their friends, supporters, and advisors.<br /><br />Okay--enough. It is a beautiful spring day and the Schenectady Green Market has finally moved outdoors! It is calling my name so I can scope it out for possibilities for our Guerrilla Math Circle initiatives. Here is a video created by a Union College student that captures a little of the vibrant spirit of the Schenectady Green Market atmosphere and suggests why it might be a good place for guerrilla math circle activities:<br /><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.youtube.com/embed/21FjsoZd8KM?feature=player_embedded' FRAMEBORDER='0' /></div><br /><br />More later about the details!Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com4tag:blogger.com,1999:blog-4479690110975267663.post-8743380738158116592012-05-03T11:04:00.000-07:002012-05-03T11:06:35.886-07:00Hats off to the NYSSPE!<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-GrGPZVjwxEA/T6LFtag8JaI/AAAAAAAAE9E/CSGOpM_J4O4/s1600/nysspe+copy.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="78" src="http://1.bp.blogspot.com/-GrGPZVjwxEA/T6LFtag8JaI/AAAAAAAAE9E/CSGOpM_J4O4/s400/nysspe+copy.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Albany Area Math Circle is grateful to the <a href="http://www.nysspe.org/">New York State Society of Professional Engineers</a> for their donation to supporting our students selected for the AllStar Upstate New York Math Team, which will represent Upstate New York at the national high school championships early next month.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">NYSSPE is a particularly awesome sponsor for our Upstate NY AllStar Math Team high school students because the Professional Engineers are also founding sponsors of MATHCOUNTS and run the chapter and state programs which gave many of our local students their initial taste of the excitement of math team experiences. We are also very happy to report that many of our high school students have continued their involvement with MATHCOUNTS by volunteering to coach middle school math teams. </div><div class="separator" style="clear: both; text-align: center;"><br /></div><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-75068012922160845022012-04-29T14:11:00.002-07:002012-04-30T03:06:35.046-07:00Keeping math contests in perspectiveIt is sometimes easy to lose sight of the fact that math contests are meant to be fun and engaging, but not ultimate ends in and of themselves.<br /><br /> The main value of math contests is not to be found in the honors and awards (which are very nice, of course, but somewhat beside the point). The main value of math contests is to be found in wonderful mathematics it can draw students into discovering. Not only do they discover mathematics, but they can also discover the joys of working hard towards shared goals with a community of kindred spirits.<br /><br /> Math contests are a little bit like mountain climbing. The views from the top are nice, but even spectacular views do not justify the extreme efforts it can take to get there. What can justify those mountain-climbing efforts are the joys of the journey, especially if shared along with others, and the beautiful things you can learn about the natural world and the power within yourselves as you help one another to discover hidden potentials and problem solving abilities within you that you did not know existed.<br /><br />Just as you should "stop and smell the flowers" as you climb the mountain, so too should you remember to "savor the problems" you encounter in math competitions. By construction, those contest problems have already been solved, but reflecting on them after the contests are over may inspire you to create new and fresh ones of your own devising--or you may discover exciting new ways to solve old problems.<br /><br /> A recently revived discussion on the Art of Problem Solving discussion forums reminded me of a <a href="http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=280673">remarkable essay</a> written three years ago by a student on his contest experiences, which has resonated with many readers. The essay is very moving, thoughtful, and beautifully written. Both the essay (linked in the first post on the thread) and the discussion which followed it are readings that I would highly recommend to students, parents, and math teachers and coaches.<br /><br />I would also recommend reading an inspiring <a href="http://mathprizeforgirlscommunity.blogspot.com/2012/02/wise-and-heartfelt-words-from-our.html">speech</a> given by our alumna speaker at Math Prize for Girls last fall, which also addresses these issues, and gives some excellent advice well worth bearing in mind for making the most of your math contest adventures. <br /><br />You may also want to explore the links to the authors' blogs, which discuss some of the wonderful mathematics they have been inspired to learn and share with others. There is more recommended reading on these topics <a href="https://sites.google.com/site/mathcircle/inspiring-stories">here</a>. Some of our older alumni may also find <a href="https://docs.google.com/viewer?url=http%3A%2F%2Fwww.math.missouri.edu%2F~pete%2Fpdf%2Fteach%2F140.MAA.pdf">useful advice and insights in a similar vein here</a>.Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com1tag:blogger.com,1999:blog-4479690110975267663.post-25854243506111569982012-04-23T10:52:00.000-07:002012-04-23T13:13:09.382-07:00Drawing new circles<span style="font-family: inherit;">The folks at the <a href="http://www.fussonline.org/index.php?option=com_content&view=section&id=1&Itemid=2">First Unitarian Society of Schenectady</a> celebrate this poem:</span><br /><blockquote class="tr_bq"><span style="font-size: large;"><span style="font-family: 'Bookman Old Style', Georgia, 'Times New Roman', Verdana, Calibri, serif;">He drew a circle that shut me out</span><span style="font-family: 'Bookman Old Style', Georgia, 'Times New Roman', Verdana, Calibri, serif;">—</span> </span></blockquote><blockquote class="tr_bq"><span style="font-family: 'Bookman Old Style', Georgia, 'Times New Roman', Verdana, Calibri, serif; font-size: large;">Heretic, rebel, a thing to flout.</span></blockquote><blockquote class="tr_bq"><span style="font-size: large;"><span style="font-family: 'Bookman Old Style', Georgia, 'Times New Roman', Verdana, Calibri, serif;">But Love and I had the wit to win:</span> </span></blockquote><blockquote class="tr_bq"><span style="font-family: 'Bookman Old Style', Georgia, 'Times New Roman', Verdana, Calibri, serif; font-size: large;">We drew a circle that took him in!</span> </blockquote><blockquote class="tr_bq"><blockquote class="tr_bq"><span style="font-family: 'Bookman Old Style', Georgia, 'Times New Roman', Verdana, Calibri, serif;">— "Outwitted" </span><span style="font-family: 'Bookman Old Style', Georgia, 'Times New Roman', Verdana, Calibri, serif;">— Edwin Markham</span></blockquote></blockquote>This poem resonates with me in many ways, but today I want to focus on the way it connects to my vision for guerrilla math circles. <span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Many people feel "shut out" of the mathematical community. They see math as a superpower that others have but that they hopelessly lack. They can't imagine math as a joyful and empowering activity, as hard yet rewarding work. They see the world as divided into non-intersecting circles of "People who can do math," and "People who can't do math." They place themselves squarely in the latter and can't imagine that they could ever find joy and empowerment in visiting the other circle. They may even be inclined to disparage or make fun of others who claim to enjoy math.</span><br /><br /><span style="font-family: inherit;">Can we find a way to draw math circles in a way that draws those folks in? I think we can. That is where my concept of "Guerrilla Math Circles" come in.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">To be continued ...</span>Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-29119373726696787772012-04-23T10:23:00.001-07:002012-04-23T11:13:34.737-07:00Guerrilla Math Circles, Math Super Powers, Math as Performance Art, and Math for the 99%?<img height="400" src="https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-ash3/554462_10150775694320419_153302905418_9761008_935574540_n.jpg" width="349" /><br /><br />I love the dual messages encoded in the T-shirt logo design above:<br /><br /><ul><li>Math is a superpower!</li><li>Share with it with everybody! <br />(<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 13px; line-height: 19px;">∀ </span>is a mathematical symbol that means "for all.")</li></ul><div>If you also love this logo (designed by mathematician <a href="http://www.math.wustl.edu/~ct/">Cindy Traub</a> of the always awesome St. Mary's College <a href="http://www.smcm.edu/mathcs/">math department</a>), please <a href="https://www.facebook.com/questions/10150775715655419/">go here</a> to vote for it. If the design wins the contest, then mathematicians from all over the country attending this summer's <a href="http://www.maa.org/mathfest/">Math Fest</a> will get t-shirts with this logo, and I think it would be outstanding to have this message spread far and wide.</div><div><br /></div><div><a href="http://mathbabe.org/">Mathbabe</a> has been blogging about how math is a superpower, and that wonderfully evocative and inspirational phrase has been reverberating around in my head ever since I encountered it for the first time on her blog.</div><div><br /></div><div>Those messages especially reverberated in my head last weekend, when I was in Washington, DC helping out at the <a href="http://www.msri.org/web/msri/static-pages/-/node/288">Julia Robinson Math Festival</a> held at the Smithsonian during the <a href="http://www.msri.org/web/msri/scientific/workshops/all-workshops/show/-/event/Wm9446">Math Circles on the Road</a> event. </div><div><br /></div><div>You will have to forgive me--my head is truly exploding with all the inspiration and ideas I brought away from that experience, so this post (and most likely my next few posts) will be rambling all over the place as I share them. A giant brainstorm hit me at the end of the weekend, a new concept I will call "Guerrilla Math Circles," which I will explain in a later post. I will get there...I promise.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-VoFC3Emlxx4/T5Vr7SyB7uI/AAAAAAAAE5M/j8QpRxki9YY/s1600/circles+on+road+2012.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-VoFC3Emlxx4/T5Vr7SyB7uI/AAAAAAAAE5M/j8QpRxki9YY/s320/circles+on+road+2012.jpg" width="247" /></a></div><div>The event at the Smithsonian was really wonderful, with 60 enthusiastic math circle leaders from all over the country (including Elizabeth Parizh and myself from Albany Area Math Circle) helping to run free and fun public math circle demonstration activities for hundreds of enthusiastic participants.</div><div><br /></div><div>There was a strong theme of "math as performance art" running through many of the sessions, including <a href="https://docs.google.com/document/d/1UA81Y-bVd8Qdl9jjQXOCkTXjM2ehsVnYx6-2IChonAk/edit">the one</a> that <a href="http://albanyareamathcircle.blogspot.com/2011_06_01_archive.html">Elizabeth</a> and I helped <a href="http://assagames.com/nas/Teachers.html">Anna Burago</a> to run, along with <a href="http://www.artofproblemsolving.com/School/index.php?page=school.instructors">Ashley Reiter Ahlin</a>, <a href="http://www.ece.ucsb.edu/~parhami/">Berhrooz Parmani</a>, Yulin Qing, and <a href="http://www.wickedlocal.com/melrose/news/lifestyle/x1870693823/Roosevelt-School-program-aims-to-make-math-fun#axzz1ssSzc3ZH">Jack Reynolds</a>. We engaged a group of students (around 8 or 9 years old) in acting out mathematical logic problems set on an island inhabited by Knights (who always tell the truth), Liars (who always lie), and Tourists (who can go either way.) Simple props (leis for the tourists and pennants bearing a K or an L for the knights and liars) added greatly to the engagement of the event. (The kids loved waving the pennants--and it was a really nice way to get their heads inside the logic exercise. We had originally intended to use paper hats bearing K or L, but after consideration of hygiene/sanitation issues that could arise from switching hats around, we decided to go with pennants instead. Props to my ever-resourceful 80-year-old problem-solving mother for suggesting that chopsticks leftover from takeout orders work much better than drinking straws for constructing inexpensive pennants! The kids loved waving the pennants around so much that drinking straws would have quickly drooped.)</div><div><br /></div><div>Another great session I had the chance to observe also involved math as performance art. Blake Thornton of the <a href="http://www.dehn.wustl.edu/~blake/circles/">Washington University in St. Louis Math Circle</a> adapted an idea from Terry Tao's blog into a great session on the <a href="http://www.mathcircles.org/content/island-blue-and-brown-eyes">Island of the Blue and Brown Eyes</a>. (Again, it was fascinating to see what a difference the use of a simple but concrete prop made with the young children, who were acting out the roles of islanders trying to reason through a problem of inferring their own "eye-colors" based on their observations of the "eye-colors" they observed on the other islanders along with a remark made by a clueless tourist who did not understand the island's taboo against discussing eye color. In the first run of this activity, Blake and his assistants gave each child an index card that told the child how many of the other islanders in the room had blue eyes, and how many of the other islanders had brown eyes. In the second run of the activity, Blake and his assistants asked all the children to close their eyes as they placed a colored sticker on each child's forehead to designate that child's "eye color". When the children were told to open their eyes, they could then immediately observe the eye color of all the other islanders. This very simple expedient worked *much* better for the students involved, and I was really impressed at the way the children were then able to reason through the problems presented to them.)</div><div><br /></div><div>I also got the chance to observe a <a href="http://www.mathcircles.org/content/wrangle">Math Wrangle</a> organized by <a href="http://www.awm-math.org/biographies/contest/tatianashubin2004.html">Tatiana Shubin</a> from the <a href="http://www.sanjosemathcircle.org/">San Jose Math Circle</a>. The wrangle involved six very impressive young members of the <a href="http://www.fairfax-mathcircle.org/">Fairfax Math Circle</a>, who wore awesome t-shirts bearing a translation of a famous quote from Georg Cantor as they wrangled in front of an adult audience awed by their poise in presenting their mathematical reasoning.</div><div><br /></div><div>Their shirts said: "The essence of mathematics of mathematics is its freedom."</div><div><br /></div><div>Freedom...yes, freedom and free were more words that reverberated in my head last weekend. Math is free--you can do it with scratching in the sand or dirt (as Archimedes did) or even just in your head (as prisoners of war have done in order to maintain their sanity) or with the simplest of materials such as stones or paper and string or colored sidewalk chalk.</div><div><br /></div><div>And I was troubled by that message.</div><div><br /></div><div>Why?</div><div><br /></div><div>Turnout at the free math festival and at the nearby free <a href="http://www.si.edu/Exhibitions/Details/MathAlive-4731">Math Alive! </a>exhibit at the Smithsonian was excellent. It was a beautiful spring day with a Cherry Blossom Parade that had brought huge crowds downtown. </div><div><br /></div><div>There were thousands of children eagerly passing through the Math Alive! exhibits, with hundreds of them checking into our math festival and staying to participate in an activity or game with us.</div><div><br /></div><div>So why was I troubled?<br /><br />Because, among the hundreds of students that I personally observed passing through the festival and the museum that day I did not see a single African-American child visit our festival--and this in a city where the overwhelming majority of public school students are African-American and where the <a href="http://www.washingtonpost.com/local/education/dc-schools-have-largest-black-white-achievement-gap-in-federal-study/2011/12/06/gIQArNnMcO_story.html">black-white educational gap is the greatest in the country</a>. (I did hear a report from other attendees that they did see a few African-American students attending, but there was general agreement that they were very few in number.)</div><div><br /></div><div>We were at the Smithsonian in a FREE math festival, held in a FREE museum, on a national mall surrounded by monuments and memorials in the capital of a country that cherishes FREEDOM. Our society is far from perfect, and yet it represents a beacon of freedom and opportunity to the entire world. The free museums of the Smithsonian and our free-to-the-public math festival were emblematic of that freedom. </div><div><br /></div><div>The newest memorial celebrating freedom near the national mall just opened last fall, the Martin Luther King Memorial. For me, it brought back many memories of my childhood growing up in Washington, DC in the 1960s. I spent much of the summer of 1963 at my grandmother's apartment, where she was dying of cancer, and tenderly cared for by a much-beloved African-American woman. I still remember us sitting together in the living room as we watched the black-and-white television in awe of the vast crowds assembled on the mall downtown and heard Martin Luther King's powerful words reverberate: "Free at last! Free at last! Thank God Almighty, we are free at last!" </div><div><br /></div><div>I too have a dream. And it began to take concrete shape last weekend as I contemplated all these memories that reverberated in my head last weekend in Washington, DC.</div><div><br /></div><div>To be continued....</div>Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com2tag:blogger.com,1999:blog-4479690110975267663.post-57047298795552445392012-03-26T09:04:00.000-07:002012-03-26T11:34:32.333-07:00"Dumb" questions and STEM bullies<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-7x2WJ4UnDOw/T3CJET2XgrI/AAAAAAAAErM/aBEuTSgyknA/s1600/220px-Daphne_Koller_(3275989960).jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://2.bp.blogspot.com/-7x2WJ4UnDOw/T3CJET2XgrI/AAAAAAAAErM/aBEuTSgyknA/s1600/220px-Daphne_Koller_(3275989960).jpg" /></a></div><br /><br />I hasten to point out that the folks in these pictures are most definitely NOT bullies!<br /><br /><a href="http://4.bp.blogspot.com/-pqReqgcsEgg/T3CFRVzv0-I/AAAAAAAAErE/fNvvrNQJU4c/s1600/sebastian+peter.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-pqReqgcsEgg/T3CFRVzv0-I/AAAAAAAAErE/fNvvrNQJU4c/s320/sebastian+peter.png" width="164" /></a><br /><br /><br />They are the Stanford professors who have been teaching some wonderful on-line classes that I have been taking this year. In the fall, I took <a href="https://www.ai-class.com/">Introduction to Artificial Intelligence</a> with Professors Peter Norvig and Sebastian Thrun. (They were amazing. Among other things, Prof. Thrun headed the Stanford team that designed and built the driverless car that won the DARPA desert challenge. He has an inspiring <a href="http://www.ted.com/talks/sebastian_thrun_google_s_driverless_car.html">Ted Talk</a> that I highly recommend.) Now I am taking <a href="https://class.coursera.org/pgm/class/index">Probabilistic Graphical Models</a> with Professor Daphne Koller. (Her photo above is from <a href="http://en.wikipedia.org/wiki/Daphne_Koller">wikipedia</a>. This <a href="http://www.nytimes.com/2008/05/03/technology/03koller.html">NYT article</a> tells a bit more about the cool work she does.)<br /><br />There are tens of thousands of students all over the world taking these classes along with me, and students helping one another on the course discussion boards has been an essential and exciting part of the learning process. <br /><br />There is absolutely no way that Professors Thrun, Norvig, and Koller or the few official teaching assistants who help them could answer all our questions. There are so many unanticipated sources of confusion and technical difficulties (for example, some students live in countries where they use commas instead of periods to denote decimal points, people are using many different operating systems on their computers, for many students English is a second language, etc.) I am once again struck by the spirit of generosity among my classmates. While observing the rules of the Stanford Honor Code (which prohibit giving help on the substantive content of graded homework assignments), my classmates have generously provided assistance in dealing with various technical issues that have arisen with downloading and installing and running the required software. This has been very helpful to many of us.<br /><br />However, very occasionally there is an obnoxious comment posted on the discussion boards making a snide remark such as "Anyone who asks such a dumb question clearly does not belong in this class."<br /><br />I cringe when I read remarks like these. I think of the people who make such posts as STEM bullies.<br /><br />My feeling is that the askers of the questions DO belong in the course. The ones who do NOT belong are those who put others down for asking "dumb questions". <br /><br />I feel the same way about our math circle as I do about the on-line classes I am taking.<br /><br />Thus, I was heartened to read this powerful post on the subject of "dumb questions" by Professor Thrun--it captures my own beliefs so well that I wanted to share it--I will be reading this aloud at this Friday's math circle:<br /><br /><blockquote class="tr_bq"><span style="font-size: large;"><i>I really hope that this new digital medium makes it easier to ask "stupid" questions. Let me report on myself. I work with a 200+ people team at Google (reporting into me), I co-founded Udacity, I am an authority in my area of research. I ask many many "stupid" questions. I have learned that asking questions is power. The problem is if others respond to such questions with "you should have known." People rarely do this to me, but they do this to my students. I really dislike this, and I usually confront them. We should remember that there is NO learning without asking questions. In this class, there are people with many different levels of knowledge and skills. What brings us together at this point is that we are all 100% dedicated to make this class. be kind. Reach out to people asking questions whose answer appears trivial to you. Be a friend. And make a friend. remember the question that seems obvious to you once was non-obvious to you. You find that people respect you for being kind. Being kind is one of the highest levels of achievement. I will respect you for it, and so will the people around you. There will come the day when you are asking the stupid question - and you will appreciate the kindness of others.</i></span></blockquote>Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-15393139509699742032012-03-03T10:16:00.003-08:002012-03-03T16:26:29.544-08:00Young student honorsThe American Mathematics Competition has a special national public honor list for students who score high on a contest designed for older students. <br /><br />Congratulations to the following students who made those national honor lists this year:<br /><br /><b>AMC12A:</b><br />(Students in tenth grade or below with scores over 90)<br /><span style="background-color: cyan;">Cecilia Holodak (Niskayuna HS) 99</span><br /><br /><br /><b>AMC12B:</b><br />(Students in tenth grade or below with scores over 90)<br /><span style="background-color: cyan;">Matt Gu (Guilderland HS) 93</span><br /><br /><br /><b>AMC10A:</b><br />(Students in eighth grade or below with scores over 90)<br /><br /><table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 390px;"> <colgroup><col span="2" style="width: 48pt;" width="64"></col> <col style="mso-width-alt: 4900; mso-width-source: userset; width: 101pt;" width="134"></col> <col span="2" style="width: 48pt;" width="64"></col> </colgroup><tbody><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt; width: 48pt;" width="64"><br /><table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 326px;"> <colgroup><col span="2" style="width: 48pt;" width="64"></col> <col style="mso-width-alt: 4900; mso-width-source: userset; width: 101pt;" width="134"></col> <col style="width: 48pt;" width="64"></col> </colgroup><tbody><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt; width: 48pt;" width="64"><span style="background-color: cyan;">Alex</span></td> <td style="width: 48pt;" width="64"><span style="background-color: cyan;">Wei</span></td> <td style="width: 101pt;" width="134"><span style="background-color: cyan;">Van Antwerp MS</span></td> <td align="right" style="width: 48pt;" width="64"><span style="background-color: cyan;">127.5</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">William</span></td> <td><span style="background-color: cyan;">Wang</span></td> <td><span style="background-color: cyan;">Farnsworth MS</span></td> <td align="right"><span style="background-color: cyan;">123</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Patrick </span></td> <td><span style="background-color: cyan;">Chi</span></td> <td><span style="background-color: cyan;">Iroquois MS</span></td> <td align="right"><span style="background-color: cyan;">120</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Ziqing</span></td> <td><span style="background-color: cyan;">Dong</span></td> <td><span style="background-color: cyan;">Farnsworth MS</span></td> <td align="right"><span style="background-color: cyan;">117</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Junsu</td> <td>Park</td> <td>Albany Academies</td> <td align="right">113</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Andrei</span></td> <td><span style="background-color: cyan;">Ahkmetov</span></td> <td><span style="background-color: cyan;">Van Antwerp</span></td> <td align="right"><span style="background-color: cyan;">105</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Liam</span></td> <td><span style="background-color: cyan;">McGrinder</span></td> <td><span style="background-color: cyan;">Van Antwerp</span></td> <td align="right"><span style="background-color: cyan;">105</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Gideon</span></td> <td><span style="background-color: cyan;">Schmidt</span></td> <td><span style="background-color: cyan;">Iroquois MS</span></td> <td align="right"><span style="background-color: cyan;">102</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Jason</span></td> <td><span style="background-color: cyan;">Tang</span></td> <td><span style="background-color: cyan;">Van Antwerp</span></td> <td align="right"><span style="background-color: cyan;">100.5</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Chenyang</td> <td>Wang</td> <td>Shaker JHS</td> <td align="right">99</td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Alex</span></td> <td><span style="background-color: cyan;">Cao</span></td> <td><span style="background-color: cyan;">Shaker JHS</span></td> <td align="right"><span style="background-color: cyan;">93</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Luke</td> <td>Lubel</td> <td>O'Rourke MS</td> <td align="right">90</td> </tr></tbody></table></td><td style="width: 48pt;" width="64"><br /></td><td style="width: 101pt;" width="134"><br /></td><td align="right" style="width: 48pt;" width="64"><br /></td><td style="width: 48pt;" width="64"><br /></td></tr></tbody></table><br /><br /><br /><b>AMC10B:</b><br />(Students in eighth grade or below with scores over 90)<br /><br /><br /><table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 326px;"> <colgroup><col span="2" style="width: 48pt;" width="64"></col> <col style="mso-width-alt: 4900; mso-width-source: userset; width: 101pt;" width="134"></col> <col style="width: 48pt;" width="64"></col> </colgroup><tbody><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt; width: 48pt;" width="64"><span style="background-color: cyan;">Alex</span></td> <td style="width: 48pt;" width="64"><span style="background-color: cyan;">Wei</span></td> <td style="width: 101pt;" width="134"><span style="background-color: cyan;">Van Antwerp MS</span></td> <td align="right" style="width: 48pt;" width="64"><span style="background-color: cyan;">135</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Ziqing</span></td> <td><span style="background-color: cyan;">Dong</span></td> <td><span style="background-color: cyan;">Farnsworth MS</span></td> <td align="right"><span style="background-color: cyan;">126</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">William</span></td> <td><span style="background-color: cyan;">Wang</span></td> <td><span style="background-color: cyan;">Farnsworth MS</span></td> <td align="right"><span style="background-color: cyan;">124.5</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Jason</span></td> <td><span style="background-color: cyan;">Tang</span></td> <td><span style="background-color: cyan;">Van Antwerp MS</span></td> <td align="right"><span style="background-color: cyan;">118.5</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Andrei</span></td> <td><span style="background-color: cyan;">Akhmetov</span></td> <td><span style="background-color: cyan;">Van Antwerp MS</span></td> <td align="right"><span style="background-color: cyan;">108</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Alex</span></td> <td><span style="background-color: cyan;">Cao</span></td> <td><span style="background-color: cyan;">Shaker JHS</span></td> <td align="right"><span style="background-color: cyan;">108</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Patrick</span></td> <td><span style="background-color: cyan;">Chi</span></td> <td><span style="background-color: cyan;">Iroquois MS</span></td> <td align="right"><span style="background-color: cyan;">106.5</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Liam</span></td> <td><span style="background-color: cyan;">McGrinder</span></td> <td><span style="background-color: cyan;">Van Antwerp MS</span></td> <td align="right"><span style="background-color: cyan;">103.5</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Vladimir</span></td> <td><span style="background-color: cyan;">Malcevik</span></td> <td><span style="background-color: cyan;">Van Antwerp MS</span></td> <td align="right"><span style="background-color: cyan;">99</span></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Gwenda</span></td> <td><span style="background-color: cyan;">Law</span></td> <td><span style="background-color: cyan;">O'Rourke MS</span></td> <td align="right"><span style="background-color: cyan;">97.5</span></td> </tr></tbody></table><br /><br /><span style="background-color: white; color: #333333; font-family: Georgia, serif; font-size: 13px; line-height: 20px; text-align: left;">Students with light blue backgrounds behind their names are members of Albany Area Math Circle and/or our affiliated middle school outreach programs. (If you know any of the others--or any other local students who might enjoy our math circle activities, please invite them to subscribe to our email lists by sending an email to AlbanyAreaMathCircle-subscribe@yahoogroups.com for high school students and their parents or middleschoolmathcircle-subscribe@yahoogroups.com for parents of middle school students.) </span>Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-71493239341218411092012-03-03T09:56:00.000-08:002012-03-03T19:09:22.384-08:00Congratulations to our American Invitational Math Exam qualifiers<br /><table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 390px;"><colgroup><col span="2" style="width: 48pt;" width="64"></col><col style="mso-width-alt: 4900; mso-width-source: userset; width: 101pt;" width="134"></col><col span="2" style="width: 48pt;" width="64"></col></colgroup><tbody><tr height="20" style="height: 15.0pt;"><td colspan="3" height="20" style="height: 15.0pt; mso-ignore: colspan; width: 197pt;" width="262">Congratulations to all the Albany area students who embraced the "extreme math" challenge of this year's AMC10 and AMC12 contests. <br /><br />Here are the criteria for invitation to the AIME along with the honor lists:<br /><br /><b>American Invitational Math Exam (AIME) qualification:</b><br />115.5 or above on AMC10A<br />120 or above on AMC10B<br />94.5 or above on AMC12A<br />99 or above on AMC12B<br /><br />Congratulations and best wishes to the following students from the Albany area who have qualified to take the AIME, the next step in a series of progressively more challenging mathematics exams leading to the International Mathematics Olympiad.<br /><br /><b>American Invitational Math Exam (AIME) </b><br /><b>AMC12B qualifiers:</b></td> <td style="width: 48pt;" width="64"></td> <td style="width: 48pt;" width="64"></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Matthew Babbitt (heeg) 117</span></td><td><span style="background-color: cyan;"><br /></span></td><td><span style="background-color: cyan;"><br /></span></td> <td align="right"><span style="background-color: cyan;"><br /></span></td> <td></td></tr><tr height="20" style="height: 15.0pt;"><td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Wyatt Smith (heeg) 114</span></td><td></td><td><span style="background-color: cyan;"><br /></span></td><td align="right"><span style="background-color: cyan;"><br /></span></td> <td></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Elizabeth Parizh (Niskayuna HS) 99</span></td> <td></td><td><br /></td> <td align="right"><br /></td> <td></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"></td> <td></td> <td></td> <td></td> <td></td> </tr><tr height="20" style="height: 15.0pt;"> <td colspan="3" height="20" style="height: 15.0pt; mso-ignore: colspan;"><b>American Invitational Math Exam (AIME)<br />AMC10B qualifiers:</b></td> <td></td> <td></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Alex Wei (Van Antwerp MS) 135<br />Ziqing Dong (Farnsworth MS) 126<br />William Wang (Farnsworth MS) 124.5<br />Aniket Tolpadi (Niskayuna HS) 123</span></td> <td><br /></td> <td><br /></td> <td align="right"><br /></td> <td></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"></td><td><br /></td><td><br /></td><td align="right"><br /></td><td><br /></td></tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><br /></td><td></td> <td></td> <td></td> <td></td> </tr><tr height="20" style="height: 15.0pt;"> <td colspan="3" height="20" style="height: 15.0pt; mso-ignore: colspan;"><b>American Invitational Math Exam (AIME)<br />AMC12A qualifiers:</b></td> <td></td> <td></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><span style="background-color: cyan;">Matthew Babbitt (heeg) 130.5<br />Zubin Mukerjee (Guilderland HS) 102<br />Sherry He (Emma Willard School) 101<br />Cecilia Holodak (Niskayuna HS) 99<br />Wyatt Smith (heeg) 99</span><br />J Chung (Emma Willard School) 95<br />N Xie (Albany Academies) 95</td><td><br /></td><td><br /></td><td align="right"><br /></td><td><br /></td></tr><tr height="20" style="height: 15.0pt;"><td height="20" style="height: 15.0pt;"><br /></td><td><br /></td><td><br /></td><td align="right"><br /></td><td><br /></td></tr><tr height="20" style="height: 15.0pt;"> <td colspan="3" height="20" style="height: 15.0pt; mso-ignore: colspan;"><b>American Invitational Math Exam (AIME) </b><br /><b>AMC10A qualifiers</b><br /><br /><span style="background-color: cyan;">Alex Wei (Van Antwerp MS) 127.5<br />Philip Sun (Shenendahoah HS East) 126<br />William Wang (Farnsworth MS) 123<br />Patrick Chi (Iroquois MS) 120</span><br /><span style="background-color: cyan;">Vineet Velandula (Niskayuna HS) 120<br />Ziqing Dong (Farnsworth MS) 117</span><br /><span style="background-color: cyan;">Gili Rusak (Shaker HS) 117</span></td> <td></td> <td></td> </tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;"><br /></td><td><br /></td><td><br /></td><td align="right"><br /></td><td></td></tr><tr height="20" style="height: 15.0pt;"> <td height="20" style="height: 15.0pt;">Students with light blue backgrounds behind their names are members of Albany Area Math Circle and/or our affiliated middle school outreach programs. (If you know any of the others--or any other local students who might enjoy our math circle activities, please invite them to subscribe to our email lists by sending an email to AlbanyAreaMathCircle-subscribe@yahoogroups.com for high school students and their parents or middleschoolmathcircle-subscribe@yahoogroups.com for parents of middle school students.) <br /><br />Please report any errors or omissions by sending email to mathcircle at gmail.<br /><table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 390px;"><tbody></tbody></table></td><td><br /></td><td><br /></td><td><br /></td><td><br /></td></tr></tbody></table>Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0tag:blogger.com,1999:blog-4479690110975267663.post-50613784748828617772011-12-28T13:04:00.000-08:002011-12-28T13:16:01.422-08:00Winter holiday mathematicsAlbany Area Math Circle is taking a brief break from our regular Friday evening meetings, but that doesn't mean we aren't surrounded by wonderful mathematics, so here are some treasures to share with your friends and family members. I would love to hear from other math circle members about interesting mathematical aspects of their cultures. I am sure there are many that I do not know about.<br /><br />Last night was the last of the eight nights of Hanukkah. There is all sorts of fun math in Hanukkah, such as figuring out how many candles you need in a box to cover all eight nights of Hanukkah, which will be one less than a <a href="http://mathworld.wolfram.com/TriangularNumber.html">triangular number</a>. There are many fun combinatorics problems to construct and explore as well. How many different color combinations can be constructed if you have n different colors of candles available?<br /><br />Today's Albany <i>Times Union</i> had a great mathematics of Hanukkah story, <a href="http://www.timesunion.com/local/article/A-one-in-trillions-dreidel-game-2427950.php">A one-in-trillions dreidel game</a>, about a remarkable string of luck by a first-time dreidel player, who managed to spin the four-sided top 68 consecutive times without ever seeing the losing side come up and winning the entire pot 56 of those spins. This inspired his great-nephew, a Princeton sophomore studying operations research and financial engineering, to pull out his calculator to compute the astronomically large odds against such a long streak of good luck. <br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-EvDf13CQv54/Tvt60QsnqJI/AAAAAAAAEbY/h25uL2kT5ws/s1600/dreidel.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="214" src="http://3.bp.blogspot.com/-EvDf13CQv54/Tvt60QsnqJI/AAAAAAAAEbY/h25uL2kT5ws/s320/dreidel.jpg" width="320" /></a></div><br />There are several ways to model this probability calculation and it would be interesting to discuss the pros and cons of each approach. One simple possibility is to compute the likelihood of never losing in 68 spins, which would be 1 - (3/4)<sup>68</sup>, which works out to 1 in 22.5 trillion. You can make the odds even more astronomical if you also consider the likelihood that he actually wins the pot on 56 of those 68 non-losing spins, because the remaining three sides are equally likely to come up, and only one of those spins yields the entire pot to the spinner. <br /><br />Of course, this kind of analysis gives rise to interesting philosophical discussions of the sort that physicist Richard Feynman raised in his book, <i><a href="http://e%3Dbl%26ots%3Dvcvgqrbrwt%26sig%3Dtntues2kiny3fhe10krx6qurxmg%26hl%3Den%26sa%3Dx%26ei%3Drxb7ttxrf6f30gh1_omadq%26ved%3D0cgoq6aewbw/#v=onepage&q&f=false">The Meaning of It All: Reflections of a Citizen Scientist</a>, </i>when he talked about the probability of seeing a particular license plate in a parking lot as well as the work of Stanford mathematician Persi Diaconis on the <a href="http://www.nytimes.com/1990/02/27/science/1-in-a-trillion-coincidence-you-say-not-really-experts-find.html?pagewanted=all&src=pm">mathematics of coincidences</a>. <br /><br />Moving onto Christmas, we are currently in the midst of the fabled "Twelve Days of Christmas," as memorialized in the song that starts with one gift given on the first day (December 25, "a partridge in a pear tree"), three gifts given on the second day (December 26, "two turtle doves" plus another "partridge in a pear tree"), and so on through the twelfth day (January 6, which happens to be our next math circle meeting date!)<br /><br />John Cook at the Endeavor blog has a <a href="http://www.johndcook.com/blog/2009/12/08/tetrahedral-numbers/">great post </a>on the mathematics of the Twelve Days of Christmas. He observes that the total number of gifts received each day is a triangular number and also notes that the cumulative number of gifts received through the end of each day is a <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">tetrahedral </a>number. He has written up several nice proofs demonstrating that this is true in general, and he also includes a wonderful link and illustration from the <a href="http://www.mathsisfun.com/">Math is Fun blog</a>. <br /><br /><a href="http://3.bp.blogspot.com/-YwQBT4QKiNc/TvtNp1xY_xI/AAAAAAAAEbM/NPLTcAk3zXI/s1600/tetrahedral-number.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-YwQBT4QKiNc/TvtNp1xY_xI/AAAAAAAAEbM/NPLTcAk3zXI/s1600/tetrahedral-number.jpg" /></a>The Math is Fun blog's illustration at right is a great way to illustrate the triangular/tetrahedral nature of the 12 Days of Christmas song for your younger friends and relatives. The image shows the situation for the first five days of Christmas, with the top layer representing the number of presents given on the first day (1), the next layer representing the number of presents given on the second day (3), the next layer the presents given on the third day (6), the next layer the presents given on the fourth day (10), the next layer the presents given on the fifth day (15). The cumulative number of presents given on the first through fifth day is the number in the entire five layer tetrahedron, or 1+3+6+10+15 = 35. You can extend this indefinitely, of course. If you stop after 12 days, you will have a 12-layer tetrahedron with a cumulative total of 1+3+6+10+15+21+28+36+45+55+66+78 presents, which turns out to be 364, a very nice number, since it is one less than the number of days in a typical year! <br /><br />Another fun fact to share with your younger friends and relatives: take the number of cumulative gifts received during the 12 days and multiply it by the number of days in 2012 and you get a nice opportunity to discuss factoring differences of squares since 365<sup>2</sup> - 1<sup>2</sup> = (365-1)(365+1).<br /><br />There are wonderful mathematical possibilities to explore in every religion and culture--including the modular arithmetic of the various calendar systems generally designed to reconcile discrepancies between lunar and solar numbering systems, which move many holiday observations around relative to one another. It's also interesting to note the frequency with which calendars in so many widely divergent calendars use a <a href="http://en.wikipedia.org/wiki/Seven-day_week">7-day week</a>. This is mathematically very convenient, since the number nearest to<span style="font-family: inherit;"> <span style="background-color: white; font-size: 13px; line-height: 19px;">365.24</span> </span>with a conveniently large number of factors is 364, which is divisible by 7.<br /><br />The Hebrew calendar has a 19-year cycle with a leap month in seven of those years. The Islamic calendar has a 30-year cycle with a leap day added to the final month in 11 out of those 30 years. The Gregorian calendar commonly used in the west appears to have a four year cycle with a leap day every four years, but it's actually <a href="http://en.wikipedia.org/wiki/Leap_year#Gregorian_calendar">more complicated</a> than that.<br /><br />New years festivals are observed at many different times in different calendars, starting with the Jewish new year, Rosh Hashanah, which arrives in early fall. The Hindu new year celebration happens on their festival of lights, Divali, in mid-fall. The Chinese New Year generally comes later in winter than the Gregorian new year on January 1. The early <a href="http://en.wikipedia.org/wiki/Roman_calendar#cite_note-Macrobius-2">Roman calendar</a> (before Caesar came along and reformed it) began its new year in March, had only ten lunar months, and then had a mysterious unlabeled winter period of 61 day that were apparently not considered to belong to any month. Caesar changed the New Year to January 1, but later Christian rulers moved it to March, before Gregory moved it back to January.<br /><br /><br />Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.com0