Wednesday, May 13, 2015

Intriguing guest speaker: Professor Ivana Alexandrova

This spring, our math circle was fortunate to have a special treat:   Professor Ivana Alexandrova 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.

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.

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 intriguing!

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 problems and solutions here.   The current problem is very nice:  Solve 1 + sin x + cos x < 0.

Sunday, October 20, 2013

Math Circle plans for the 2013-2014 school year: new time/day/location

Albany Area Math Circle will be starting up its 13th year!

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

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.

Wednesday, May 29, 2013

Recommended summer reading for young students (and their parents!) aspiring to climb mathematical mountains together this summer

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 this book could provide a much-needed breath of fresh air.

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.

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.

Written in a good-natured conversational style, Hard Math for Elementary School 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. This book and its earlier counterpart for somewhat older students, Hard Math for Middle School, are great solutions to questions frequently posed by parents of young students looking for summer reading for their mathematically voracious students.

Sumer is icumen in,

Lhude sing cuccu!

Groweth sed and bloweth med

And springth the wude nu,

Sing cuccu!

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. 

(Disclosure:  thanks to Professor Ellison for sharing a prepublication review copy of the manuscript with me.)

Thursday, April 4, 2013

Doing justice to describing the work of other math circles that have inspired us

Last week, Sol Lederman interviewed Gili Rusak and myself for a podcast now featured on his blog, Wild About Math.   Thanks to Catherine Miller for typing up a transcript of that conversation, which will soon be available in a link on Sol's blogpost.  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.

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.

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 Girls' Angle, 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 SUMiT 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 Hypatia of Alexandra.

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 Harold Reiter from the Charlotte Math ClubBob and Ellen Kaplan from the Boston Math Circle, Zvezda Stankova from the Berkeley Math Circle, Tatiana Shubin from the San Jose Math Circle, Paul Zeitz and Brandy Weigers from the San Francisco Math Circle,  Joshua Zucker from the MSRI Julia Robinson Math Festivals, Amanda Serenevy from the Riverbend Community Math Center, Ken Fan from Girls' Angle, or Japheth Wood from the NYC Math Circle and Bard Math Circle.

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.

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 MSRI National Association of Math Circles 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.

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 the MSRI Math Circle book series, Bob and Ellen Kaplan's books, subscribing to the Girls' Angle Bulletin, participating in a future SUMiT, and/or just making a donation directly to any of these circles 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.

Wednesday, March 27, 2013

Math Circle student research honors

Math 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 Hudson Undergraduate Math Research Conference, which will be held at Williams College on Saturday April 6.

Gili's applied mathematics project, An Analysis of Teenage Twitter Communities, 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 Intel  International Science and Engineering Fair (ISEF) 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 here.

Matt Babbitt's graph theory research project, Counting number of edges, thickness, and chromatic number of k-visibility graphswon semifinalist honors in this year's Intel Science Talent Search.  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 Jack Kent Cooke Scholar and plans to attend MIT next year.

Siemens Foundation - Iselin, NJ

Zubin Mukerjee's number theory research project, Random Involutions and the Number of Prime Factors, is based on his joint work with a fellow student, Uthsav Chitra, at PROMYS last summer.  Their research mentor was Dr. Kristen Wickelgren, a research fellow at Harvard.   The project won semifinalist honors in the Siemens Competition in Math Science and Technology.  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 Zubin here.

Friday, February 8, 2013

Gili Rusak, mathematical community builder

Gili Rusak launches students on investigations of Archimedean solids.

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.

Last winter, she participated in the first annual SUMiT, a "fully collaborative, math intensive event" organized by Girls' Angle and the Undergraduate Society for Women in Mathematics 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.

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 Gili's blog here.

Gili leading a Math Treasure Hunt she designed and organized for younger girls at the Kenney Community Center  at Union College late last summer .

After hearing about Gili's very successful local treasure hunt, Ken Fan at Girls' Angle 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.

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.

Gili's account of that night is here.  Ken describes one fun part of their treasure hunt, Mental Madness, here.  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 video clip of RoboApe here.)

Ken Fan from Girls' Angle and Gili in the Robo-Ape event

Attendees at the Math Prize social event included Stephen Wolfram 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 this video (starting at 3:27).   Gili described some of their activities in her blog here.

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.

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.

 Zagreb is now off in college, 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!

Thursday, January 24, 2013

Sign up for AMC10B or AMC12B at Siena College!

Thanks to Siena College Math Department and especially to Professor Mohammad Javaheri (a silver medalist at the 1995 International Math Olympiad) for sponsoring this exciting math contest for high school students in the Capital District.  The AMC10/12 is the first in a series 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 Math Prize for Girls at MIT next September!

 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 for more information about how to prepare. Please use the form below to sign up to take the contest at Siena on February 20.