Japheth Wood

the math wizard

Month: August 2010

  • Following Math Blogs

    I’ve slowly been entering the world of math blogging, first by reading blogs, and now by posting a note occasionally on this blog. There is an amazing world of math bloggers out there, some I’m proud to know in person, and so many worth reading.

    Here’s a post claiming to be the top 25 classroom math bloggers: http://www.onlinedegrees.org/top-25-blogs-for-math-in-the-classroom/, which may be the best list to get started. Give it a read!

  • Math Delights, a webpage.

    A wonderful website of Math Delights. Full of rich mathematical activities for 5-12 year olds. Collected by Nancy Blachman, founder of the Julia Robinson Math Festival.

  • Legacy of R.L. Moore Conference

    R.L. Moore
    Portrait of R.L. Moore

    Inquiry Based Learning (IBL) is an exciting approach to mathematics education that has a track record and great potential. The challenge is how to you make this approach work in your classroom and for your students?

    I attended the annual Legacy of R.L. Moore Conference in 2005, 2006 and 2007 and hope to return sometime soon.

    The Legacy of R.L. Moore Project helps popularize this method and assist math educators to take steps to bring it to their classrooms.

  • Math Physics Explore

    Excerpt from website: http://www.mathphysicsexplore.org

    We develop a curiosity and interest in mathematics so students, parents and teachers can improve their math and science education. Activities focus on various topics in mathematics and their application to physical phenomenon.

    This website and our exploratorium:

    • Encourage each person to reach his/her potential
    • Provide guidance for children participating in science fairs
    • Help teachers to explain math concepts
    • Provides travel exhibits for schools

    We are located at 1054 Freedom Plains Road, Poughkeepsie, NY 12603.

  • Bard Math Circle

    The Bard Math Circle primarily targets middle school and elementary school students in the Mid-Hudson Valley region of New York State.
    In Kingston, NY (a small city in which 15% of residents live below the poverty line and 27% of children live below the poverty line) , the target audience for the past two years has been members of the Boys & Girls Club, whose members are primarily minority youth from low socio-economic households. The highlight of the activities in Kingston was a group visit to the Bard campus, in which the Boys & Girls Club members participated in math workshops led by Bard College math professors. In 2010, the primary location is the Kingston Library in Midtown Kingston and targets a wider middle school audience, a diverse socio-economic, racial and gender balanced group.
    In Tivoli, (a semi-rural community north of Bard College) the Bard Math Circle holds monthly sessions at the Tivoli Library, The audience consists of families with children in middle school and younger.
    In Red Hook, (a suburban and semi-rural rural community east and south of Bard College), we also target a middle school audience, in partnership with a math teacher at the Linden Avenue Middle School.

    Origins

    The Bard Math Circle was formed in 2007 by Bard College Professors Lauren Rose and Japheth Wood and then students Shelley Stahl and Ezra Winston. The Bard Math Circle is run jointly by students, under Bard’s Trustee Leader Scholar Program, and faculty at Bard College.

  • Limaçon 2011

    Long Island Math Conference
    Nassau County Math Teachers Association

    Date: Friday, March 18, 2011
    Time: 7:45 A.M. to 2:35 P.M.
    Location: SUNY College at Old Westbury Campus Center
    URL: http://ncmta.net/limacon.htm

    This is the annual Long Island Math Teachers’ Conference.

  • Rubik’s Cube Conversation over Breakfast

    If you read my previous post then you know that I’m at HCSSiM for the second half of the second half, teaching a mini on the Fundamental Theorem of Algebra. I’m very impressed with everything, from the teaching faculty to the students, and am really enjoying soaking in interesting mathematics every day. There is really high level mathematics going on here, and the students are truly immersed in mathematical knowledge and culture.

    Conversation at breakfast with Lucas and Gabe.

    I walked into a conversation about Rubik’s Cube records this morning at breakfast. Talking about new cube records, Lucas complained about kids who ask him if he solves the cube by just doing the same sequence of moves over and over again. Of course not! This would only work in a cyclic group!

    However, I argued that it is possible, if you look at it another way. Suppose that g is a long sequence of moves that traverses through all possible cube positions. Then you only have to do the sequence g once, and somewhere along the way, you’ll have solved the cube. Notice that the end result of performing the moves in sequence g is the identity permutation on the cube.

    We can improve this by finding a cube permutation g that generates a large cyclic subgroup of the cube group. Let G be the cyclic subgroup generated by g. If we can express g as a long sequence of cube moves that traverses through a complete set of coset representatives of G, then we have the cube neophyte’s dream: a sequence of cube moves, that it you do over and over again, will eventually solve the cube (of course, in the worst case scenario you’ll move through all possible configurations of the cube, but I’m not making any claim about the efficiency of this method!)

    We finished our breakfast conversation by posing a more reasonable problem: try this for a small group.

    1. Show that g = (1, 2, 3)(4, 5) is an element of S_5 of maximal order.
    2. Find a sequence of 120/6 = 20 permutations s_1, s_2, …, s_20 whose product is g, and whose partial products (s_1), (s_1 s_2), (s_1 s_2 s_3), …, (s_1 s_2 s_3 … s_20) is a set of coset representatives of the cyclic subgroup .
    3. Solve problem 2, where each s_i is a transposition.
    4. Solve problem 2, where each s_i is a transposition of adjacent elements.

    This seems like a good start to investigating the breakfast conversation problem. Let me know what you think!