Category: Photos

Japheth takes lots of photos. Here are some favorites.

  • Kevin’s Books


    One of the great friends that I made in my time at Vanderbilt University was Kevin Blount. Kevin knew all the graduate students and professors, and often hosted dinners and movies at his nearby apartment.
    Kevin ended up writing his Ph.D. dissertation On the Structure of Residuated Lattices with Constantine Tsinakis, and moved on to an academic position at Sacred Heart University in Connecticut.

    Kevin passed away on May 30, 2006, which surprised all of us. I had just moved back East, and so one of the first trips was attending his memorial service at Sacred Heart.

    At the end of 2008, Kevin’s wife, Xiaoyu, gave me Kevin’s math books. After some brief discussions with some mathematical colleagues, the books ended up being stored in my attic. I’m now offering these books to those who knew Kevin. I am sure that Kevin would have been happy to have his math books shared among his friends and colleagues, and I hope that this will help keep Kevin’s memory alive in the mathematical community.

    If you are interested in some of the books below, leave a comment or contact me privately. I’ll send them your way. (Pardon the typos – I’ll correct those as they are noticed).

    Kevin’s Math Books

    1. Albert, Introduction to Algebraic Theories, Matt Insall
    2. Artin, Geometric Algebra, Tracts in Mathematics Number 3 – John Raymonda
    3. Baumslag and Chandler, Group Theory
    4. Bennet, Affine and Projective Geometry
    5. Bjarni Jonsson, Topics in Universal Algebra, Lecture Notes, Vanderbilt University, 1969-70 – John Snow
    6. Bollobas, Graph Theory, GTM 63, Matt Insall
    7. Bond/Keane, An Introduction to Abstract Mathematics, Instructors
    8. Bondy and Murty, Graph Theory with Applications, Matt Insall
    9. Bonele, Non-Euclidean Geometry, Dover
    10. Bourbaki, Elements of Mathematics, General Topology, Part 1, Addison Wesley
    11. Burnside, Theory of Groups of Finite Order, Princeton
    12. Curry, Foundations of Mathematical Logic, Dover
    13. Dieudonne, Introduction to the Theory of Formal Groups, Dekker
    14. Gruenberg and Weir, Linear Geometry, Van Nostrand
    15. Hodel, An Introduction to Mathematical Logic – Jan Gałuszka
    16. Hall, The Theory of Groups, Macmillan
    17. Springer, Geometry and Analysis of Projective Spaces
    18. Sternberg, Lectures on Differential Geometry, Prentice Hall
    19. Hennie, Introduction to Computability
    20. Lang, Introduction to Algebraic Geometry, Tracts in Mathematics Number 5 – John Raymonda
    21. Hochschild, Introduction to Affine Algebraic Groups
    22. Nagaia, Local Rings, Tracts in Mathematics Number 13
    23. Spanier, Algebraic Topology
    24. Lipschitz, Discrete Mathematics, Schaum McGraw Hill
    25. Solutuion Manual for, Brooks/Cole
    26. Curtis Clark, An Approach to Graph Achievement Games: Ultimately Economical Graphs
    27. Hungerford, Algebra, Springer 73 – John Snow
    28. Mendelson, Introduction to Mathematical Logic, 3e, Wadsworth & Brooks/Cole Mathematics Series
    29. Moore, Elementary General Topology, Prentice-Hall
    30. Mitchell, Theory of Categories, Academic Press, Matheamtics XVII
    31. Herken, The Universal Turing Machine, Oxford – John Snow
    32. ??, Fundamental Concepts of Algebra, Addison Wesley
    33. Kelley, General Topology, Van NostrandO??, Theory of LIE Groups, Princeton
    34. Munkres, Elements of Algebraic Topology
    35. Sawyer, A Geometric Approach to Abstract Algebra, Freeman
    36. McCoy, Rings and Ideals – John Raymonda
    37. Smullyan, First-Order Logic, Dover
    38. Veblen and Young, Projective Geometry, Volume 1
    39. Gelfond, Transcendental & Algebraic Numbers, Dover – John Snow
    40. Freese & McKenzie, Commutator Theory for Congruence Modular Varieties – Jonathan Farley
    41. Davey & Priestley, Introduction to Lattice and Order, Cambridge – John Snow
    42. An Algebraic Introduction to Matheamtical Logic, GTM 52 – John Snow
    43. Categories for the Working Mathematician, GTM 5 – John Snow
    44. Manin, A Course in Mathematical Logic, GTM 53
    45. Burris/Sankappanavar, A Course in Universal Algebra, GTM 78 – John Snow
    46. Hirsch, Differential Topology, GTM 33
    47. Gaum, Elements of Point Set Topology, Prentice-Hall
    48. Bourbaki, Elements of Mathematics, General Topology Part 2
    49. Eisenberg, Topology, Holt Rinehart Winston
    50. Pareigis, Categories and Functors
    51. Kaplansky, Set Theory and Metric Spaces – John Raymonda
    52. McKenzie, McNulty, Taylor, Algebras, Lattices, Varieties, Volume I, Wadsworth & Brooks/Cole Matheamtics Series, – Jonathan Farley
    53. Monk, Mathematical Logic, GTM 37 – John Snow
    54. Lightstone, Symbolic Logic and the REAL NUMBER SYSTEM – John Snow
    55. The Essentials of Logic
    56. Halmos & Givant, Logic as Algebra – Jan Gałuszka
    57. Jacobson, Lectures in Abstract Algebra, I Basic Concepts, Van Nostrand – John Raymonda
    58. Husain, Introduction to Topological Groups, Matt Insall
    59. Tarski, Introduction to Logic and to the methodology of deductive sciences, Dover
    60. Church, Introduction to Mathematical Logic, Princeton – John Snow
    61. Rosenbloom, an introduction to Symbolic Logic, Dover
    62. Krantz, How to Teach Mathematics: a personal perspective
    63. Thomas Rishel, Teaching First – A Guide for New Mathematicians, MAA
    64. Hobby and McKenzie, The Structure of Finite Algebras, AMS Comm 76, – Jonathan Farley
  • Math Formula Poetry Slam

    Last December, I got to meet Daniel, aka Jarabe Del Sól, a poet from the Readnex Poetry Squad. He showed me in his notebook where he had written all sorts of arcane symbols and characters, perhaps from undiscovered alphabets. I got to fill up a few pages of his notebook with math symbolism off the top of my head, and then he proceeded to respond with a poetic response and free verse. This was a lot of fun, and a few days later, he sent me photos of what I had written. If you click on the photos below, you can see what Jarabe and I wrote, a math formula poetry slam! Play this track while you’re looking, for the full experience.

    11 If gravity could fly one 64

  • Math Conference photos

    Going through some old papers, I found the following conference photos from

    • Fall 1996 Fields Institute, Algebraic Model Theory Program
    • July 1-10, 1998, XI Simposio Latinoamericano Lógica Matemática, Mérida, Venezuela
    • 1998 Szeged Conference on Lattices and Universal Algebra

    1996 Fields Institute
    The Fall 1996 Algebraic Model Theory Program at the Fields Institute
    Photo key

    XI Simposio Latinoamericano Lógica Matemática
    1998 Szeged Conference on Lattices and Universal Algebra
  • An Interesting Prime Number Fact, Rubik’s Cube and the Gömböc

    In the summer of 2010 I traveled to Hungary for the 25th anniversary reunion of the Budapest Semesters in Mathematics program, and had the pleasure of seeing the inauguration of another study abroad program for computer science, the Aquincum Institute of Technology.

    The interesting part of the ceremony was a series of mathematics talks to celebrate the genius of Hungarian mathematics and technology. There were also talks by Balázs Bús, the mayor of Óbuda, and by János Kocsány, the CEO of Graphisoft Park.

    The Graphisoft Park Rubik's Cube
    The Graphisoft Park Rubik's Cube

    László Babai talked about Mathematical Generalizations of Rubik’s Cube, and mentioned the following.

    The diameter of the Rubik’s Cube graph is at least 20, but probably no more than 21 (Richard Korf, UCLA, 1997), and definitely no more than 26 (Gene Cooperman, Dan Kunkle, Northeastern, 2007).

    It was very interesting that just a month later, in July, 2010, the diameter was confirmed as 20. A team used 35 years of CPU time, donated by Google, to complete the computation. Even more interesting for me was to learn that the lower bound of 20 had been established in 1995 by Mike Reid, who identified the “superflip” position that required 20 moves to solve. Here’s an interesting website that documents progress on this problem: God’s Number is 20.

    I had met Mike in person about 25 years ago, when I attended the Hampshire College Summer Studies in Mathematics. Now that I am involved with the New York Math Circle, I’ve had the pleasure of meeting Mike’s old math teachers, who have wonderful stories to tell.

    Babai had brought up the diameter of the Rubik’s Cube graph because his talk was really about the connection between the size of a group at the diameter of its Cayley graph. For the Rubik’s cube, the group has about 34 quintillion elements (The exact number is 43,252,003,274,489,856,000. Remember: thousand, million, billion, trillion, quadrillion, quintillion, sextillion, septillion, …), but its diameter is just 20, which is on the order of the logarithm of the size of the group.

    Babai mentioned a recent result of Harald Helfgott and Akos Seres, On the diameter of permutation groups, which gives a “quasipolynomial upper bound” for the diameter.

    One beautiful formula that Babai presented was:

    $latex \prod_{p \leq x} p \approx e^x$.

    This seems related to the prime number theorem, that $latex \pi(x) \approx \frac{x}{\ln{x}}$, where $latex \pi(x)$ denotes how many primes are less than x. I leave it to the readers to find the connection.

    Another great talk was by Gábor Domokos, The Story of Gömböc. The gömböc is a solid object with just one stable point of equilibrium (and also one unstable point). If you place the gömböc on a flat surface, it rocks back and forth, and eventually stabilizes in the same position each time.

    Amazing invention–I want one!

  • Poster Sessions

    After completing a research project or making a mathematical discovery of some sort, it’s important to communicate your results. One nice way to do this is with posters.

    If you’ve never made a poster before, it’s simply a collection of boxes that tells a story, in this case, your mathematical research. It should tell a story to someone reading it, but work even better if you’re standing in front of the poster conversing with your audience.

    Here are some photos I’ve taken of posters and poster sessions:

    There are a lot of useful websites out there about making a poster. Here is one of my favorites:
    Creating Effective Poster Presentations :: An Effective Poster