Application material for
Steve Butler

On this website is collected material related to my research and teaching to help give a sense of who I am, and why you would want me to join your faculty. If you have any questions please feel free to contact me by email, butler@math.ucla.edu.

A good place to start is with my curriculum vitae.

Jump to Teaching.
Jump to Research.
Jump to Additional material.

Steve Butler


Teaching
Teaching mathematics has been one of the most enjoyable experiences in my academic career. I have taught at three different major universities and have had over 900 students. A summary of some of my teaching experience and approach can be found in my teaching statement.
University Courses taught
UCLA (2008-2010)
(BruinWalk reviews)
  • Calculus of several variables (course website) (teaching evaluations)
  • Differential and Integral Calculus (course website) (videos of lectures) (teaching evaluations)
  • Combinatorics (course website) (lecture notes) (teaching evaluations)
  • Calculus for life science students (course website) (teaching evaluations)
  • Introduction to discrete structures (course website) (teaching evaluations)
    • UCSD (2007)
  • Differential calculus (course website) (student comments)
    • BYU (2001-2003)
  • Differential calculus
  • Integral calculus
  • Trigonometry (5 classes) (lecture notes)

    • Research
    I have authored, or co-authored, many papers in a variety of subjects including spectral graph theory, discrete geometry, and hypercube orientation as well as algebraic combinatorics, recreational mathematics and game theory. A summary of some of my past research and some problems I will be considering in future research can be found in my research statement. Much of my research into the normalized Laplacian can be found in my dissertation Eigenvalues and Structures of Graphs.

    Publication list
    1. S. Butler, K. Costello and R. Graham, Finding patterns avoiding many monochromatic constellations, Experimental Mathematics 19 (2010), number 4, 399-411.
    2. S. Butler and R. Graham, Iterated triangle partitions, Fete of Combinatorics and Computer Science, G. Katona, A. Schrijver, T. Szonyi, eds., Bolyai Society Mathematical Studies 29, Springer-Verlag, Heidelberg (2010), 23-42.
    3. S. Butler, F. Chung, R. Graham and M. Laczkovich, Tiling polygons with lattice triangles, to appear in Discrete & Computational Geometry 44 (2010), 896-903.
    4. S. Butler, R. Graham, G. Guettler and C. Mallows, Irreducible Apollonian configurations and packings, Discrete & Computational Geometry 44 (2010), 487-506.
    5. S. Butler, Eigenvalues of 2-edge-coverings, Linear and Multilinear Algebra 58 (2010), 413-423.
    6. S. Butler and R. Graham, Shuffling with ordered cards, Journal of Combinatorics 1 (2010), 121-139.
    7. S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, Annals of Combinatorics 13 (2010), 413-424.
    8. S. Butler and F. Chung, Small spectral gap in the combinatorial Laplacian implies Hamiltonian, Annals of Combinatorics 13 (2010), 403-412.
    9. S. Butler, P. Horn and E. Tressler, Intersecting domino tilings, The Fibonacci Quarterly 48 (2010), 114-120.
    10. S. Butler, R. Graham and J. Mao, How to play the majority game with a liar, Discrete Mathematics 310 (6 February 2010), 622-629.
    11. S. Butler, Cospectral graphs for both the adjacency and normalized Laplacian Matrices, Linear and Multilinear Algebra 58 (2010), 387-390.
    12. S. Butler and P. Karasik, A note on nested sums, Journal of Integer Sequences 13 (2010), article 10.4.4, 8 pp.
    13. S. Butler, Induced-universal graphs for graphs with bounded maximum degree, Graphs and Combinatorics 25 (2009), 461-468.
    14. S. Butler, The lost daughters of Gergonne, Forum Geometricorum 9 (2009), 19-26.
    15. S. Butler, R. Graham and N. Zang, Optimal jumping patterns, Journal of Combinatorics and Number Theory 1 (2009), 1-13.
    16. S. Butler, M. T. Hajiaghayi, R. D. Kleinberg and T. Leighton, Hat guessing games, SIAM Journal on Discrete Mathematics 22 (2008), 592-605. Republished in SIAM Review 51 (2009), 399-413.
    17. S. Butler, R. Graham and N. Zang, Jumping sequences, Journal of Integer Sequences 11 (2008), 13 pp.
    18. S. Butler, Estimating the number of graphs containing very long induced paths, Ars Combinatoria 88 (2008), 321-332.
    19. AIM minimum rank-special graphs work group, Zero forcing sets and the minimum rank of graphs, Linear Algebra and its Applications 428 (2008), 1628-1648.
    20. M. Bousquet-Melou and S. Butler, Forest-like permutations, Annals of Combinatorics 11 (2007), 335-354.
    21. S. Butler, R. Graham and J. Mao, How to play the majority game with liars, AAIM 2007, Lecture Notes in Computer Science 4508, Springer-Verlag, 221-230.
    22. S. Butler, Interlacing for weighted graphs using the normalized Laplacian, Electronic Journal of Linear Algebra 16 (2007), 90-98.
    23. S. Butler, Using discrepancy to control singular values for nonnegative matrices, Linear Algebra and its Applications 419 (2006), 486-493.
    24. S. Butler, Relating singular values and discrepancy of weighted directed graphs, Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm (Miami, FL, 2006), 1112-1116.
    25. S. Butler, Tangent line transformations, The College Mathematics Journal 34 (2003), 105-106.
    Submitted papers
  • W. Barrett, S. Butler, H. T. Hall, J. Sinkovic, W. So, C. Starr and A. Yielding, Computing inertia sets using atoms.
  • J. Buhler, S. Butler, W. de Launey and R. Graham, Origami rings.
  • S. Butler and R. Graham, A note on marking lines in [k]n.
  • S. Butler and R. Graham, Subdivision by bisectors is dense in the space of all triangles.
  • J. Buhler, S. Butler, R. Graham and E. Tressler, Hypercube orientations with only two in-degrees.
  • S. Butler and J. Grout, Constructing cospectral graphs for the normalized Laplacian.
  • S. Butler, E. Demaine, R. Graham and T. Tachi, Constructing points through folding and intersection.
  • S. Butler, R. Graham, G. Guettler and C. Mallows, An interstice relationship for flowers with four petals.

    •  

     

     

    Coauthors AIM minimum rank-special graphs work group, Wayne Barrett, Mireille Bousquet-Melou, Joe Buhler, Fan Chung, Kevin Costello, Warwick de Launey, Erik Demaine, Ron Graham, Jason Grout, Gerhard Guettler, Mohammad Hajiaghayi, H. Tracy Hall, Paul Horn, Pavel Karasik, Robert Kleinberg, Miklos Laczkovich, Tom Leighton, Colin Mallows, Jia Mao, John Sinkovic, Wasin So, Colin Starr, Tomohiro Tachi, Eric Tressler, Amy Yielding, Nan Zang

    Additional material

  • Awarded an NSF Postdoctoral Fellowship, under the direction of Benny Sudakov, July 2008-June 2011.

  • Visiting scholar at Center for Combinatorics, Nankai University, Tianjin, China, September 2006. (Lecture notes for three lectures delivered during the visit.)

  • Organized combinatorics reading seminar at UC San Diego, Summer 2005.

  • The paper "Hat guessing games" was chosen for publication in SIGEST section of SIAM Review. ("SIGEST highlights an exceptional paper, chosen for its readability and wide appeal to the SIAM community.")

  • Have written reviews for Math Reviews, and refereed for Applied Mathematics Letters, Ars Combinatoria, Chinese Annals of Mathematics, Discrete Applied Mathematics, Discrete Mathematics, Electronic Journal of Combinatorics, European Journal of Combinatorics, Experimental Mathematics, Hacettepe Journal of Mathematics and Statistics, Information Processing Letters, Involve, Journal of Combinatorial Theory A, Journal of Combinatorics, Journal of Graph Theory, Linear Algebra and its Applications, Linear and Multilinear Algebra, Mathematics Magazine, New York Journal of Mathematics, Random Structures & Algorithms, Rendiconti del Seminario Matematico di Padova, and SIAM Journal on Discrete Mathematics.

  • Experience in programming. Examples include JAVA applets written for triangle subdivision and minimizing colorings; and MAPLE worksheets written for circle packings and minimizing colorings.

  • Work on generating mathematical images. Examples can be found in the papers "Finding patterns avoiding many monochromatic constellations", "Irreducible Apollonian configurations and packings" and "Subdivision by bisectors is dense in the space of all triangles". Another example are some of the figures in the blog of Loic Seguin-Charbonneau "Triangulations creatives", as well as YouTube videos taking slices of spherical packings.

  • Posed a number of problems which have appeared in print including American Mathematical Monthly #11030, #11265 and Mathematics Magazine #1668, #1730, #1761.

  • Delivered lectures at several conferences and combinatorics seminars. Below are a selection of some of these talks.
    1. Finding patterns avoiding many monochromatic constellations (slides), delivered at UCSD combinatorics seminar; UCLA combinatorics seminar; AMS 2009 Fall Western Section Meeting; AMS 2010 Spring Central Section Meeting; Colloquim at Michigan Technological University.
    2. Cospectral graphs for the normalized Laplacian (slides), delivered at 2010 SIAM Conference on Discrete Mathematics.
    3. Hat games and hypercube orientations (slides), delivered at Discrete Mathematics Seminar at Iowa State University; Drake University; Combinatorics Seminar at UC San Diego.
    4. Shuffling with ordered cards (slides), delivered at Combinatorics, Groups, Algorithms, and Complexity: Conference in honor of Laci Babai's 60th birthday; 2010 Western Number Theory Conference.
    5. Iterated partitions of triangles, delivered at The 20th Canadian Conference on Computational Geometry (co-presenter with Ron Graham); The Mathematical Interests of Peter Borwein (co-presenter with Ron Graham); Drake University.
    6. Tiling polygons with lattice triangles (slides), delivered at INTEGERS Conference 2009.
    7. Jumping sequences (slides), delivered at UCSD combinatorics seminar; UCLA combinatorics seminar.
    8. Induced universal graphs (slides), delivered at UCSD combinatorics seminar; SDSU REU; BYU colloquium; Sixth Czech-Slovak International Symposium; AMS 2007 Western Sectional Meeting.
    9. Eigenvalues of 2-edge-coverings, delivered at CMS Winter 2007 Meeting; UCSD cobinatorics seminar.
    10. An Erdos-Ko-Rado problem on the strip (slides), delivered at GSCC 2008.
    11. How to play the majority game with liars (slides), delivered at AAIM07.
    12. Enumerating (multiplex) juggling sequences, delivered at Horizon of Combinatorics; UCSD combinatorics seminar.
    13. On permutations which are 1324 and (bar 2143) avoiding, delivered at UC Berkeley combinatorics seminar; UCSD combinatorics seminar; CalTech combinatorics seminar.

    • Last modified: 24 January 2011