Professor Butler with a beard Steve Butler

E-mail address

400C Carver Hall



Videos available on YouTube

I am an Assistant Professor in the Department of Mathematics at Iowa State University (ISU). Prior to coming to ISU I did a three year NSF PostDoc under the supervision of Benny Sudakov at UCLA. Before that I earned my doctorate degree in mathematics at UC San Diego under the supervision of Fan Chung where I also worked extensively with Ron Graham.

From September 2012-February 2014, I maintained the Weekly Undergraduate Math Mailing (WUM^2) at Iowa State University. The archived announcements are available online.

A news story about by mathematics of juggling class I taught in the Fall of 2013.

Jump to Teaching, Miscellaneous--research, Talks/presentations, Links.

Teaching mathematics is one of the fun parts about my job. I have taught hundreds of students at four different universities.

Past courses:
Iowa State (2011-present)
  • Math 265: Calculus of several variables (Fall 2013)
  • Math 595: Mathematics of juggling (Fall 2013)
  • Math 607: Graph theory (Fall 2013)
  • Math 492: Undergraduate seminar (Spring 2013)
  • Math 314: Graph theory (Spring 2013)
  • Math 265: Calculus of several variables (Fall 2012)
  • Math 304: Combinatorics (Fall 2012)
  • Math 265: Calculus of several variables (Spring 2012)
  • Math 201: Introduction to proofs (Fall 2011)
  • Math 265: Calculus of several variables (Fall 2011)
  • Math 304: Combinatorics (Fall 2011 -- independent study)
  • UCLA (2008-2010)
  • Math 32A: Calculus of several variables
  • Math 31A: Differential and Integral Calculus (videos of lectures)
  • Math 180: Combinatorics (lecture notes)
  • Math 3B: Calculus for life science students
  • Math 61: Introduction to discrete structures
  • UCSD (2007)
  • Math 10A: Differential calculus
  • BYU (2001-2003)
  • Differential calculus
  • Integral calculus
  • Trigonometry (5 classes) (lecture notes)

  • Graduate students:
  • Steven Osborne (joint student with Leslie Hogben); Ph.D. Fall 2013.
  • Kristin Heysse; Ph.D. Spring 2017 (expected).
  • Jephian Chin-Hung Lin (joint student with Leslie Hogben); Ph.D. Spring 2017 (expected).
    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, Steven Osborne, John Sinkovic, Wasin So, Colin Starr, Richard Stong, Tomohiro Tachi, Eric Tressler, Amy Yielding, Nan Zang


    Eigenvalues and structures of graphs -- Ph.D. dissertation written at UC San Diego under the direction of Fan Chung. Much of this has shown up in various papers I have published.

    Bounding the number of graphs containing very long induced paths -- Masters thesis written at Brigham Young University under the direction of Wayne Barrett.

    JAVA applets written to look at what happens to daughters when bisecting triangles using some well defined central point. This is related to the papers Iterated triangle partitions and The lost daughters of Gergonne.

    The papers have generated many beautiful images and some can be found in the blog of Loic Seguin-Charbonneau "Triangulations creatives".

    For the paper Finding patterns avoiding many monochromatic constellations we generated a Maple worksheet that gives a method to compute the coefficient of a block pattern given a constellation. We also have an extended Maple worksheet that contains more information about good block colorings. There is also an interactive JAVA applet that allows you to see what happens to the coefficient of a pattern as we perturb the pattern and/or the constellation. In addition we have the JAVA programs used to generate block patterns for 4-APs as well as the general pattern [0,q,1].

    For the paper Irreducible Apollonian configurations and packings we generated a Maple worksheet that automates finding the center and radii of a packing placed in standard position. We also have a list of all irreducible configuration of circles with between 10 and 15 circles that can be used in the worksheet. Finally, there is also a collection of packings with various curvatures marked in the circles.

    While visiting The Center for Combinatorics at Nankai University in September 2006 I gave three lectures that served as an introduction to the field of graph theory.
  • The first lecture was an introduction to three common spectra that looked at the adjacency matrix, the Laplacian matrix, and the normalized Laplacian and why each one might be used.
  • The second lecture was about applications of Courant-Fischer and gave some basic applications including examining what happens with the removal of a subgraph.
  • The third lecture discussed Cheeger constants and discrepancy and looked at various properties of edge expansion in graphs.

  • I have posed various problems which have appeared. These include American Mathematical Monthly #11030, #11265 and Mathematics Magazine #1668, #1730, #1761, #Q1008.

    In Fall of 2004 Fan Chung taught a course about the combinatorics of patterns in subsets and graphs. I worked to collect and collate the notes for the course into a PDF document; of course Fan did all the hard work of teaching the course.

    A collection of the simplest aperiodic strongly connected directed graphs and their spectrums under the definition of the normalized Laplacian (as defined by Chung).

    Miscellaneous unpublished notes:
  • Relating the arboricity with the chromatic number of a graph
  • Determining the underlying functions for Cauchy power and exponential forms
  • A property of the gcd; and The Moebius transform of the triangular numbers
  • The art of juggling with two balls
  • A property of positive semidefinite matrices
  • Tangent line transformations
  • Method for doing the (approximate) Markov chains for bisection

  • A letter to the editor of my old school about the slogan do the math used for a fundraising campaign.

    Last modified: 19 July 2015