Mohamed Omar




Welcome to my website! I am an Associate Professor in the Department of Mathematics at Harvey Mudd College.

I am interested in seeing algebra come alive in discrete mathematics, primarily in combinatorics, graph theory and discrete/convex geometry. I am also interested in enumerative and geometric combinatorics. Below is my work. Student co-authors are in orangered.

It is my mission to transform our society from math phobic to math loving. For more, click here.


  1. Number Theory Toward RSA Cryptography: in 10 undergraduate lectures
    CreateSpace, 2017.

  2. Algebraic and Geometric Methods in Applied Discrete Mathematics
    Contemporary Mathematics, Proceedings of the AMS Special Session, Volume 685, 2017.
    w/ Heather Harrington, Matthew Wright

  3. On Volumes of Permutation Polytopes
    Fields Institute Communications, Discrete Geometry and Optimization, pp. 55-77, 2013.
    w/ Katherine Burggraf, Jesus De Loera


  1. Counting Peaks on Graphs
    submitted, 11 pp.
    w/ Alex Diaz-Lopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio
  2. Lattice Point Visibility On Power Functions
    INTEGERS, to appear, 6 pp.
    w/ Pamela E. Harris
  3. Descent Polynomials
    Discrete Mathematics, to appear, 26pp.
    w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko, Bruce Sagan
  4. Sparse Neural Codes
    Involve, to appear, 12 pp.
    w/ R. Amzi Jeffs, Natchanon Suaysom, Aleina Wachtel, Nora Youngs
  5. Neural Ideal Preserving Homomorphisms
    Journal of Pure and Applied Algebra, Vol 222, Issue 11, pp.3470-3482, 2018.
    w/ R. Amzi Jeffs, Nora Youngs
  6. The q-analog of Kostant's partition function and the highest root of the classical Lie algebras
    Australasian Journal Of Combinatorics , Vol 71, Issue 1, pp.68-91, 2018.
    w/ Pamela E. Harris, Erik Insko
  7. A Proof of the Peak Polynomial Positivity Conjecture
    Journal of Combinatorial Theory Series A, Vol 149, pp. 21-29, 2017.
    w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
  8. What makes a neural code convex?
    SIAM Journal on Applied Algebra and Geometry, Vol 1, Issue 1, p. 222-238, 2017.
    w/ Carina Curto, Elizabeth Gross, Jack Jeffries, Katherine Morrison, Zvi Rosen, Anne Shiu, Nora Youngs
  9. Low Degree Nullstellensatz Certificates for 3-Colorability
    Electronic Journal of Combinatorics, 23(1), P1.6, 2016.
    w/ Bo Li, Benjamin Lowenstein
  10. Chromatic Bounds on Orbital Chromatic Roots
    Electronic Journal of Combinatorics, 21(4), P4.17, 2014.
    w/ Dae Hyun Kim, Alexander H. Mun
  11. Strong Nonnegatvity and Sums of Squares on Real Varieties
    Journal of Pure and Applied Algebra 217 (5), pp. 843-850, 2013.
    w/ Brian Osserman
  12. On The Hardness of Counting and Sampling Center Strings
    IEEE/ACM Transactions on Computational Biology and Bioinformatics Vol. 9 Issue 6, pp. 1843-1846, 2012.
    w/ Christina Boucher
  13. Recognizing Graph Theoretic Properties with Polynomial Ideals
    Electronic Journal of Combinatorics, 17(1), R114, 2010.
    w/ Christopher Hillar, Jesus De Loera, Peter N. Malkin
  14. Asymptotics of Largest Components in Combinatorial Structures
    Algorithmica 46 (3-4), pp. 493-503, 2006.
    w/ Daniel Panario, Bruce Richmond, Jacki Whitely


  1. New Perspectives on Flexibility in Simple Temporal Planning
    International Conference on Automated Planning and Scheduling (ICAPS) 2018, 18pp., 2018.
    w/ J. Boerkoel, A. Huang, L. Lloyd
  2. A Proof of the Peak Polynomial Positivity Conjecture
    Formal Power Series and Algebraic Combinatorics 2017
    , 10pp., 2017. w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
  3. On The Hardness of Counting and Sampling Center Strings
    Proceedings of the 17th Annual Symposium on String Processing and Information Retrieval, pp. 128-135, 2010.
    w/ Christina Boucher
  4. Distribution of the Number of Encryptions in Revocation Schemes for Stateless Receivers
    Discrete Mathematics and Theoretical Computer Science, Fifth Colloquium on Math and Computer Science, pp. 195-206, 2008.
    w/ Christopher Eagle, Zhicheng Gao, Daniel Panario, Bruce Richmond


  1. I Felt Like a Mathematician: Combining Challenging Theorems with Creative Effort and Metacognition
  2. PRIMUS, to appear. 16pp.
    w/ Houssain El-Turkey, Gulden Karakok, Milos Savic, Gail Tang

  3. Pedagogical Practices for Fostering Mathematical Creativity and Proof-Based Courses: Three Case Studies
  4. Proceedings of the 20th Annual Conference on Research In Undergraduate Mathematics Education, 2017.
    w/ Emily Cilli-Turner, Houssain El-Turkey, Gulden Karakok, David Plaxco, Milos Savic, Gail Tang

  5. Tame The GRE Math Subject Test
  6. Math Horizons, Vol. 24, Issue 2, p.28-29, 2016.


  1. Applications of Convex and Algebraic Geometry to Graphs and Polytopes
    Ph.D. Thesis. Advisor: Jesus De Loera. UC Davis, 2011.
  2. Combinatorial Approaches to the Jacobian Conjecture
    Master's Thesis. Advisor: Ian P. Goulden. University of Waterloo, 2007.