Mohamed Omar
Bio/Contact
Teaching
Outreach
Talks
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 coauthors are in
orangered.
It is my mission to transform our society from math phobic to math loving. For more,
click here.
BOOKS/BOOK CHAPTERS
 Number Theory Toward RSA Cryptography: in 10 undergraduate lectures
CreateSpace, 2017.
 Algebraic and Geometric Methods in Applied Discrete Mathematics
Contemporary Mathematics, Proceedings of the AMS Special Session, Volume 685, 2017.
w/ Heather Harrington, Matthew Wright
 On Volumes of Permutation Polytopes
Fields Institute Communications, Discrete Geometry and Optimization, pp. 5577, 2013.
w/ Katherine Burggraf, Jesus De Loera
ARTICLES
 Distinct Distances Between Points On A Variety And An Arbitrary Point Set
in preparation, w/ Bryce McLaughlin
 Counting Peaks on Graphs
submitted, 11 pp.
w/ Alex DiazLopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio
 Lattice Point Visibility On Power Functions
INTEGERS, to appear, 6 pp.
w/ Pamela E. Harris
 Descent Polynomials
Discrete Mathematics, to appear, 26pp.
w/ Alex DiazLopez, Pamela E. Harris, Erik Insko, Bruce Sagan
 Sparse Neural Codes
Involve, to appear, 12 pp.
w/ R. Amzi Jeffs, Natchanon Suaysom, Aleina Wachtel, Nora Youngs
 Neural Ideal Preserving Homomorphisms
Journal of Pure and Applied Algebra, Vol 222, Issue 11, pp.34703482, 2018.
w/ R. Amzi Jeffs, Nora Youngs
 The qanalog of Kostant's partition function and the highest root of the classical Lie algebras
Australasian Journal Of Combinatorics , Vol 71, Issue 1, pp.6891, 2018.
w/ Pamela E. Harris, Erik Insko
 A Proof of the Peak Polynomial Positivity Conjecture
Journal of Combinatorial Theory Series A, Vol 149, pp. 2129, 2017.
w/ Alex DiazLopez, Pamela E. Harris, Erik Insko
 What makes a neural code convex?
SIAM Journal on Applied Algebra and Geometry, Vol 1, Issue 1, p. 222238, 2017.
w/ Carina Curto, Elizabeth Gross, Jack Jeffries, Katherine Morrison, Zvi Rosen, Anne Shiu, Nora Youngs
 Low Degree Nullstellensatz Certificates for 3Colorability
Electronic Journal of Combinatorics, 23(1), P1.6, 2016.
w/ Bo Li, Benjamin Lowenstein
 Chromatic Bounds on Orbital Chromatic Roots
Electronic Journal of Combinatorics, 21(4), P4.17, 2014.
w/ Dae Hyun Kim, Alexander H. Mun
 Strong Nonnegatvity and Sums of Squares on Real Varieties
Journal of Pure and Applied Algebra 217 (5), pp. 843850, 2013.
w/ Brian Osserman
 On The Hardness of Counting and Sampling Center Strings
IEEE/ACM Transactions on Computational Biology and Bioinformatics Vol. 9 Issue 6, pp. 18431846, 2012.
w/ Christina Boucher

Recognizing Graph Theoretic Properties with Polynomial Ideals
Electronic Journal of Combinatorics, 17(1), R114, 2010.
w/ Christopher Hillar, Jesus De Loera, Peter N. Malkin
 Asymptotics of Largest Components in Combinatorial Structures
Algorithmica 46 (34), pp. 493503, 2006.
w/ Daniel Panario, Bruce Richmond, Jacki Whitely
CONFERENCE ARTICLES
 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
 A Proof of the Peak Polynomial Positivity Conjecture
Formal Power Series and Algebraic Combinatorics 2017
, 10pp., 2017.
w/ Alex DiazLopez, Pamela E. Harris, Erik Insko
 On The Hardness of Counting and Sampling Center Strings
Proceedings of the 17th Annual Symposium on String Processing and Information Retrieval, pp. 128135, 2010.
w/ Christina Boucher
 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. 195206, 2008.
w/ Christopher Eagle, Zhicheng Gao, Daniel Panario, Bruce Richmond
PEDAGOGY ARTICLES
 I Felt Like a Mathematician: Combining Challenging Theorems with Creative Effort and Metacognition
PRIMUS, to appear. 16pp.
w/ Houssain ElTurkey, Gulden Karakok, Milos Savic, Gail Tang
 Pedagogical Practices for Fostering Mathematical Creativity and ProofBased Courses: Three Case Studies
Proceedings of the 20th Annual Conference on Research In Undergraduate Mathematics Education, 2017.
w/ Emily CilliTurner, Houssain ElTurkey, Gulden Karakok, David Plaxco, Milos Savic, Gail Tang
 Tame The GRE Math Subject Test
Math Horizons, Vol. 24, Issue 2, p.2829, 2016.
THESES

Applications of Convex and Algebraic Geometry to Graphs and Polytopes
Ph.D. Thesis. Advisor: Jesus De Loera. UC Davis, 2011.

Combinatorial Approaches to the Jacobian Conjecture
Master's Thesis. Advisor: Ian P. Goulden. University of Waterloo, 2007.