IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Joshua Cooper

  • Associate Professor
  • Department of Mathematics
  • University of South Carolina


Ph.D. Mathematics University of California, San Diego 2003
B.S. Mathematics MIT, Cambridge, MA 1998


2010 – Present Associate Professor Department of Mathematics, Univ. of South Carolina
2006 – Present Palmetto Assistant Professor Department of Mathematics, Univ. of South Carolina
2006 Post-doctoral Researcher Department of Mathematics, UCSD
2005 – 2006 Senior Scientist Combinatorial Structures and Algorithms Group, ETH-Zürich
2003 – 2005 Postdoctoral Research Fellow Courant Institute of Mathematical Sciences, NYU
2003 Consultant Microsoft Research (Theory Group), Redmond, WA


Research Interests

  • Quasirandomness
  • Spectral Hypergraph Theory
  • Discrete Geometry
  • Universal Cycles
  • Combinatorial Number Theory
  • Coding Theory
  • Extremal Graphs
  • Matrices over GF(2) and Graph Pressing
  • Applied Machine Learning
  • Permutation Patterns

Current Projects

  • Graph pressing sequences. We use matrix algebra over GF(2) to study graph-theoretic problems arising from computational phylogenetics: Can sortings-by-reversal be efficiently sampled? When are they unique? Are they highly connected by "small edits"?

  • Spectral hypergraph theory. We study the connection between the homogeneous spectra of hypermatrices/tensors (e.g., the adjacency hypermatrix and Laplacian) associated with hypergraphs and the properties of those hypergraphs, such as degree sequences, subgraph counts, k-partiteness, and connectivity.

  • CNNs in Biology. We apply modern image processing techniques (especially, deep convolutional neural networks) to perform classification and quantitation of cell phenotypes in microscopy performed during immunological/hematological experiments.


Teaching Activities

Current Courses

  • Math 374 - Discrete Mathematics for Computer Science
  • Math 574 - Discrete Mathematics

Previous Courses

  • Math 141 - Calculus I
  • Math 142 - Calculus II
  • Math 241 - Vector Calculus
  • Math 374 - Discrete Mathematics for Computer Science
  • Math 511 - Probability
  • Math 544 - Linear Algebra
  • Math 570 - Discrete Optimization
  • Math 574 - Discrete Mathematics
  • Math 575 - Discrete Mathematics II
  • Math 776 - Graph Theory I
  • Math 777 - Graph Theory II
  • Math778C - Topics in Combinatorics: Combinatorial Complexity
  • Math778G - Topics in Combinatorics: Discrete Geometry
  • Math778P - Topics in Combinatorics: Probabilistic Methods


Honors and Other Special Scientific Recognition

  • University of South Carolina Distinguished Undergraduate Research Mentor 2009
  • 6 times awarded Magellan Scholarship to mentor undergraduate research 2007--2011
  • Co-PI (with Linyuan Lu) of National Science Foundation (NSF) Division of Undergraduate Education: Course, Curriculum, and Laboratory Improvement (Type 2), "Collaborative Research: STEM Real World Applications of Mathematics" (DUE-CCLI-1020692) 2010-2012.
  • PI of National Science Foundation (NSF) Division of Mathematical Sciences: Algebra, Number Theory, and Combinatorics Award, "Combinatorial Quasirandomness and its Applications" (DMS-ANTC-1001370) 2010--2013.
  • NSF Mathematical Sciences Postdoctoral Research Fellow 2003


5 Selected Publications

  • J. N. Cooper, A. Dutle, Spectra of Hypergraphs, Linear Alg. and Appl., to appear.
  • J. N. Cooper, B. Doerr, J. Spencer, G. Tardos, Deterministic Random Walks on the Integers, Euro. J. Comb., 28 (2007), no. 8, 2072--2090.
  • J. N. Cooper, A Permutation Regularity Lemma, Electronic J. Comb., 13 (2006), #R22.
  • J. N. Cooper and R. L. Graham, Generalized de Bruijn Cycles, Ann. Comb., 8 (2004), no. 1, 13--25.
  • J. N. Cooper, Quasirandom Permutations, J. Comb. Th. Ser. A, 106 (2004), no. 1, 123--143.


IMI Preprints and Seminars

Go to the list of 14 seminars by Joshua Cooper.


Curriculum Vitae

© Interdisciplinary Mathematics Institute | The University of South Carolina Board of Trustees | Webmaster