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Courtney Gibbons


Courtney Gibbons
Courtney Gibbons

Assistant Professor of Mathematics

Christian A. Johnson Hall 109
315-859-4886

Courtney Gibbons received her doctorate from the University of Nebraska-Lincoln, where she studied homological properties of modules over quadratic algebras. A Connecticut native, Gibbons graduated summa cum laude with a bachelor's degree in mathematics from Colorado College in 2006. Her work appears in the Journal of Pure and Applied Algebra and will soon appear in the Journal of Commutative Algebra. She also codes for Macaulay 2, an open-source algebra software package. Gibbons plans to include Hamilton students in her research agenda and to design algebra electives that blend classical theory and modern applications.

I teach because I want to help students follow their enthusiasm — especially if that enthusiasm is for math.  Too often, mathematics is portrayed as a cold, austere subject. In reality, good mathematical thinking requires creativity, perseverance, teamwork and experimentation. Math is beautiful, but it's also a lot of fun.

Recent Courses Taught

Calculus I
Calculus II
Linear Algebra
Modern Algebra
Cryptography

Research Interests

My research area is commutative algebra, and I have a special interest in infinite free resolutions of modules over graded rings. Polynomial rings over a field (and quotients thereof) are especially nice because they can be viewed as a direct sum of finite dimensional vector spaces, and the same is true for their modules. These graded rings and modules arise in many settings - and have beautiful properties that make them interesting to study in their own right.

Distinctions

  • John R. Hatch Class of 1925 Excellence in Teaching Award, 2015
  • Project NExT Fellow, Academic Year 2013-14
  • Outstanding Graduate Teaching Assistant U. of Nebraska–Lincoln, 2011
  • Emeritus Faculty Fellow U. of Nebraska–Lincoln, 2010
  • Graduate fellowship U. of Nebraska–Lincoln, 2009
  • Outstanding qualifying exams U. of Nebraska–Lincoln, 2008
  • Florian Cajori Prize in Mathematics Colorado College, 2006

Selected Publications

  • “Modules Over Short Gorenstein Rings” (with Luchezar Avramov and Roger Wiegand), in preparation.
  • “NCAlgebra: A noncommutative algebra package for Macaulay2” (with Andrew Conner and Frank Moore), in preparation.
  • “Grandma Makes Granola”(with Dick Bedient); To appear in the College Mathematics Journal.
  • “Critical Pebbling Numbers of Graphs,” with J. D. Laison and E. J. Paul. Submitted.
  • "Critical Pebbling Numbers of Graphs," with C. R. Gibbons, J. D. Laison, E. J. Paul. Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 99, 2016, 199-224.
More... Less...
  • “Non-simplicial decompositions of Betti diagrams of complete intersections,” with J. Jeffries, S. Mayes, C. Raicu, B. Stone, and B. White. To appear, Journal of Commutative Algebra. arXiv:1301.3441
  • “The cone of Betti diagrams over a hypersurface ring of low embedding dimension,” with C. Berkesch, J. Burke, and D. Erman. Journal of Pure and Applied Algebra, Volume 216, Issue 10, October 2012, Pages 2256–2268
  • “Fixing numbers of graphs and groups,” with J. D. Laison. Electronic Journal of Combinatorics, Volume 16, Issue 1, 2009, R39

College Service

Honor Court
Phi Beta Kappa (vice president)
Vegan Club faculty advisor
Mathletics co-advisor

Professional Affiliations

American Mathematical Society
Association for Women in Mathematics
Mathematics Association of America
Society for Industrial and Applied Mathematics
Phi Beta Kappa

Appointed to the Faculty: 2013

Educational Background

Ph.D., University of Nebraska–Lincoln
M.S., University of Nebraska–Lincoln
B.A., Colorado College

Personal Interests

Rock climbing, reading, crocheting

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