Dr. Clelland's research uses methods from geometry to study a variety of problems in differential equations, including differential equations that arise naturally in various contexts in differential geometry. Her recent and current research in this area includes the study of Backlund transformations for hyperbolic partial differential equations, dynamic equivalence and dynamic feedback linearization for control systems, and isometric immersion of Riemannian manifolds, among other topics. More recently, Dr. Clelland has begun studying the mathematics of redistricting, and in particular, mathematical methods for identifying and analyzing gerrymandering, with a particular focus on Colorado's Congressional and State Legislative district plans.
keywords
Geometry of differential equations, Exterior differential systems, Cartan's method of moving frames, Backlund transformations, Geometry of control systems, Dynamic equivalence for control systems, Isometric embeddings of Riemannian manifolds, Darboux integrability, Mathematics of redistricting and elections, Ensemble analysis
MATH 2001  Introduction to Discrete Mathematics
Primary Instructor

Spring 2019 / Fall 2019
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
MATH 3430  Ordinary Differential Equations
Primary Instructor

Spring 2018 / Fall 2019
Involves an elementary systematic introduction to firstorder scalar differential equations, nth order linear differential equations, and ndimensional linear systems of firstorder differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness and numerical solutions. Formerly MATH 4430.
MATH 4230  Differential Geometry of Curves and Surfaces
Primary Instructor

Fall 2018 / Fall 2020 / Fall 2022
Introduces the modern differential geometry of plane curves, space curves, and surfaces in 3dimensional space. Topics include the Frenet frame, curvature and torsion for space curves; Gauss and mean curvature for surfaces; Gauss and Codazzi equations, and the GaussBonnet theorem. Same as MATH 5230.
MATH 4470  Partial Differential Equations
Primary Instructor

Spring 2020 / Spring 2021
Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green's function, and variational methods. Same as MATH 5470.
MATH 4810  Special Topics in Mathematics
Primary Instructor

Fall 2020
Covers various topics not normally covered in the curriculum. Offered intermittently depending on student demand and availability of instructors. May be repeated up to 7 total credit hours. Same as MATH 5810.
MATH 5230  Differential Geometry of Curves and Surfaces
Primary Instructor

Fall 2018 / Fall 2020 / Fall 2022
Introduces the modern differential geometry of plane curves, space curves, and surfaces in 3dimensional space. Topics include the Frenet frame, curvature and torsion for space curves; Gauss and mean curvature for surfaces; Gauss and Codazzi equations, and the GaussBonnet theorem. Same as MATH 4230.
MATH 5470  Partial Differential Equations
Primary Instructor

Spring 2020 / Spring 2021
Studies initial boundary and eigenvalue problems for the wave, heat and potential equations. Solution by separation of variables, Green's function, and variational methods. Department enforced prerequisite: MATH 3430 or MATH 5430. Instructor consent required for undergraduates. Same as MATH 4470.
MATH 5810  Special Topics in Mathematics
Primary Instructor

Fall 2020
Covers various topics not normally covered in the curriculum. Offered intermittently depending on student demand and availability of instructors. May be repeated up to 7 total credit hours. Same as MATH 4810.
MATH 6230  Introduction to Differential Geometry 1
Primary Instructor

Spring 2018 / Spring 2019
Introduces topological and differential manifolds, vector bundles, differential forms, de Rham cohomology, integration, Riemannian metrics, connections and curvature. Department enforced prerequisites: MATH 2130 and MATH 4001. Instructor consent required for undergraduates.