My research interest is in Mathematical Biology, in particular applications in ecology, infectious diseases, pollination biology and agriculture.
I am looking for undergraduate or graduate students who want to pursue research in this area. If you are interested, please email me.
|California State University, Chico|
|Department of Mathematics and Statistics|
|400 W 1st St|
|Chico, CA 95929|
First order separable, linear, and exact equations; second order linear equations, Laplace transforms, series solutions at an ordinary point, systems of first order linear equations, and applications.
Systems of first order linear equations, existence and uniqueness theorems, stability, Sturm separation theorems, power series methods
The definite integral and applications to area, volume, work, differential equations, etc. Sequences and series, vectors and analytic geometry in 2 and 3-space, polar coordinates, and parametric equations.
Partial differential equations, separation of variables, orthogonal sets of functions, Sturm-Liouville problems, Fourier series, boundary value problems for the wave equation, heat equation, and Laplace equation; Bessel functions, Legendre polynomials
A rigorous introduction to discrete mathematical structures for computer science majors (fulfills a requirement for the minor in math). Topics include propositional and predicate calculus; basic proof methods; sets, functions, and operations with them; algorithms and their complexity; applications of number theory to computer science and computer security; matrices and matrix arithmetic; mathematical induction, recursive definitions and algorithms; combinatorics and counting techniques; relations and their representation by matrices and digraphs, applications to databases; equivalence relations and partitions of sets; partially ordered sets, lattices, and Boolean algebras; Boolean functions and circuits; graphs, trees, and their applications; formal languages and grammars; finite-state automata and language recognition, regular languages.
Limits and continuity. The derivative and applications to related rates, maxma and minima, and curve sketching. Transcendental functions. An introduction to the definite integral and area.
This course involves collaborative learning. It is an introduction to single variable calculus aimed at students who have seen some calculus before, either before matriculation or in introductory calculus course (Math 1). Math 3 begins by revisiting the core topics in Math 1 - convergence, limits, and derivatives - in greater depth before moving to applications of differentiation such as related rates, finding extreme values, and optimization. The course then turns to integration theory, introducing the integral via Riemann sums, the fundamental theorem of calculus, and basic techniques of integration.
This course is a sequel to Math 3 and provides an introduction to Taylor series and functions of several variables. The first third of the course is devoted to approximation of functions by Taylor polynomials and representing functions by Taylor series. The second third of the course introduces vector-valued functions. It begins with the study of vector geometry, equations of lines and planes, and space curves. The last third of the course is devoted to studying differential calculus of functions of several variables.
This course is designed to provide students with the basic tools for building and analyzing mathematical models in Biology primarily using ordinary differential equations. In addition, you will learn how to analyze and simulate the models. You will also learn to interpret and communicate the results in the context of biology.
This course presents the fundamental concepts and applications of linear algebra with emphasis on Euclidean space. Significant goals of the course are that the student develop the ability to perform meaningful computations and to write accurate proofs. Topics include bases, subspaces, dimension, determinants, characteristic polynomials, eigenvalues, eigenvectors, and especially matrix representations of linear transformations and change of basis. Applications may be drawn from areas such as optimization, statistics, biology, physics, and signal processing.
This course is a sequel to Math 8 and provides an introduction to calculus of vector-valued functions. The course starts with iterated, double, triple, and surface integrals including change of coordinates. The remainder of the course is devoted to vector fields, line integrals, Green’s theorem, curl and divergence, and Stokes’ theorem.
This course is a survey of important types of differential equations, both linear and nonlinear. Topics include the study of systems of ordinary differential equations using eigenvectors and eigenvalues, numerical solutions of first and second order equations and of systems, and the solution of elementary partial differential equations using Fourier series.
Recent years have seen a dramatic decline in the number of honeybee colonies in North America and Europe. There is no consensus that explains the colony losses. Possible factors include, but are not limited to, varroa mites and the deadly viruses they carry, pesticides, nosema, and extreme winter conditions. I develop mathematical models of honeybee colony infestation by Acute Bee Paralysis Virus (ABPV) that is carried and transmitted by a parasitic varroa mite. The models are formulated in terms of non-linear ordinary differential equations. Our first model uses constant coefficients, which are, strictly speaking, valid for a single season at most, under the assumption that seasonal averages are representative of environmental dynamics and under the assumption that the dynamics are fast enough, such that the system equilibrates quickly, in less than a single season.
I gave a plenary talk at Sonia Kovalevsky day which was very well-received.
In addition to the classroom teaching, I encourage my students to participate in activities like Association of Women in Mathematics (AWM) national essay competition. One of my students won this competition.
I also participated in TechWomen Ambassadors program whose purpose is to promote women in STEM fields.