Marissa Gee

The first course in the calculus sequence, this course covers the basic ideas of differential calculus. Differential calculus is concerned primarily with the fundamental problem of determining instantaneous rates of change. In this course, we study instantaneous rates of change from both a qualitative geometric and a quantitative analytic perspective. We cover in detail the underlying theory, techniques and applications of the derivative. Elementary differential equations and their applications are also introduced, along with the basics of anti-differentiation. Students who have 4 credit hours for calculus may not receive credit for MATH 111. This counts toward the core course requirement for the major. Prerequisite: solid grounding in algebra, trigonometry and elementary functions. Offered every semester.

This is the second course calculus sequence, this course focuses on integration, including Riemann sums, the Fundamental Theorem of Calculus, techniques of integration, numerical methods, and applications of integration. This study leads into the analysis of differential equations by separation of variables, Euler's method, and slope fields. This counts toward the core course requirement for the major. Prerequisite: MATH 111 or the equivalent. Offered every semester.

This course focuses on the study of vector spaces and linear functions between vector spaces. Ideas from linear algebra are useful in many areas of higher-level mathematics. Moreover, linear algebra has many applications to both the natural and social sciences, with examples arising in fields such as computer science, physics, chemistry, biology and economics. In this course, we use a computer software system, such as Maple or Matlab, to investigate important concepts and applications. Topics to be covered include methods for solving linear systems of equations, subspaces, matrices, eigenvalues and eigenvectors, linear transformations, orthogonality and diagonalization. Applications are included throughout the course. This counts toward the core course requirement for the major. Prerequisite: MATH 213. Generally offered three out of four semesters.

This is a second course focusing on the use of linear algebra to solve large-scale data and image problems. Applications may include, but are not limited to, tomography to reconstruct a 3-D image of a brain, regression to model climate data, prediction of long-term behavior of populations, fractal generation, image-blurring and edge detection, algorithmic approaches to suggest movies to users, linear classifiers to identify cancer risk, and linear optimization for resource allocation. Linear algebra concepts and tools are developed as needed to address the presented problems. In addition to extensions of topics from the first linear algebra course, this course includes a selection of topics from the following list: abstract vector spaces, orthogonal subspaces and projection operators, norms and inner products, Markov matrices, matrix decompositions (LU, Cholesky, Schur, SVD), and support vector machines. Solutions to or simulations of the applied problems presented are implemented in Matlab or similar software. This course counts toward the algebraic focus (column A) elective for the major. Prerequisite: Math 224.

This course introduces students to the concepts, techniques and power of mathematical modeling. Both deterministic and probabilistic models are explored, with examples taken from the social, physical and life sciences. Students engage cooperatively and individually in the formulation of mathematical models and in learning mathematical techniques used to investigate those models. This counts toward the computational/modeling/applied (column D) elective requirement for the major. Prerequisite: STAT 106 and MATH 224 or 258. Offered every other year.