This course introduces students to the concepts, techniques, and central theorems of vector calculus. It includes a study of line integrals, conservative vector fields, the flux of vector fields across curves and surfaces, Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem. Credit may not be earned for this class if it is earned in COS-MATH-221.

Dissertation research by the candidate for an appropriate topic as arranged between the candidate and the research advisor.

Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.

This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course.

Continuation of Thesis

The study of the dynamics of fluids is a central theme of modern applied mathematics. It is used to model a vast range of physical phenomena and plays a vital role in science and engineering. This course provides an introduction to the basic ideas of fluid dynamics, with an emphasis on rigorous treatment of fundamentals and the mathematical developments and issues. The course focuses on the background and motivation for recent mathematical and numerical work on the Euler and Navier-Stokes equations, and presents a mathematically intensive investigation of various models equations of fluid dynamics.

This course is a faculty-directed tutorial of appropriate topics that are not part of the formal curriculum. The level of study is appropriate for student in their final two years of study.

This course will provide a basic introduction to modern astrophysics, following on from Fundamental Astrophysics I. Topics will include basic celestial mechanics and galactic dynamics, the Milky Way and other galaxies, the interstellar medium, active galactic nuclei, galaxy formation and evolution, and an introduction to cosmology. This course will provide the physical background needed to interpret both observations and theoretical models in galactic and extragalactic astrophysics and cosmology and prepare students for more advanced topics and research in astrophysics.

This course introduces students to ideas and techniques from discrete mathematics that are widely used in Computer Science. Students will learn about the fundamentals of propositional and predicate calculus, set theory, relations, recursive structures and counting. This course will help increase students’ mathematical sophistication and their ability to handle abstract problems.

Continuation of Thesis

This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra.

This course introduces the programs within the School of Mathematical Sciences, and provides an introduction to math and statistics software. The course provides practice in technical writing.