A study of advanced topics in mathematics that are not considered in depth in other courses.

Student-led inquiry into a chosen area of mathematics with a final written report on the research.

In consultation with a faculty advisor students choose a mathematics topic for experiential inquiry that will develop into a senior thesis (MATH 410). Through student exploration and advisor feedback a selection of relevant readings and references are examined. A final written report is presented consisting of a detailed thesis proposal and a review of the literature.

This course includes a study of the ideas of classical number theory, their historical development, and modern applications. Topics include divisibility and prime numbers, modular arithmetic, primality tests, primitive roots, quadratic reciprocity, Diophantine equations, continued fractions, and applications such as cryptography.

The development of ideas from topology to manipulate and analyze datasets. Several topics from algebraic topology, geometry, linear algebra, abstract algebra, algorithms, and statistics will be utilized to understand recent results in data analysis. Students will use software for calculations such as persistent homology and Reeb graphs. Applications in fields such as image analysis, sensor networks, clustering, time series analysis, and genetics are discussed.

Finite geometries, transformations, Euclidean geometry, constructions, inverse geometry, projective geometry, non-Euclidean geometry.

This is a second course in the topics of pure mathematics, particularly those most commonly used in the study of Computing Science and related applications. It includes proof techniques, models of computation, formal languages, analysis of algorithms, trees and advanced general graph theory with applications, finite state and automata theory, encryption, and an elementary introduction to mathematical structures such as groups, rings, and fields.

Foundational mathematical concepts underpinning theoretical frameworks in data science that depend on linear algebra and multivariable calculus, with applications chosen from machine learning, statistical inference, and data assimilation. Possible topics include matrix decompositions, gradient and multivariate chain rule, Lagrange multipliers and constrained optimization, maximum likelihood, and Bayesian estimation.

This course covers numerical techniques for solving problems in applied mathematics, including error analysis, roots of equations, interpolation, numerical differentiation and integration, ordinary differential equations, matrix methods and selected topics from among: eigenvalues, approximation theory, non-linear systems, boundary-value problems, numerical solution of partial differential equations.

Sequences and induction; convergence of sequences and series; limits, continuity, and differentiability; Riemann integrals; sequences of functions and an introduction to topology.