This course introduces the mathematical background necessary to understand, design, and effectively deploy AI systems. It focuses on four key areas of mathematics: (1) linear algebra, which enables describing, storing, analyzing and manipulating large-scale data; (2) optimization theory, which provides a framework for training AI systems; (3) probability and statistics, which underpin many machine learning algorithms and systems; and (4) numerical analysis, which illuminates the behavior of mathematical and statistical algorithms when implemented on computers.

This course introduces a rich variety of geometry topics beyond those studied at the high school level. Each topic is augmented with connections to the arts, sciences, engineering, and other everyday applications. Course activities will emphasize problem solving in geometry and communicating mathematical arguments in the context of geometry. Geometric concepts will be explored using technology as well.

This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals.

This is the second in a two-course sequence. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates.

This is the second in a two-course sequence intended for students majoring in mathematics, science, or engineering. The course includes the same topics as MATH-182, but the focus of the workshop component is different. Whereas workshops attached to 182 emphasize concept development and real-world applications, the workshops of MATH-182A emphasize skill development and provide just-in-time review of precalculus material as needed. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates.

This is a course suitable for first-year students that covers topics not currently offered in the curriculum. This course is structured as an ordinary course and has specific prerequisites, contact hours, and examination procedures.

This course is principally a study of the calculus of functions of two or more variables, but also includes the study of vectors, vector-valued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, and includes applications in physics. Credit cannot be granted for both this course and MATH-221.

This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab or R is used for data analysis and statistical applications.

This course provides challenging problems in probability whose solutions require a combination of skills that one acquires in a typical mathematical statistics curriculum. Course work synthesizes basic, essential problem-solving ideas and techniques as they apply to actuarial mathematics and the first actuarial exam.

This course examines concepts in finance from a mathematical viewpoint. It includes topics such as the Black-Scholes model, financial derivatives, the binomial model, and an introduction to stochastic calculus. Although the course is mathematical in nature, only a background in calculus (including Taylor series) and basic probability is assumed; other mathematical concepts and numerical methods are introduced as needed.

This course develops strategies for solving problems that are chosen from a wide variety of areas in mathematics. Students present solutions to the class or instructor.

This course provides an introduction to boundary value problems. Topics include Fourier series, separation of variables, Laplace's equation, the heat equation, and the wave equation in Cartesian and polar coordinate systems.

This is a second course in linear algebra that provides an in-depth study of fundamental concepts of the subject. It focuses largely on the effect that a choice of basis has on our understanding of and ability to solve problems with linear operators. Topics include linear transformations, similarity, inner products and orthogonality, QR factorization, singular value decomposition, and the Spectral Theorem. The course includes both computational techniques and the further development of mathematical reasoning skills.

This course covers the algebra of complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy's integral theorem and integral formulas, Taylor and Laurent series, residues, and the calculation of real-valued integrals by complex-variable methods.

This course is an investigation and extension of the theoretical aspects of elementary calculus. Topics include mathematical induction, real numbers, sequences, functions, limits, and continuity. The workshop will focus on helping students develop skill in writing proofs.

This course is a faculty-directed project that could be considered original in nature. The level of work is appropriate for students in their final two years of undergraduate study.

This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.

This course is a cooperative education experience for undergraduate students majoring in Applied Mathematics, Computational Mathematics or Statistics.

The experiential learning requirement in the Applied Mathematics and Computational Mathematics programs can be accomplished in various ways. This course exists to record the completion of experiential learning activities that have been pre-approved by the School of Mathematical Sciences. Such pre-approval is considered on a case-by-case basis.

This course serves as a bridge course that builds the mathematical foundations needed for the IDAI-620 course, Mathematical Methods for Artificial Intelligence, a course introducing the mathematical background for AI systems in the MS in AI program. It focuses on the basic constructions, structures, and results in four key areas: (1) linear algebra (vectors, matrices, and their operations) (2) optimization theory (multivariable functions and their calculus) (3) probability and statistics (basic combinatorics, elementary statistics) and (4) numerical analysis (basic notions of approximation).

This course covers an analysis of iterations of maps, symbolic dynamics, their uses, and fractals. It includes methods for simplifying dynamical systems (center manifolds and normal forms), Melnikov's method, and applications.

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

This course is a faculty-directed project that could be considered original in nature. The level of work is appropriate for students in their final two years of undergraduate study.

This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.