This interdisciplinary program focuses on developing models to understand the inherent structure of the data. Topics include inference, least-square estimation, interpolations, adaptive approximations, numerical differentiation and integration, quadrature, multistep methods, finite difference, and applications to steady-state and time-dependent problems involving initial-value and boundary-value problems. The program also covers simulation, in terms of queuing systems, stochastic processes, random number generation, Monte Carlo methods, and software techniques for building simulators. The inverse problem is also covered, whose methods describe identifying the parameters and structures of models that give rise to the recorded observation, an essential tool to understanding physical phenomena. Students are also introduced to several case studies in science and engineering. 

 MATH 405 Learning from Data

The aim of this course is to provide students with selected topics from linear algebra, statistics, and optimization concepts with an emphasis on their applications in machine learning algorithms like Linear Regression and Neural Networks using numerical software, toolboxes, and libraries.

Topics: basic matrix operations, Factorizations, Basic Probability Theory, Inference, Least-Square Estimation, Maximum Likelihood Estimation, and Gradient Descent. 

Prerequisite: MATH 102 and STAT 201 or 212, or 319, and ICS 104

 MATH 477 Numerical Methods and Computing

This course introduces some numerical methods with applications in the field of the Science and Engineering. Topics include concepts of numerical mathematics, approximation tools, system of equations, least squares, numerical differentialtion and integration, quadrature on different geometries, Runge-Kutta and multistep methods for initial value problems, finite difference methods for initial and boundary value problems. Applications to steady-state and time-dependent problems. 

Prerequisite: MATH 102

COE 401: Modeling and Simulations

Approaches to the simulation problem (event scheduling, process-based, etc.). Modeling and simulation of queuing systems. Probability, stochastic processes, and statistics in simulation. Random number generation. Monte Carlo methods. Building valid and credible simulation models. Output data analysis. Simulation formalisms. Software techniques for building simulators. Case studies.

Prerequisite: Senior Standing

MATH 485: Computational Inverse Problem

This course introduces students to fundamental concepts of linear and nonlinear inverse problems. Emphasis is placed on describing how to integrate various information sources from measured data and prior knowledge about the inverted model. Computer lab sessions will be organized to combine classroom learning with hands-on applications.

Topics: Regression, least squares, Maximum likelihood estimation, Ill-conditioning, SVD solutions, regularizations (Tikohonov, spectral filtering), proximal and primal-dual iterative schemes, gradient-based & global optimization methods, OCCAM method.

Prerequisite: MATH 405