**Computational Analytics (Final Approval Needed)**

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.

Hosting Dept. | MATH | Open To | MATH, PHYS, ICS, ME, EE |

Courses | MATH 405: Learning from Data MATH 477: Foundation of Scientific Computing MATH 485: Computational Inverse Problem COE 401: Modeling and Simulations | | |

* **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 or MATH 106 and STAT 201 or 212, or 319, and ICS 103

** ***MATH 477 Foundation of Scientific Computing*

Main topics include: Concepts of numerical mathematics, approximation tools, system of equations, least squares, numerical differentiation 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 models.

**Prerequisite:** MATH 371 is desirable

*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