This course will introduce students to foundational concepts in numerical computation that are useful for engineering and the mathematical, computational, and physical sciences. Topics will include floating-point arithmetic, error analysis, linear and nonlinear equations, numerical solution of systems of algebraic equations, constrained and unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, and basic methods for sampling stochastic processes. Implementation of various numerical methods and solvers will be done in Python, MATLAB, and R. Connections to computational modeling of cognition will be made throughout the course as motivating examples for various key concepts and tools.

This course will introduce students to the mathematical and philosophical foundations of cognitive modeling as well as the key concepts and tools needed for developing and applying cognitive architectures. Furthermore, the course will survey seminal papers as well as leading computational frameworks used in understanding human cognition and intelligence.Topics will include fundamentals of signal detection theory, probability modeling and information theory, the Lens Model, statistical (Bayesian) modeling of various cognitive actions and behavior, dynamical systems, symbolic and sub-symbolic representations, and simulation using artificial neural networks. Students will learn how to use one or more major cognitive architectures, e.g., MicroSAINT, Act-R, Soar, Nengo, and build basic computational models of cognitive processes, including those related to categorization, language, memory, decision making, and reasoning, fitting and evaluating their models to different kinds of behavioral data.

An introduction to both foundational and modern machine learning theories and algorithms, and their application in classification and regression. Topics include: Mathematical background of machine learning (e.g. statistical analysis and visualization of data), Bayesian decision theory, parametric and non-parameteric classification models (e.g., SVMs and Nearest Neighbor models) and neural network models (e.g. Convolutional, Recurrent, and Deep Neural Networks). Programming assignments are required.

There have been significant advances in recent years in the areas of neuroscience, cognitive science and physiology related to how humans process information. In this course students will focus on developing computational models that are biologically inspired to solve complex problems. A research paper and programming project on a relevant topic will be required. A background in biology is not required.

The course will introduce students into the current state of artificial neural networks. It will review different application areas such as intrusion detection and monitoring systems, pattern recognition, access control and biological authentication, and their design. The students will be required to conduct research and analysis of existing applications and tools as well as to implement a course programming project on design of a specified application based on neural networks and/or fuzzy rules systems.

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