These are some characteristic courses offered:
Introduction to Nonlinear Dynamics and Chaos
Dynamical systems are mathematical objects used to model phenomena of natural and social phenomena whose state changes over time. Nonlinear dynamical systems are able to show complicated temporal, spatial and spatio-temporal behavior. They include oscillatory and chaotic behaviors and spatial structures including fractals. Students will learn the basic mathematical concepts and methods used to describe dynamical systems. Applications will cover many scientific disciplines, including physics, chemistry, biology, economics, and other social sciences.
The first goal is to teach why nonlinear dynamics and chaos theory is important in understanding complicated behaviors. The second goal is to give an introductory overview about how the basic methods of nonlinear dynamic works. The course teaches the fundamental mathematical concepts of dynamical systems, such as state space, attractors, stability analysis, bifurcations etc. The course is designed for physics and math students, but other (eg. social) science majors interested in mathematical modeling might take the class.
Prerequisite: MATH 113 or permission.
Introduction to Cognitive Science
Cognitive science is the interdisciplinary study of mind and the nature of intelligence. It is a rapidly evolving field that deals with information processing, intelligent systems, complex cognition, and large-scale computation. The scientific discipline lies in the overlapping areas of neuroscience, psychology, computer science, linguistics and philosophy. Students will learn the basic physiological and psychological mechanisms and computational algorithms underlying different cognitive phenomena. This course is designed mostly for psychology and computer science students, but other students interested in interdisciplinary thinking might take the course. Prerequisite: PSYC-101 or COMP-105
Machine learning is a scientific discipline concerned with the design and development of algorithms that allows computers to modify their actions based on empirical data. In the age of the data deluge it is very important to see the existing current techniques and to understand applications used in various disciplines of the natural and social sciences including bioinformatics, financial engineering, robotics, data mining etc.
This course will provide a survey of some of the most popular machine learning algorithms, including neural networks, genetic algorithms, reinforcement learning, and statistical methods. Students will implement and test a subset of these algorithms on real data sets.
Prerequisites for the course are COMP210 and Calculus.
Introduction to Complex Systems
Study of how collective behavior emerges from the interaction between a system’s parts and its environment. Model systems from the natural sciences and social sciences will be used as examples. Both historical and contemporary approaches will be discussed.
Study of mathematical models, computational algorithms, and simulation methods that contribute to our understanding of neural mechanisms. Brief introduction to neurobiological concepts and mathematical techniques. Both normal and pathological behaviors will be analyzed by using neural models. Prerequisite: PSYC-101 and MATH-113
Predictability, Theory and Applications
Dynamic Modules in Social Sciences
The goal is to explain why and how concepts and methods of physics has influenced the development of economics. While classical theories of economics study mostly equilibrium behaviors, dynamical models of mathematical physics contribute to understanding the dynamics of economical behavior. In the first half of the course you will learn typical non-equilibrium, nonlinear phenomena, as economical cycles and chaotic phenomena. In the second half of the term probabilistic methods will be presented to study large fluctuations, extreme events. This second area belongs narrowly speaking a new field, called econophysics.
Complex World Problems
The intention of this class is demonstrate the role of complex systems thinking in two classes of problems: in language and decision making, respectively.
The structure, evolution and acquisition of language is studied from the perspective of complex systems. Network representation and the role of chaos theory is
A new field, the overlapping area of economics and psychology, explains, why people are not making rational decisions, despite their best efforts. Belief in the ultimate rationality of humans, organizations and markets now challenged, but our behavioral patterns seems to be predictable. We are predictably irrational.