Complexity Theory: An Introduction | Math Online Course by Udemy

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An intuitive and clear introduction to the exciting new area of complex systems theory

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Complexity Theory: An Introduction

“I think the next [21st] century will be the century of complexity Stephen W. Hawking This course is an introduction to the core concepts of complex systems theory, an exciting new area that is offering us a fresh perspective on issues such as understanding our financial system, the environment and large social organizations. The aim of this course is to bring the often abstract and sophisticated concepts of this subject down to earth and understandable in an intuitive form. After having started with an overview to complex systems this course will focus upon five of the core concepts. Systems: We will start with two sections on systems theory and systems thinking, this should introduce students to the bigger picture of why complex systems is seen as a new paradigm in science; what exactly this new paradigm is; why we need it and lastly how it differs from our traditional methods of scientific inquiry. Nonlinear systems: The term nonlinear science and complex systems are often used interchangeably showing how essential the concept of nonlinearity is to this subject. In this section we draw the distinction between linear and nonlinear systems and see why it matters. The second part of this section covers the subject of chaos theory and the dynamics of nonlinear systems. Network theory: network theory and networks in general have arisen in almost all fields of inquiry in the past few decades making it one of the most active and exciting areas of scientific study. We will explore many different types of networks, their properties and examples in the real world from social networks to logistics networks. This section will conclude by looking at graph theory, the mathematical foundations that lie behind networks. Complex adaptive systems(CAS): CAS is increasingly being used to model a wide variety of systems from, electrical power grids to economies and cultures it represents a powerful new way of seeing the world. This section will also cover CASs close relative cybernetics and the basic concept of adaptation and evolution. Self-organization: Self-organization is another of the foundational concepts within complex systems that is proving particularly relevant to the world of the 21st century as we see collaborative self-organizing groups such as Wikipedia and the Linux foundation emerge. But self-organization is more than just a social phenomenon, we explore how it is in fact ubiquitous in our world from the formation of fish schools to magnetization and traffic jams. In conclusion a short film on complex systems Is presented to give you an idea of where the subject is today and what are the main challenges going forward. Each subject is broken down into three lessons the first being an introduction to the topic delivered through video. This will be followed by a slide presentation that digs deeper into the main themes introduced in the first lesson, followed up with a quick(optional) quiz to get you thinking.”

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