MAT 1980H - THE ESSENTIALS OF CHAOS THEORY

credits: 3.0
Every once in a while in the history of science, an idea surfaces that revolutionizes the way we understand our world. Recent advances in dynamical systems theory (a branch of mathematics) have led researchers to discover amazing hidden orders in many phenomena that appear to be completely disorganized. The study of these phenomena, and the mathematics used to understand them, has come to be known as chaos theory. The way in which chaos theory has developed in the scientific community resembles a path outlined in Thomas Kuhn’s book The Structure of Scientific Revolutions. Central to Kuhn’s thesis is the notion of a paradigm shift, a moment in which the scientific community begins to evaluate evidence in a completely new fashion. Acceptance of chaos theory as a means of describing complicated phenomena can be taken as evidence that a paradigm shift has indeed occurred in the sciences. In this course, students will investigate the basic mathematics behind chaotic phenomena. Through experimentation and simulation, will see chaos theory in action. Will study the history of chaos theory and compare it to the history of other scientific revolutions. Will learn about the ways in which chaos theory and fractal geometry have become an important part of modern life, with examples that range from medicine to filmmaking. Objectives: A) Applied algebraic and geometric methods to analyze the behavior of chaotic systems; B) Through experimentation and computer simulation, observed and documented several physical phenomena that exhibit chaotic behavior; C) Identified key moments in the history of chaos theory, analyzed its history and compared it to the history of other scientific revolutions, and evaluated the idea that chaos theory represents a paradigm shift in scientific thinking; D) Identified many ways in which chaos theory has been applied, including (but not limited to) examples from medicine, information theory, and engineering. Method of Instruction: Lecture, discussion, computer simulation, laboratory experiments, and a small amount of video viewing. Method of Evaluation: Homework-Discussions 25%, Quizzes-Exams 25%, Laboratory reports 25%, Computer projects 25%.

Prerequisite(s): Enrollment in the Honor Program or Permission of Instructor and either of MAT 1030 - COLLEGE ALGEBRA (or) MAT 1930 - IMMERSION COLLEGE ALGEBRA (or) MAT 1090 - PRECALCULUS (or) MAT 1091 - PRE-CALCULUS I (or) MAT 1092 - PRE-CALCULUS II (or) MAT 2010 - CALCULUS I(or) MAT 2020 - CALCULUS II