This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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Description

MATH 452 is a one semester introduction to dynamics and chaos. The course focuses on the basic structures of one and two dimensional dynamical systems and families of systems. Below is listed the core topics of the course. The instructor should feel free to augment this basic material with more advanced subjects.

Prerequisites

Minimum grade of C- in MATH341; or Minimum grade of C- in MATH246 and (MATH240 or MATH461). It is also recommended that the student have some additional 400 level courses in Mathematics, Science, or Engineering. (In some classes, each student will develop a project usually involving numerical investigations.) 


Level of Rigor

Advanced


Sample Textbooks

First Course in Chaotic Dynamical System by DeVaney

An Introduction to Chaotic Dynamical Systems, by DeVaney


Applications

Philosophy, economics, physics, astronomy


If you like this course, you might also consider the following courses



Additional Notes

Duplicate credit with AMSC452

Topics

One and Two Dimensional Dynamics

Fixed and periodic points

Families of functions and bifurcation

The Li-Yorke theorem and Sarkovskii's theorem

Stable and unstable manifolds

Horseshoe maps

Sensitive dependence

Lyapunov exponents