MATH 499C Basic Concepts and Examples in Chaos
Dr. Denny Gulick from the University of Maryland will give an undergraduate mini course on Basic Concepts and Examples in Chaos in the Spring semester of 1998. The class will meet during the weeks of March 9-20 only. Anyone interested is welcome to attend. Undergraduates wanting to take the course for one credit of MATH 499 should ask Deb Webb in the mathematics department for a course section permit. An abstract, course requirements, and syllabus follow.Short Abstract Recently chaos has become increasingly popular, in mathematics and with a wide variety of applications. In the mini course "Basic Concepts and Examples in Chaos" we will dwell on interesting properties of the famous tent function. Then we will analyze properties of the renowned quadratic functions, and will study one of the basic concepts in chaos: bifurcations. Our discussions will lead us to a definition of chaos, and to applications of chaos in the real world.
Course Requirements: Required Text: Encounters with Chaos by Denny Gulick, McGraw-Hill, Inc., 1992
Reading Assignment: Read, during March 9-13, sections 1.1-1.3 of Encounters with Chaos
Problem Assignment: Due March 16, 1998
- Sections 1.1-1.3 of Encounters with Chaos
1.1: 3, 4, 10, 11
1.2: 3, 4, 9a (using a computer or calculator), 14, 15
1.3: 1, 2, 3, 7, 10, 11, 23a
March 9-10: Chaos, Fractals, and Dynamics videotape by Robert Devaney shown and discussed
March 11-13 & 16: Professor Muenzenberger
- Sections 1.1-1.3 of Encounters with Chaos
- The tent function
The quadratic family
Different kinds of bifurcations
Chaos, and applications of chaos