• Instructor: Bruce Peckham, Professor, Dept. of Mathematics and Statistics
• Office: 140C Campus Center, 726-6188, bpeckham@d.umn.edu
  Office Hours: M 11-12, W 12-1, Th 2-3, F 11-12, or by appointment
  
• Meeting times: MWF 10-10:50 in EduE 50
  EXCEPTION: Tests will be given at night to allow for more time. Monday Oct 12 and Tuesday Nov 24 will be 6-7:30 in order to allow 90 minutes. Computer labs will occasionally be done in class.
  
  
• Texts:
• A First Course in Chaotic Dynamical Systems: Theory and Experiment by R. L. Devaney, Addison-Wesley, 1992. Introductory text for discrete dynamical systems, including complex dynamics (Mandelbrot set, Julia Sets). Aimed at the junior-senior mathematics major level.
• Nonlinear Dynamics and Chaos, by Steven Strogatz, 1994. Introductory senior-graduate text in dynamical systems. Covers both continuous and discrete dynamical systems, although we will use this text primarily for its coverage of continuous dynamical systems.

The material is mostly covered in Chapters 1-17 of Devaney and Chapters 1-9 of the Strogatz text. Not all sections of all chapters will be covered. Some supplemental material, not included in the text, will occasionally be presented in lecture.

For regular homework sets, you are encouraged to exchange ideas with each other, but each person should write up his/her solutions completely in his/her own words. It is never appropriate to give a written version of a problem/proof to another classmate, except to have the classmate read and evaluate your work with you present. It is OK to verbally explain your ideas to another classmate, as long as the classmate then writes up his/her work on his/her own. One person copying a classmate's solution(s) is expressly forbidden and will result in both students receiving zeroes for that complete homework set and facing academic disciplinary action. Copying from textbooks or online resources is also expressly forbidden and will result in zero for that assignment. ANY WORK YOU HAND IN THAT IS NOT COMPLETELY YOUR OWN SHOULD BE PROPERLY REFERENCED. THIS INCLUDES COLLABORATION WITH OTHER STUDENTS AND MATERIAL TAKEN FROM OTHER TEXTBOOKS OR ONLINE RESOURCES. You need not reference material taken from either textbook.

It is often instructive to read the problems at the end of each section and think about how you would solve them, even if you don't actually attempt to solve them.

Late homework will be accepted, but unless you make specific prior arrangements with me, points will be taken off. Deduction schedule: 10% off per day late. Weekends count as one day. (For example, one week late will be 50% off.) Work more than one week late will count 50%. Grace days: the first 5 days late - either for one homework, or split between multiple homeworks.

Assignments will be posted on the course homepage at http://www.d.umn.edu/~bpeckham/5260/F2013/Math5260F2013.html

Computational expectations. Most labs for discrete dynamical systems will be performed with spreadsheets or software from the Boston University Dynamics Website. Labs for continuous dynamical systems (differential equations) will use either software linked to the course homepage, or Mathematica. No computer programming will be required, but writing your own programs to do your own investigations, or to duplicate tasks performed by the course software, is encouraged. Use of the ``Manipulate'' command in Mathematica could be especially productive!

• Lower level and Popular:
  • Differential Equations, by Blanchard, Devaney and Hall, 1995. Emphasizes the qualitative and numerical as well as analytical approach.
  • Fundamentals of Differential Equations, by Nagle and Saff. Text for UMD's old Differential Equations I course (prior to 2000).
  • Differential Equations and Linear Algebra, by Edwards and Penny, 2nd edition, 2005. UMD's text for Math 3280, Differential Equations with Linear Algebra.
  • Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics, by R. L. Devaney, Addison-Wesley, 1990. Introduction to discrete dynamical systems, aimed at high school level (but containing much more).
  • Chaos: Making a New Science, by J. Gleick, Viking, 1987. A novel giving the history of some of the ``players'' in Chaos theory. Alludes to mathematics which will be taught in this course.
  • Does God Play Dice?, by Ian Stewart, 1989. Another popular book about the mathematics of chaos. More mathematics than Gleick, but less than Math 5260.
  • A Tool Kit of Dynamics Activities, by Robert Devaney, Jonathon Choate, and Alice Foster. A series of four workbooks about dynamical systems. Designed for high school teachers to either supplement or replace material in their high school math courses. Used in a Freshman Seminar course (Math 1234) taught by Prof. Peckham in Spring 2003.
• Comparable level
  • Differential Equations, Dynamical Systems, and An Introduction to Chaos, by Morris Hirsch, Stephen Smale, and Robert Devaney, 2004. Advanced undergraduate / beginning graduate text which emphasizes continuous dynamical systems (differential equations). Emphasis on theory, but with great treatment of classical applications: predator-prey, van der Pol equation, n-body problem, Lorenz attractor. Used in the past for the continuous part of 5260.
  • Chaos: An introduction to dynamical systems by Alligood, Sauer, and Yorke, Springer-Verlag, 1996. Second choice for text for Math 5260. Includes both differential equations and discrete dynamical sytems.
  • Differential Equations and Dynamical Systems, by L. Perko, Springer-Verlag, 1991.
  • Differential Equations: A Dynamical Systems Approach, by Hubbard and West, Springer-Verlag, 1991.
  • Dynamics and Bifurcations, by Hale and Kocak, Springer-Verlag, 1991. Text used for the old (pre-1999) quarter course Differential Equations II (Math Q5385). Differential equations and discrete dynamical systems.
  • An introduction to dynamnical sytems: continuous and discrete, by Clark Robinson, Pearson/Prentice Hall, 2004. Large overlap with Math 5260. Second choice for text for Math 5260.
• Higher level
  • Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, by Guckenheimer and Holmes, Springer-Verlag, 1982. Classic introductory graduate differential equations text.
  • An Introduction to Chaotic Dynamical Systems, second edition, by R. L. Devaney, Addison-Wesley, 1989. (Discrete dynamical systems. Intro graduate level text.)
  • Dynamical Systems: Stability, Symbollic Dynamics, and Chaos , by Clark Robinson, 1995. Excellent introductory graduate level book.

• Go to the Fall 2015 Math 5260 Home Page
• Go to Bruce Peckham's Home Page
• Go to the Department of Mathematics and Statistics Home Page