• Instructor: Bruce Peckham, Professor, Dept. of Mathematics and Statistics
• Office: 166 Campus Center, 726-6188, bpeckham@d.umn.edu
  Office Hours (tentative): M 11-12; T -; W 11-12; Th 2-3 OR 3-4 (if there is a colloquium 2-3); Fri 11-12:30, or by appointment
  
• Meeting times: MWF 10-10:50 in Eng 118
  EXCEPTION: Tests will be given at night to allow for more time: Mon. Oct 7 and Mon Nov. 18, 5-6:30+ in order to allow 90+ minutes. The tests will take the place of two classes during the semester. Which classes are to be cancelled will be announced at a later date. Computer labs will occasionally be done in class.
  
  
• Texts (free electronic versions of both texts are availble through Canvas for Math 5260):
• 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, second edition 2015. 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 1-10, 15-17 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 SHOULD CLEARLY STATE ANY WORK THAT WAS NOT COMPLETELY YOUR OWN: PEOPLE WHO CONTRIBUTED TO THE WORK, WEBSITES, SOLUTIONS MANUALS, TEXTBOOKS, AND ANY OTHER REFERENCES THAT WERE USED SHOULD BE LISTED. THE SPECIFIC PROBLEM(S) FOR WHICH OUTSIDE REFERENCES WERE USED SHOULD ALSO BE STATED CLEARLY. You need not explicitly reference material taken from either textbook. See the links for Academic Integrity and the Student Conduct Code below.

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. GRACE DAYS: all students will be allowed 5 grace days for the course. No point will be deducted for these grace days. Grace days can be distributed between any number of assignments, from all 5 days for a single course, to one grace day for 5 different assignments. After grace days have been used, points will be deducted for late work. 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%.

Assignments will be posted on the course homepage at http://www.d.umn.edu/~bpeckham/5260/F2019/Math5260F2019.html

Computational expectations. Most labs for discrete dynamical systems will be performed with spreadsheets or software from the Boston University Dynamics Website (requires JAVA) or other sites. 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!

• recognize, define and explain basic dynamical systems terminology
• determine strategies to investigate the behavior of a dynamical system, especially when the system is low-dimensional
• demonstrate proficiency in using software, numerical techiniques, and analytic techniques
• demonstrate proficiency in scientific visualization

• 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 2019 Math 5260 Home Page
• Go to Bruce Peckham's Home Page
• Go to the Department of Mathematics and Statistics Home Page