Syllabus
Math 642 (lectures MWF 2) Fall 2003
Course title: Dynamical Systems I
Lectures:
MWF 2:00 - 2:50 P.M.
Lectures location: Math 2300
Prerequisite: MATH 432 (differential geometry of
curves and surfaces); and MATH 630 (Real analysis) or equivalent.
Description: Foundations of
topological dynamics, homeomorphisms, flows, periodic
and recurrent points, transitivity and minimality, symbolic dynamics.
Elements of ergodic theory, invariant measures and sets, ergodicity,
ergodic theorems, mixing, spectral theory, flows and sections.
Applications of dynamical systems to number theory, the Weyl theorem,
the distribution of values of polynomials, Vander Waerden's theorem on
arithmetic progressions.
Professor: Daniel J. Rudolph (djr@math.umd.edu)
Office: Room 2110, Math Building
Phone: 301-405-5162
Office hours.
Tuesday and Thursday, 11-12 and by arrangement.
Required text:
Brin and Stuck: Introduction to Dynamical Systems
Syllabus. We will cover Chapters 1-5 of Brin and Stuck
Assigned Work. Homework will be assigned and
collected weekly. Usually problems will be assigned every
day. Problems assigned during a week are due at the end of class
the Monday of the following week. Selected problems will be
graded. There
will be two take-home open-book midterms, tentatively scheduled for the
weekends of October 18-19 and December 6-7. The final exam will
be in-class at the scheduled time, Thursday Dec. 18, 1:30-3:30
Course Grade. Homework will
count for 10% of your course grade, each midterm will count for 20% and
the final
will count toward 50% of your final
grade. This is an advanced graduate level course and
students enrolled will come with varying backgrounds and
interests. I intend to take this into account when
assigning grades.