This is the homepage for MATH 3705 (Symbolic Dynamics). This page will be updated throughout the term with important information for our course, including homework assignments, review materials, and more. |
Course meets every MW from 4:00 p.m. - 5:50 p.m. in John Greene Hall 219.
Text: An Introduction to Symbolic Dynamics and Coding by Lind and Marcus.
Symbolic dynamics is the study of sets of sequences taken from a finite set (think zeroes and ones), and the dynamical properties of such a set when combined with the shift operation which moves a sequence one unit to its left. We will study various facets of symbolic dynamics, mostly concerning some simple classes of symbolic systems, namely shifts of finite type and sofic shifts.
We will focus mostly only Chapters 1-4 of the textbook, and some selected important results from later chapters. Topics will include various notions of isomorphism between symbolic systems, entropy theory, and connections to coding theory and information theory. If time permits, we will finish by discussing some topics in multidimensional symbolic dynamics (e.g. two-dimensional arrays of letters instead of sequences)
The prerequisites are basic linear algebra (MATH 2060 or equivalent) and a course in mathematical proof (MATH 2200 or equivalent). Knowledge of some point-set topology (e.g. definition of open/closed sets, compact space, metric space) is suggested.
Your term grade will consist of homework assignments (which will mostly be taken from the text), one midterm exam, and one final exam, broken down in the following way:
You will have a midterm exam on Monday, May 2nd, and a final exam on May 31st. Both exams will be in our classroom during classtime (4:00 p.m. - 5:50 p.m.)