http://www.math.columbia.edu/~bayer/S16/Seminar/Bayer
Dave Bayer
Office Hours
bayer@math.columbia.edu
426 Mathematics
The topic automatic groups combines the subjects of group theory, studied in mathematics, and automata theory, studied in computer science. A primary motivation is to understand examples in low dimensional topology.
We will learn the computer science and topology that we need, as we go.
Modern Algebra I is a required course for math majors, and introduces the subject of group theory. I will assume that students have either taken this course, or are now taking this course. We will require a comfort with the idea of an abstract group, and we will develop a facility for working with generators and relations, and Cayley graphs of groups. Otherwise, Modern Algebra I takes a different approach to group theory, treating it as an introduction to abstract algebra.
Here is a nice, brief introduction to automatic groups:
The following Wikipedia pages offer a survey of these topics:
We will work through as much of this text as we can, taking time to also study together background material and work examples:
I cannot recommend that you buy a new copy of this book; the print quality is markedly inferior to vintage copies. The sample text on the left is from a new copy. The sample text on the right is from a vintage copy:
I recommend that you track down a vintage copy. Check return policies in advance, and consider asking the seller about the text quality; the above image file may be useful for such queries.
There are also digital resources available for this seminar. These files are available privately on CourseWorks.