Pólya counting theory: How many different ways are there of coloring a 3x3 tile with two colors? Two colorings count as equal if one is obtained from the other by a rotation.

Peter Selinger: Mat 3343, Fall 2003

Mat 3343, Applied Algebra
Fall 2003
Peter Selinger

Professor: Peter Selinger.
Office: KED 205D.
Phone: 562-5800 ext. 3510
Email: selinger@mathstat.dal.ca (please put "3343" into the subject line)
Office Hours: TBA.

Time: Tue 11:30-1, Fri 1-2:30.
Location: KED B5.

Course Description: This course is an introduction to modern algebra and its applications. You will learn about some of the central concepts of algebra in a rigorous and proof-oriented manner. A distinguishing feature of this course is that the abstract concepts are not studied in isolation. Instead, each topic is studied with the ultimate goal of a real-world application.

Topics: The four core topics to be covered in this course are: (1) groups and finite fields; (2) linear algebra modulo p, with applications to error correcting Hamming codes; (3) polynomial algebra, factoring algorithms, with applications to BCH codes; (4) some number theory, with applications to public-key cryptography. Additional topics will be chosen from the following, depending on interest: (5) permutation groups, with applications to counting problems; (6) monoids and semigroups, with applications to finite-state automata.

Prerequisites: Mat 2141 or 2341, Mat 2143 or 2343.

Textbook: W. Keith Nicholson, Introduction to Abstract Algebra, 2nd Edition. The textbook is available from the Agora Bookstore, 135 1/2 Besserer Street.

Course Work: There will be weekly homework, one or two in-class midterms, and a final exam.

Course Homepage: Updated information will be available from the course homepage, http://www.mathstat.dal.ca/~selinger/3343/

Peter Selinger / Department of Mathematics and Statistics / Dalhousie University
selinger@mathstat.dal.ca / PGP key