189-251B: Algebra II

Professor: Henri Darmon
URL: http://www.math.mcgill.ca/~darmon
Email: [email protected]
Office Hours: MW 11:00-12:00.

Classes: MWF 8:30-9:30.
Room: Burnside 1B18 (Basement)

TA: Spiro Karigiannis

Required Texts: Abstract Algebra, by Hungerford; Saunders publisher, and
Algebra by M. Artin, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1991.
The latter is not yet available in the McGill Bookstore, but is on reserve in the Math library on the 10th floor of Burnside Hall. Anyway, we will be working with Hungerford in the first few weeks, and after that I hope that Artin's book will be available.

Syllabus: This course is a continuation of Math 189-235A (Basic Algebra) which I taught in the Fall. Our main focus will be group theory and linear algebra, which are concerned with groups and vector spaces respectively. These two algebraic structures are ubiquitous in mathematics, and they interact in a variety of ways: the study of vector spaces and their automorphisms gives rise to a rich supply of examples of groups - the so-called matrix groups. In the other direction, representation theory studies how a given abstract group can be realized as a subgroup of a matrix group, sheddding considerable light on the structure of the group itself.

Prerequisites: Math 235A, an enthusiasm for learning mathematics, and a willingness to work hard! If you had a grade of A in Math 235A, and wish to pursue studies in pure mathematics, or are simply interested in the material, I encourage you strongly to take 251B. If you had a grade of B, then I would also be happy to see you continue with 251B, but you should be aware that you will probably need to work harder in this course than you did last semester! Finally, if you had a grade of C, but feel very motivated to go into the honors program, you are still free to give it a try - but probably you need to change your attitude towards studying for the class. You should come to my office hours at some point to discuss this.

Grading Scheme : 40% Bi-weekly assignments , 20% Midterm, 40% Final, or 100% final.