189-251B: Algebra 2

Professor: Henri Darmon

TA: Matthew Greenberg

Marker: David Zeber

Classes: MWF 8:35-9:25. in Burnside Hall 1B23

Tutorials:
There will be weekly tutorials on
Tuesday 2:30-3:30 in Burnside Hall 10th floor lounge *** Note the room change!! ***
Friday 2:30-3:30 in BH 1205.

Office Hours:
Darmon MW 10:30-12:00, in Burnside Hall 1111.

Recommended Text:
Linear Algebra by Seymour Lipschutz (Shaum's Outline series).

Syllabus:
This course will cover the basics of linear algebra. Linear algebra can be defined, somewhat circularly, as the branch of mathematics concerned with the study of vector spaces over a field. Vector spaces are an important instance of an abstract mathematical structure, just like the rings and groups that were studied in Math 235A. They arise naturally in modelling a bewildering variety of phenomena (both within mathematics, and in the ``real world".)

Key topics to be covered will include: Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators.

Should I register for 251, or 236?
Since Math 251 is an honors class, emphasis will be placed on rigorous proofs, and on developping mathematical maturity and problem-solving skills. The content will be abstract, and the pace, challenging, just as it was with Math 235A, only more so. The grading curve will thus be alot tougher. This reflects the stiffer competition arising from the fact that at most half (and, roughly, the stronger half) of the students who were in 235 will be moving on to 251.

In particular, anyone who did not get an A in 235 will have to work alot harder to earn a passing grade in 251, and should consider registering for Math 236 instead. If you did not get an A in 235 but are still keen on taking 251, that is possible in principle, but I would like to meet with you face to face to discuss how you plan to approach your coursework in 251.

Assignments:
Assignments are to be turned in on Fridays and returned, graded, the following Wednesday. There will be ten assignments in all during the semester.

Grading Scheme : As in last semester's clas, there will be three possible schemes, and I will take the maximum of those.

1. 20% Weekly assignments, 30% Midterm, 50% Final.
2. 20% Weekly assignments, 80% Final.
3. 100% Final.

Midterm :
Here is the corrected midterm, in pdf, tex, ps, or dvi format.
Here are the grades.

Here are the final grades for the course.
Have a great summer!