189-251B: Algebra 2

Professor: Henri Darmon

Marker: Mireille Schnitzer

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

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

Tutorials: Unfortunately there will be no tutorials for this course. However, there is a Math Help Desk in BH911 operating Mondays to Fridays from 12:30-5:00pm. This is a valuable ressource if you need extra help on the material or assignments, and are strongly encouraged to make use of it.

Main Textbook: Linear algebra done right by Sheldon Axler.

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 Wednesdays and returned, graded, the following Monday. There will be around 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 this year's midterm, in pdf, tex, ps, or dvi format.
Here are the grades.

Final exam :
The final exam will be on Tuesday, April 18.
This week (April 10-14) I will have office hours on Monday 10:30-3:00, Tuesday 9:00-2:00, and Wednesday 8:30-10:00 and 12:00-2:00.
Here is a practice final exam to help you in your studying, in pdf, tex, ps, or dvi format.

Final grades Here are the final grades for the class.

If you have any question about your grades or want to see your final exam, please come by my office.

Otherwise I wish you an excellent summer!

The obligatory statement

McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/integrity for more information).