189-251B: Algebra 2
Our schedule in the last two weeks is going to be a bit irregular, so here
is a list of all the changes:
Monday, April 7: Class and office hours cancelled (because of the elections).
Tuesday, April 8: Extra office hours from 1:00-3:00 (to make up for those of Monday).
Wednesday, April 9: Classes and office hours as usual.
Friday, April 11: Classes and office hours cancelled (I will be out of town).
Monday, April 14: Extra review session 1:30-3:00.
Wednesday, April 16: Extra review session, 1:30-3:00.
Wednesday, April 23, from
2:00 to 5:00 PM: Final exam!
from previous years to assist you in your studying.
-------------- Course blog --------- Assignments ----------------
Professor: Henri Darmon
Classes: MWF 1:35-2:25 PM, in Rutherford Physics RPHYS 118
Darmon MW 2:45-4:00, in Burnside Hall 1111.
Tutorials: There will be no tutorials for this
course. However, there is a
Math Help Desk in BH911
Mondays to Fridays from noon to 5:00pm.
This is a valuable ressource if you need extra
help on the material or assignments, and you are strongly
encouraged to make use of it.
I will be following the excellent
course notes that Eyal Goren has
developped for this course in 2007-08.
Linear algebra done right by Sheldon Axler.
Linear Algebra by Seymour Lipschutz (Shaum's Outline series).
In a more challenging vein, I
highly recommend the textbook
d'analyse et d'algèbre (et de théorie des nombres) by Pierre Colmez.
It covers a lot more ground than we will in this course,
and would be equally appropriate for the analysis courses that you might be
It is very beautifully written and belongs on the bookshelf of any
mathematics student who is passionate about her or his subject (and not
afraid of reading about math in French...)
Several of you have asked for a supplement to the class notes which might contain a somewhat more detailed account of parts of the material and further exercises and problems for independent study.
Linear Algebra by Jim Hefferon is a book that
I found on the web which looks very well written and
contains plenty of exercises.
This course will cover the basics of linear
algebra. Linear algebra can be defined, somewhat
as the branch of mathematics concerned with the study
of vector spaces over a field.
are an important instance
of an abstract mathematical structure, just like the rings
and groups that were studied
in Math 235A. Surprisingly ubiquitous and flexible,
they can model 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
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 tougher. This reflects the
stiffer competition arising from the fact that around a third
(and, roughly, the more motivated third) of
the students who were in 235 will be moving on to 251.
who did not get a B in 235 will have to work much harder
to earn a decent grade
in 251, and should consider registering for Math 236 instead.
If you got less than a B in 235 but are still keen on taking 251, that
is possible in principle, but you should try to discuss with me
how you plan to approach your coursework in 251.
are to be turned in on Wednesdays and
will be returned, graded, the following Monday. There will be around
ten assignments in
all during the semester.
Grading Scheme : There will be
two possible schemes,
and I will take the maximum of those.
1. 20% Weekly assignments, 30% Midterm, 50% Final.
2. 20% Weekly assignments, 80% Final.
Midterm Exam:. The midterm exam will be held, in class,
on Wednesday, February 26 at the usual time (1:30-2:30).
I cannot make it to the office on Tuesday. If you
have questions send me an email and I will respond quickly.
My office hours of Wednesday will be moved to 9:45-11:00 instead of the usual
Here is a sample midterm
from a previous year for you to practice on.
The obligatory statements
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
In accord with McGill University's Charter of
Students' Rights, students in this course have the right to
submit in English or in French any written work that is to be graded.
In the event of extraordinary circumstances beyond the University's
control, the content and/or evaluation scheme in this course is subject