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189-235A: Algebra 1

Some Links: ---------- Course blog --------- Assignments --------- Sample midterm ---------

Professor: Henri Darmon
Classes: MWF 11:35-12:25. in McDonald-Harrington G-10

Dylan Atwell-Duval. F 13:05-14:25 in TBA.
Bahare Mirza. W 13:05-14:25 in TBA.
Jason Polak. Th 14:35-15:55 in TBA.

Alexander Sylvester
Bowen Gang

Office Hours:
Darmon F 12:35-2:25, in Burnside Hall 1111, or by appointment.

See also the Math Help Desk in BH911 operating 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.

Main text: I will be following the excellent (and free!) class notes that Eyal Goren has developped for this course in 2009.

Optional Textbooks:
If you feel the need for a more formal textbook, the textbook by Dummit and Foote is highly recommended, as well as the somewhat more advanced text by Michael Artin; but be warned that both will set you back by over 100$.

In a more challenging vein, I also highly recommend the first 60 pages of the textbook
Eléments 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 taking concurrently.
It is beautifully written and belongs on the bookshelf of any mathematics student who is serious about her or his subject (and not afraid of reading about math in French...)

This course will cover the basics of Abstract Algebra; the guiding theme is the notion of abstract algebraic structures and the morphisms between them, of which rings and groups (together with the underlying notions of homomorphisms) are the simplest prototypes.
Key topics to be covered will include: the basic properties of the integers, rings, polynomial rings, quotients, finite fields, abstract groups, group actions on sets, Sylow theorems.

Assignments will be handed out every other Monday, so there will be a total of 6 assignments in 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.
In particular, not handing in assignments and going for 100% final is not an option.

Midterm Exam:. The midterm exam will be held, in class, on Wednesday, October 16 at the usual time (11:35-12:25).
Here is a copy of the midterm exam.

The average mark on the midterm was 77%, counting those who did not write the exam and were assigned a mark of 0.

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 information).

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 to change.