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189-570A: Higher Algebra I

Professor: Henri Darmon
Classes: MWF 8:30-10:00.
Room: Burnside Hall 920

Higher Algebra I on the web:
Henri Darmon's web page: http://www.math.mcgill.ca/~darmon
Math 570A: http://www.math.mcgill.ca/~darmon/courses/algebra1/algebra1.html

Office hours:
Henri Darmon: by appointment, in BH 1111.



1. Jean-Pierre Serre, Linear representations of finite groups. Springer-Verlag.

2. Emil Artin, Galois Theory, Dover Books.

Optional (may be used as references)

3. Thomas Hungerford, Algebra, Springer-Verlag (GTM).

Will be mostly useful in the second semester course but may be used a bit in the first semester as well

4. Dino Lorenzini, An invitation to arithmetic geometry. American Mathematical Society.

5. David Eisenbud, Commutative Algebra with a view toward algebraic geometry. Springer Verlag (GTM).

Syllabus: This course will cover the standard syllabus for a first year graduate course in abstract algebra. The content and pace will be challenging: emphasis will be placed on rigorous proofs, and on developping mathematical maturity and problem-solving skills.

Grading Scheme :
40% Bi-weekly assignments. The bi-weekly assignments are an essential part of the course. You should plan to devote at least ten hours (and quite possibly more) to the assignments.

If you are stuck on a problem, you may seek out the help of one of your classmates. It is OK to work on the assignments in groups, although you should hand them in individually. Do not neglect the assignments: there is a strong correlation between the work you put into them and how well you will do in the final exam, and hence in the course.

The assignments are due on Mondays and will be graded and returned to you in the same week. Late assignments will not be accepted.

60% In-class final exam. The final exam will be held on Thursday, December 7, from 1:00 to 4:00 PM, in Burnside Hall 1205.

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.