189-235A: Algebra 1

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

Professor: Henri Darmon
Classes: MWF 1:35-2:25. in Strathcona M-1

Graders:
TBA
TBA

Office Hours:
Darmon MWF 9:35-10:25, 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.

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...)

Syllabus:
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.

Assignments:
Assignments will be handed out every Monday, for a total of 10 assignments over the semester.

These assignments are not to be handed in, and hence will not be graded. To do well on the midterm and final exam, it is vital that you spend a serious amount of time actively pondering the questions, and writing up your solutions on your own, even if you are free to seek the help of your classmates, TAs, professors, old solutions if you can find them on the web, Chat-GPT, Claude, etc. How actively you engage with the assignments will largely determine your grades in the in-class midterm and final exam, since questions on these exams wll be small modifications of questions that apeared on the assignments.

Grading Scheme : The grading scheme will be
40% Midterm, 60% Final.
If you obtain a better grade on the Final than on the midterm, I will apply the higher grade.

Midterm Exam:. The midterm exam will be held, in class, on Friday, October 16 right after the midterm break.
Here is a sample midterm exam.

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.