McGill University

Department of Mathematics & Statistics

Higher Algebra I

189-570A

Detailed Syllabus

Wednesday September 4 to Friday September 13
Overview of the course. Generalities on algebraic structures. Groups, rings, vector spaces, modules. Categories and Functors. Groups and permutations.

Assignment 1 due on Monday, September 23.

Monday September 16 to Friday September 27
Representation theory of finite groups.

Assignment 2 due on Monday, October 7.

Monday September 30 to Friday October 11
Representation theory of finite groups, cont'd.

Assignment 3 due on Monday, October 28.

Monday October 14 to Friday October 25
Rationality and integrality of characters. Applications. Commutative algebra, and an introduction to schemes.

Monday October 28 to Friday November 8
Commutative algebra, and an introduction to schemes. Hilbert's Nullstellensatz.

Reference: the material covered in this section was partly taken from Chapters I.1- I.3 of the book
Introduction to Commutative Algebra and Algebraic Geometry by Ernst Kunz.

Assignment 4 due on Monday, November 11.

Monday November 11 to Friday November 22
Introduction to Dedekind domains. Localisation. Unique factorisation into prime ideals.

Reference: the material covered in this section was partly taken from Chapters 1-3 of the book
Algebraic number theory by J.S.Milne.

Assignment 5 due on Monday, November 25.

Monday November 25 to Tuesday December 3

Friday, December 6, from 2:00 PM to 5:00 PM, in BH 1205. Final in-class exam.