McGill University
Department of Mathematics & Statistics
Basic Algebra I
189-235A
Detailed Syllabus
- Sept. 1-Sept 5: (Chapter 3, ``Elementary properties'')
Overview of the course.
- Sept 8-Sept 12: (Chapter 1, first three sections).
The integers. Induction. Binomial theorem. Greatest common divisors.
The division algorithm.
The Euclidean algorithm and gcd's.
- Sept 15-Sept 19: (Chapter 1, last three sections).
The Fundamental theorem of arithmetic.
Prime numbers.
Congruences. Modular arithmetic.
Application to primality testing.
- Sept 22-Sept 26: (Chapter 3, first two sections).
Rings. Definitions and basic examples.
- Sept 29-Oct 3: (Chapter 3, next three sections).
Fields and polynomials.
Greatest common divisors. Factorization.
- Oct 6-Oct 10: (Chapter 3, next three sections).
Homomorphisms and quotient rings.
- Oct 13-Oct 17: (Miscellaneous topics).
Euclidean rings and applications. Quaternions.
- Oct 20-Oct 24: Review of the material, and mid-term test.
(In class, on Friday the 24th).
- Oct 27-Oct 31 :
(Chapter 2, first three sections).
Symmetry, and the notion of a group. Functions. Permutations.
- Nov 3-Nov 7:
(Chapter 2, next two sections).
Lagrange's theorem. Geometry.
- Nov 10-Nov 14:
(Chapter 2, next two sections).
Quotients groups and homomorphisms.
- Nov 17-Nov 21:
(Chapter 2, last two sections).
The counting formula. The Sylow theorems. Groups of small order.
- Nov 24-Nov 28:
(Chapter 4, first section).
Vector spaces.
- Dec 1-Dec 5:
Review of the material.