## 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.