McGill University

Department of Mathematics & Statistics

Basic Algebra I


Detailed Syllabus

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