McGill University

Department of Mathematics & Statistics

Basic Algebra I


Detailed Syllabus

  1. Sept. 2-Sept 9: Overview of the course. Sets, relations, and functions. Induction. Number systems including complex numbers. Equivalence relations.
  2. Sept 12-Sept 16: (Chapter 1) Arithmetic in Z. The division algorithm. The Euclidean algorithm and gcd's.
  3. Sept 19-Sept 23: (Chapter 1) Fundamental theorem of arithmetic. Prime numbers.
  4. Sept 26-Sept 30: (Chapter 2) Congruences. Modular arithmetic. Finite fields. Primality testing.
  5. Oct 3-Oct 7: (Chapter 3) Rings. Definitions and basic examples. Isomorphisms and homomorphisms.
  6. Oct 10-Oct 14: (Chapter 4) Arithmetic in polynomial rings. Division algorithm and unique factorization.
  7. Oct 17-Oct 21: (Chapter 5) Congruences in polynomial rings. More on finite fields.
  8. Oct 24-Oct 28: Review of the material, and midterm test (to be given, in-class, on Friday October 28.)
  9. Oct 31-Nov 4: (Chapter 6) Ideals and quotient rings.
  10. Nov 7-Nov 11: (Chapter 6) Ideals and quotient rings. Introduction to groups.
  11. Nov 14-Nov 18: (Sections 7.1 -7.5) Group theory. Definition and basic examples. Subgroups, isomorphism and homomorphism. Lagrange's theorem.
  12. Nov 21-Nov 25: (Sections 7.6-7.9) More group theory. Normal subgroups, quotients, and homomorphisms. Simple groups.
  13. Nov 28-Dec 2: Review of the material.
  14. Dec 5: Final exam.