McGill University

Department of Mathematics & Statistics

Algebra II

189-251B

Detailed Syllabus

1. Jan. 6-Jan 10: (Chapter 7.4-7.8, Hungerford).
   Overview of the course. More on groups. Congruences, quotient groups, normal subgroups, homomorphisms.
   
2. Jan 13-Jan 17: (Chapter 7.9-7.10, Hungerford).
   Permutation groups.
   
3. Jan 20-Jan 24 (Chapter 8.1-8.2, Hungerford).
   Permutation representations of groups.
   
4. Jan 27-Jan 31 : (Chapter 8.3, Hungerford or Chapter 6.1-6.4, Artin).
   The Sylow theorems.
   
5. Feb 3-Feb 7 : (Chapter 3.1-3.3, Artin).
   Vector Spaces. Bases and dimension.
   
6. Feb 10-Feb 14 : (Chapter 3.4-3.6, Artin).
   More vector spaces.
   
7. Feb 17-Feb 21 : (Chapter 4.1-4.3, Artin).
   Linear transformations; their connection with matrices. Eigenvectors and eigenvalues.
   
8. Feb 24-Feb 28 :
   Spring Break.
   
9. March 3-March 7 : (Chapter 4.4-4.8, Artin).
   Midterm Exam (on Wednesday)
   Characteristic polynomials, orthogonal matrices, diagonalization, application to differential equations.
   
10. March 10- March 14 : (Chapter 7.1-7.3, Artin).
    Bilinear forms. Orthogonality.
    
11. March 17- March 21 : (Chapter 7.4-7.5, Artin).
    Hermitian forms, and the spectral theorem.
    
12. March 24- March 28 : (Chapter 8.1-8.3, Artin).
    Matrix groups.
    
13. March 31- April 3 : (Chapter 8.4-8.6, Artin).
    Matrix groups, cont'd.