Topic outline
- General
- Introduction and Basic Definitions
Introduction and Basic Definitions
An introduction to the course and the basic definitions. (Must Read!)
- Rings of Matrices
Rings of Matrices
New rings from old! Construction of matrix rings to solve problems.
- Polynomials
Polynomials
Introduction to the ring of polynomials
- Finite and Finitely Generated Abelian Groups
Finite and Finitely Generated Abelian Groups
The fundamental theorem about finite abelian groups and finitely generated abelian groups.
An explicit formulation of the questions already in the notes.
- Matrices over Polynomial Rings and PIDs
Matrices over Polynomial Rings and PIDs
Generalisations of the reductions of matrices over integers to other rings. (Central part of course)
Jordan decompostion as a consequence of Hensel's Lemma (skip at first reading!)
- Symmetric Bilinear Forms and Quadratic Forms
Symmetric Bilinear Forms and Quadratic Forms
- Orthogonal Matrices, Complex Numbers and Quaternions
Orthogonal Matrices, Complex Numbers and Quaternions
- Complex Inner Product Spaces
Complex Inner Product Spaces
- End Semester Examination
End Semester Examination