MAT240F Algebra I

We will cover the first 4 chapters of the textbook, plus some material from the appendices.

1. Sets, fields. (Textbook: Appendix A - Appendix D)
   • Sets, relations, functions
   • Fields
   • The field Z/pZ
   • Complex numbers

2. Vector spaces (Textbook: Chapter 1)
   • Definition of vector spaces
   • Subspaces
   • Linear combinations
   • Bases of vector spaces
   • Coordinate vectors
   • Linear systems
   • Existence of bases

3. Linear maps (Textbook: Chapter 2)
   • Linear maps
   • Matrices
   • Null space (kernel) and range
   • Dimension theorem
   • Composition of linear maps
   • Isomorphisms
   • Change of coordinate matrix
   • Dual spaces, dual maps

4. Systems of linear equations (Textbook: Chapter 3)
   • Elementary matrix operations
   • Rank of a matrix
   • Inverse of a matrix
   • Solving systems of linear equations

5. Determinants (Textbook: Chapter 4)
   • Determinants of nxn matrices
   • Methods for calculating determinants
   • Cramer's rule