Date  Sections in Text  Brief Description 
3/29  
Mathematical Induction and Basic Set Theory 
3/31  1.2 
Fields and Vector Spaces 
4/2 
1.2, 1.3 
Vector Spaces and Subspaces 
4/5 
1.3, 1.4 
Subspaces and Linear Combinations 
4/7 
1.4 
Linear Combinations 
4/9 
1.5, 1.6 
Linear dependence, independence, and bases 

4/12 
1.6 
Bases and dimension 
4/14 
1.6 
Bases and dimension 
4/16 
2.1 
Linear Transformations 
4/19 
2.1 
Nullspace and Range 
4/21 
2.1 
Rank and Nullity 
4/23 
2.2 
Matrix repensentations of a linear map 
4/26 
2.2, 2.3 
Matrix repensentations of linear transformations 
4/28 
2.3, 2.4 
Matrix representations and compositions 
4/30 
2.4 
Invertibility and Isomorphism 
5/3 
2.4 
Invertibility and Isomorphism 
5/5 
3.1, 3.2 
Elementary matrices and rank of matrices 
5/7 
3.1  3.4 
Systems of equations, Elementary matrices 
5/10 
2.5 
Change of Basis 
5/12 
4.2  4.4 
An Overview of Determinants 
5/14 
5.1 
Eigenvalues and Eigenvectors 
5/17 
5.1 
Eigenvalues and Eigenvectors 
5/19 
5.2 
Diagonalizability 
5/21 
5.2 
Diagonalizability 
5/24 
5.2 
Diagonalizability 
5/26 
6.1  Inner Product Spaces 
5/28  6.2  GramSchmidt Orthogonalization 
6/2  6.7  Introduction to Quadratic forms 