 Lecture 1: (The language of sets)
 Lecture 2: (Maps between sets)
 Lecture 3: (Systems of linear equations)
 Lecture 4: (Vector spaces)
 Lecture 5: (Example of vector spaces)
 Lecture 6: ("Proofs" using axioms: properties of vector spaces)
 Lecture 7: (Vector subspaces I)
 Lecture 8: (Vector subspaces II)
 Lecture 9: (Linear combinations)
 Lecture 10: (From linear combinations to linear equations)
 Lecture 11: (Linear independence and dependence I)
 Lecture 12: (Linear independence and dependence II)
 Lecture 13: (From belonging to a span to existence of solutions to linear equations I)
 Lecture 14: (From belonging to a span to existence of solutions to linear equations II)
 Lecture 15: (From belonging to a span to existence of solutions to linear equations III)
 Lecture 16: (Matrices and row operations I)
 Lecture 17: (Matrices and row operations II)
 Lecture 18: (Solving systems of linear equations)
 Lecture 19: (Generating sets)
 Lecture 20: (Bases and coordinates)
 Lecture 21: (Dimension of a vector space)
 Lecture 22: (Linear transformations)
 Lecture 23: (Image of a linear transformation)
 Lecture 24: (Kernel of linear transformation)
 Lecture 25: (From linear transformations to matrices, and back)
 Lecture 26: (Image and kernel of matrices)
 Lecture 27: (The ranknullity theorem)
 Lecture 28: (From linear transformations to linear equations, and back)
 Lecture 29: (Operations on matrices I)
 Lecture 30: (Operations on matrices II)
 Lecture 31: (Invertible linear transformations)
 Lecture 32: (Determinants)
 Lecture 33: (Eigenvalues and Eigenvectors I)
 Lecture 34: (Eigenvalues and Eigenvectors II)
 Lecture 35: (Eigenvalues and Eigenvectors III)
