Math 52 List of Topics

week 1: (Ch. 1)

• Tuesday: General remarks about linear algebra, systems of linear equations
• Thursday: Gaussian eliminaton

week 2: (Ch. 1)

• Tuesday: Matrices and their arithmetic
• Thuesday: Inverting a matrix and finding solutions to equations

week 3: (Ch. 2)

• Tuesday: triangular and symmetric matrices. Intro to proofs.
• Thursday: determinants, cofactors, Cramar's rule

week 4: (Ch. 2)

• Tuesday: other methods of evaluating determinants
• Thursday: properties of the determinant

week 5: (Ch. 3)

• Tuesday: Midterm 1
• Thursday: 2 and 3 dimensional vectors

Week 6: (Ch. 4)

• Tuesday: n-dimensional Euclidean space
• Thursday: Linear transformations

Week 7: (Ch. 5)

• Tuesday: vector spaces
• Thursday: linear independence and span

Week 8: (Ch. 5)

• Tuesday: bases and dimension
• Thursday: linear independence and span

Week 9: (Ch. 5-6)

• Tuesday: row space, column space, rank
• Thursday: inner products

Week 10: (Ch. 6)

• Tuesday: midterm
• Thursday: Cauchy-Schwartz inequality. further properties of inner products

Week 11: (Ch. 6)

• Tuesday: orthonormal bases and Gram-Schmidt
• Thursday: least squares approximation

Week 12: (Ch. 6-7)

• Tuesday: eigenvalues and eigenvectors
• Thursday: Thanksgiving break

Week 13: (Ch. 7-8)

• Tuesday: diagonalization
• Thursday: linear transformations

Week 14: (Ch. 8)

• Tuesday: kernal, image, and isomorphism
• Thursday: matrix representation of linear transformations