- 08/27: some applications of linear algebra, vectors over the reals, Pythagorean Theorem, length (1.1)
- 08/29: scalar multiples, addition of vectors and their properties (Thm 1.3)
- 08/31: line given by 2 points, law of cosines, angle between vectors, dot product (1.2)
- 09/05: projections (1.2)
- 09/07: Cauchy-Schwartz inequality, triangle inequality (1.2)
- 09/10: matrices, addition, scalar multiples (1.4), multiplication and their properties (1.5)
- 09/12: systems of linear equations, Gaussian elimination, free variables, parametrized solutions (2.1)
- 09/14: coefficient and augmented matrix, row echelon form (2.2)
- 09/17: existence and number of solutions of linear systems
- 09/19: linear combinations, span of vectors
- 09/21: consistency of Ax=b for all vectors b
- 09/24: homogenous systems, nullspace of a matrix,
- 09/26: axioms and properties of fields
- 09/28: axioms of vectorspaces over arbitrary fields (4.1)
- 10/01: review for 1st midterm [pdf]
- 10/03: 1st midterm
- 10/05: subspaces (4.2)
- 10/08: spans and nullspaces are subspaces
- 10/08: linear independence of vectors (4.3)
- 10/12: basis of a vector space as minimal spanning set, standard basis of F^n (4.5)
- 10/15: basis for F^n, basis for polynomials of degree at most n
- 10/17: basis of column spaces
- 10/19: each basis has the same size, dimension of a vector space (4.5)
- 10/22: any n linear independent vectors in F^n form a basis, any n spanning vectors of F^n form a basis
- 10/24: coordinates w.r.t. a basis, change-of-coordinates-matrix (4.7)
- 10/26: inverse of a square matrix (2.4)
- 10/29: linear transformations (5.1), isomorphisms between vector spaces (5.5)
- 10/31: standard matrix of a linear transformation (5.2)
- 11/02: standard matrices of rotation, reflection in R^2 (5.2)
- 11/05: review for 2nd midterm [pdf]
- 11/07: 2nd midterm
- 11/09: interview
- 11/12: discussion of 2nd midterm, matrices for linear maps with respect to arbitrary bases (5.2)
- 11/14: range and kernel of linear maps as subspaces, injective, surjective maps, dimensions of range and kernel (5.4)
- 11/16: determinant of a matrix, definition by cofactor expansion, rule of Sarrus for 3x3 matrices (3.1)
- 11/26: determinant via row reduction, invertible matrices have non-zero determinant (3.2)
- 11/28: eigenvectors and eigenvalues of matrices (3.4)
- 11/30: characteristic polynomial (3.4)
- 12/03: diagonalization of matrices (3.4)
- 12/05: dynamic systems, Fibonacci numbers
- 12/07: orthogonal and orthonormal basis (6.1)
- 12/10: least square solutions of linear systems
- 12/12: review for the final [pdf]

- due 08/31 [pdf]
- due 09/07 [pdf] [tex]
- due 09/14 [pdf] [tex]
- due 09/21 [pdf] [tex]
- due 09/28 [pdf] [tex]
- due 10/05 [pdf] [tex]
- due 10/12 [pdf] [tex]
- due 10/19 [pdf] [tex]
- due 10/26 [pdf] [tex]
- due 11/02 [pdf] [tex]
- due 11/09 [pdf] [tex]
- due 11/16 [pdf] [tex]
- due 11/30 [pdf] [tex]
- due 12/10 [pdf] [tex]

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