Fall 2022

Time and venue:  TR 12:45–2:00 p.m., BLOC 163

First day hand-out

Office hours (BLOC 301b):
Office hours (ZOOM meeting):
Help sessions for MATH 304 (BLOC 133):
Help sessions for MATH 304 (online at MLC):
Help sessions for MATH 323 (online at MLC): Office hours during the finals (ZOOM meeting):
  • Friday, December 9, 5:00–6:00 p.m.
  • Monday, December 12, 5:00–6:00 p.m.
  • by appointment

Office hours during the finals (BLOC 301b):
  • Tuesday, December 13, 11:00 a.m.–1:00 p.m.

Homework assignment #1 (due Thursday, September 8)

Homework assignment #2 (due Friday, September 16)

Homework assignment #3 (due Thursday, September 22)

Homework assignment #4 (due Friday, September 30)

Test 1: Thursday, October 6 (Sample problems)

Homework assignment #5 (due Friday, October 14)

Homework assignment #6 (due Monday, October 24)

Homework assignment #7 (due Friday, October 28)

Homework assignment #8 (due Friday, November 4)

Homework assignment #9 (due Friday, November 11)

Test 2: Thursday, November 17 (Sample problems)

Homework assignment #10 (due Friday, November 25)

Homework assignment #11 (due Monday, December 5)

Final exam: Wednesday, December 14, 8:00-10:00 a.m. (Sample problems)

Course outline:

Part I: Elementary linear algebra


Leon/de Pillis: Chapters 1-2

Lecture 1: Systems of linear equations.
Lecture 2: Gaussian elimination. Gauss-Jordan reduction.
Lecture 3: Gauss-Jordan reduction (continued). Applications of systems of linear equations. Matrix algebra.
Lecture 4: Matrix multiplication. Diagonal matrices. Inverse matrix.
Lecture 5: Inverse matrix (continued).
Lecture 6: Matrix algebra (continued). Determinants.
Lecture 7: Determinants (continued).
Lecture 8a: Determinants (continued).

Part II: Abstract linear algebra


Leon/de Pillis: Chapters 3-4

Lecture 8b: Vector spaces.
Lecture 9: Vector spaces (continued). Subspaces of vector spaces.
Lecture 10: Span. Spanning set. Linear independence.
Lecture 11: Linear independence (continued). Basis and dimension.
Lecture 12: Review for Test 1.
Lecture 13: Basis and dimension (continued). Rank of a matrix.
Lecture 14: Rank of a matrix (continued). Basis and coordinates.
Lecture 15: Change of basis. Linear transformations.
Lecture 16: Linear transformations (continued). General linear equations.
Lecture 17: Matrix of a linear transformation. Similar matrices.
Lecture 18a: Similar matrices (continued).

Part III: Advanced linear algebra


Leon/de Pillis: Sections 5.1-5.6, 6.1, 6.3

Lecture 18b: Eigenvalues and eigenvectors.
Lecture 19: Eigenvalues and eigenvectors (continued). Diagonalization.
Lecture 20: Diagonalization (continued). Euclidean structure in Rn. Orthogonality.
Lecture 21: Orthogonal complement. Orthogonal projection. Least squares problems.
Lecture 22: Review for Test 2.
Lecture 23: Norms and inner products.
Lecture 24a: Orthogonality in inner product spaces. The Gram-Schmidt process.

Part IV: Topics in applied linear algebra


Leon/de Pillis: Sections 5.7, 6.2, 6.4

Lecture 24b: Orthogonal polynomials.
Lecture 25: Complexification. Orthogonal matrices. Rigid motions.
Lecture 26: Review for the final exam.