Schedule

Here is the tentative course schedule; there may be small changes as the semester progresses.

Week of 7/1

Class 1:

Appendix C: Fields

Section 1.2: Vector Spaces

Section 1.3: Subspaces

Class 2:

Section 1.4: Linear Combinations and Systems of Linear Equations

Class 3:

Section 1.5: Linear Dependence

Section 1.6: Bases and Dimension

Independence Day on Thursday, July 4: No class

Week of 7/8

Class 4:

Section 1.6: Bases and Dimension (cont.)

Class 5:

Section 2.1: Linear Transformations, Null spaces and Ranges

Class 6:

Section 2.2: The Matrix Representation of a Linear Transformation

Class 7:

Section 2.3: Composition of Linear Transformations and Matrix Multiplication

Week of 7/15

Class 8:

Section 2.4: Invertibility and Isomorphisms

Class 9:

Section 2.5: The Change of Coordinates Matrix

Class 10:

Examples and midterm review

Class 11:

MIDTERM 9:00-10:20AM

Lecture to follow 10:30-11:15am

Section 3.1: Elementary Matrix Operations and Elementary Matrices

Section 3.2: The Rank of a Matrix and Matrix Inverses

Week of 7/22

Class 12:

Section 3.2: The Rank of a Matrix and Matrix Inverses (cont.)

Section 3.3: Systems of Linear Equations Theoretical Aspects

Class 13:

Section 3.4: Systems of Linear Equations Computational Aspects

Section 4.1-4.5: Determinants

Class 14:

Section 4.1-4.5: Determinants (cont.)

Class 15:

Section 4.1-4.5: Determinants (cont.)

Section 5.1: Eigenvalues and Eigenvectors

Week of 7/29

Class 16:

Section 5.2: Diagonalizability

Class 17:

Section 5.4: Invariant Subspaces and the Cayley-Hamilton Theorem

Section 6.1: Inner Products and Norms

Class 18:

Section 6.2: Gram-Smidt Orthogonalization Process and Orthogonal Complements

Class 19:

Section 6.3-6.6: Selected Topics from Chapter 6

Week of 07/31

Class 20:

Section 7.1-7.2 Jordan Canonical Forms

Class 21:

Catchup and Review

Class 22:

Review

Class 23:

FINAL EXAM: 9:00AM-12:00PM