Homework & Schedule

Homework Instructions and Policies:

• All homework assignments must be submitted on Gradescope. You may find the link to the Gradescope course page on Blackboard. A video from Gradescope with instructions explaining how to submit your homework can be found here.
• One homework assignment may be submitted up to 48 hours late. This is meant to cover illness, travel, and weeks where you have lots of other work, and you do not need to provide an excuse. Beyond this one, no late homework will be accepted. *Note: to facilitate this, Gradescope will show a deadline and a late deadline for every assignment. It will not prevent you from submitting more than one assignments late, but I’ll only count the first one.
• Leave time to check that your submission is correct. It’s your responsibility to make sure you’ve submitted to the correct assignment, and have uploaded all your work. Plan to submit your work at least 15 minutes before the deadline, and check your submission after uploading it.
• Any calculator, computer program, or online tool (WolframAlpha, chatGPT, etc.) is strictly prohibited.
• Some remarks on writing mathematical proofs can be found here. If you are not familiar with writing mathematical proofs, this should be helpful.

Course Schedule:

Here is the very tentative course schedule; there may be changes during the semester.

Week of 5/20

Class 1 (5/20):

Appendix C: Fields

Secion 1.2: Vector Spaces

Class 2 (5/21):

Section 1.3: Subspaces

Section 1.4: Linear Combinations and Systems of Linear Equations

Section 1.5: Linear Dependence and Linear Independence

Class 3 (5/22):

Section 1.6: Bases and Dimension

Class 4 (5/23):

Catch-up

Week of 5/27

Memorial Day on May 27 (No class)

Class 5 (5/28):

Section 2.1: Linear Transformations, Null Spaces, and Ranges

Class 6 (5/29):

Section 2.2: The Matrix Representation of a Linear Transformation

Section 2.3: Composition of Linear Transformations and Matrix Multiplication

Class 7 (5/30):

Section 2.4: Invertibility and Isomorphisms

Week of 6/3

Class 8 (6/3):

Section 2.5: The Change of Coordinates Matrix

Section 3.1: Elementary Matrix Operations and Elementary Matrices

Section 3.2: The Rank of a Matrix and Matrix Inverses

Class 9 (6/4):

Section 3.3: Systems of Linear Equations Theoretical Aspects

Section 3.4: Systems of Linear Equations Computational Aspects

Class 10 (6/5):

Catch-up/Midterm preparation

Class 11 (6/6):

MIDTERM

Week of 6/10

Class 12 (6/10):

Section 4.1: Determinants of order 2

Section 4.2: Determinants of order n

Class 13 (6/11):

Section 4.3: Properties of Determinants

Section 4.5: A Characterization of the Determinant

Class 14 (6/12):

Section 5.1: Eigenvalues and Eigenvectors

Section 5.2: Diagonalizability

Class 15 (6/13):

Catch-up

Week of 6/17

Class 16 (6/17):

Section 5.4: Invariant Subspaces and the Cayley-Hamilton Theorem

Class 17 (6/18):

Section 6.1: Inner Products and Norms

Juneteenth on Jun 19 (No class)

Class 18 (6/20):

Section 6.2: Gram-Schmidt Orthogonalization Process and Orthogonal Complements

Week of 6/24

The materials on Section 6.3-6 are not covered in the final exam.

Class 19 (6/24):

Section 6.3: The Adjoint of a Linear Operator

Section 6.4: Normal and Self-Adjoint Operators

Class 20 (6/25):

Section 6.5: Unitary and Orthogonal Operators and Their Matrices

Section 6.6: Orthogonal Projections and the Spectral Theorem

Class 21 (6/26):

Catch-up/Final Exam Preparation

Class 22 (6/27):

FINAL EXAM