Math 354: Honors Linear Algebra

References (free download)

S. Axler, Linear Algebra Done Right, 4nd. Ed., Springer Open Access.

The author has recorded some videos to accompany the textbook, which you may find useful.

See Canvas/Gradescope for updated policies, hw, quizzes, and exams. This website is not accurate given the change in instructor. This website serves only as an approximate guide.

Outline

Honors Linear algebra is aimed at all students who are interested in a first pure mathematics course. We will emphasize proof writing, but prior knowledge in it is NOT required. However, students new to proof writing, are strongly encouraged to concurrently enroll in Math 290: Mathematical Writing taught by Dr. Gwaltney, MW 4-4.50pm (half term course).

This course will demand a lot of your time and concentration. Expect to spend upwards of 10 hours per week on it, especially if you are not enrolled in Math 290 or have not had any prior exposure to linear algebra.

While you may switch back to regular linear algebra (Math 355) until the end of the seventh week of classes (Friday February 23), I strongly encourage you to reach out and talk to me before finalizing your decision to drop the course or switch back to 355.

The plan is to engage in a rigorous discussion of the following concepts. This material is all essential background for continued study in basic and advanced data analysis, pure and applied mathematics, computer science, engineering, statistics, operations research, and many social sciences.

• Mathematical induction (handout)
• Fields, vector spaces, subspaces (Axler 1)
• Span, linear independence, bases, dimension (Axler 2)
• Linear maps, their matrices, null spaces, ranges, ranks, isomorphisms (Axler 3)
• Determinants of operators and matrices (Axler 9 + handout)
• Eigenvalues, eigenvectors, eigenspaces, invariant subspaces (Axler 5)
• Upper triangular, diagonal, diagonalizable matrices, change of basis (Axler 5)
• Inner product spaces, orthogonal and orthonormal bases, orthogonal complements (Axler 6)
• Self-adjoint operators, the spectral theorem (Axler 7)

The course is split up into three units, each with its own problem sets, quizzes, and capstone exam (Midterm I for Unit I, Midterm II for Unit II, Final Exam for Unit III):

• Unit I: Introduction to abstraction (induction, Axler 1-2),
• Unit II: Linear maps, determinants, and eigenvalues/eigenvectors (Axler 3, 5, 9).
• Unit III: Applications of eigenvalues/eigenvectors (Axler 5-7).

Additional Course Policies

Comportment Expectations. The Department of Mathematics supports an inclusive learning environment where diversity and individual differences are understood, respected, and recognized as a source of strength. Racism, discrimination, harassment, and bullying will not be tolerated. We expect all participants in mathematics courses (students and faculty alike) to treat each other with courtesy and respect, and to adhere to the Mathematics Department Standards of Collegiality, Respect, and Sensitivity as well as the Rice Student Code of Conduct. If you think you have experienced or witnessed unprofessional or antagonistic behavior, then the matter should be brought to the attention of the instructor and/or department chair. The Ombudsperson is also available as an intermediate, informal option, and contacting them will not necessarily trigger a formal inquiry.

Title IX Responsible Employee Notification. Rice University cares about your wellbeing and safety. Rice encourages any student who has experienced an incident of harassment, pregnancy discrimination or gender discrimination or relationship, sexual, or other forms interpersonal violence to seek support through The SAFE Office. Students should be aware when seeking support on campus that most employees, including myself, as the instructor/TA, are required by Title IX to disclose all incidents of non-consensual interpersonal behaviors to Title IX professionals on campus who can act to support that student and meet their needs. For more information, please visit safe.rice.edu or email titleixsupport@rice.edu.

Disability-related Academic Accommodations. In order to receive disability-related academic accommodations, students must first be registered with the Disability Resource Center (DRC). Students who may need accommodations in this course should give me a written letter from the DRC within the first two weeks. More information on the DRC registration process is available online at https://drc.rice.edu/. Registered students must present an accommodation letter to the professor before exams or other accommodations can be provided. Students who have, or think they may have, a disability are invited to contact DRC for a confidential discussion.