MA 405. Advanced Linear Algebra

Pre-requisites: MA 225 and (MA 305 or MA 306/493)

Course description: This course offers a rigorous, proof-based study of linear algebra with an emphasis on abstract vector spaces and linear maps. Topics include vector spaces and subspaces, bases and dimension; linear maps, matrix representations, change of basis, and isomorphisms; eigenvalues, eigenvectors, and diagonalization; inner product spaces, orthogonality, and the Gram–Schmidt process; and selected topics including the spectral theorem and singular value decomposition. Credit is not allowed for both MA 405 and MA 520.

Enrollment: Students who are unable to enroll in MA 405 for the Fall 2026 semester should submit an enrollment request using this form : https://forms.gle/YfJSfDaJAiBuwgC2A

Options for students interested in enrolling in MA 405:

1. Complete MA 225 and MA 305, followed by MA 405.
2. Complete MA 225 and MA 306/493 (1 credit) as a co-requisite with MA 405 (same semester, first 8-week session). MA 306/493 will count as a free elective.
3. Self-study the MA 306/493 online materials and attempt the credit-by-exam during the first week of classes (similar to the E115 model).
4. For students who do not plan to take MA 225, a placement test will be available during the first week of classes to determine whether their proof-writing background is sufficient for MA 405.

Note: For current math majors, MA 305 is not required for your degree, so it may be more “economical” to take MA 306/493 + MA 405, with MA 306/493 counting as a major or free elective. However, if you had difficulty with MA 225, it may be best to take MA 305 in the Fall and then MA 405 in the Spring.

MA 306/493. Introductory Matrix Theory

Catalog Description: MA 306/493 provides the essential matrix theory background required for the proof-oriented MA 405. This course is specifically designed for students who have not completed MA 305 but wish to take MA 405. Topics include systems of linear equations, row reduction, linear independence and spanning in Euclidean spaces, determinants, and eigenvalues and eigenvectors of matrices. This course must be taken alongside MA 405. Students cannot receive credit for both MA 305 and MA 306/493.

Corequisite: MA 405

Course Organization: This course is taught asynchronous with instructional course materials available in Moodle. This self-paced, bootcamp-style, online, 8-week, corequisite course is fast paced, and it may become difficult to catch up if you fall behind. All learning materials (videos, blank templates, and filled-in notes) are available on the course Moodle page.

Course Format & Schedule:  This is an asynchronous online 1-credit course. The 8-week schedule consists of 16 Learning Days plus two exams (midterm + final exam).

Learning Days Components:

• Online Module: learning content, learning objectives, lecture videos, and notes.
• Self-Check: graded self-quiz, unlimited access
• Graded WeBWorK Homework

Course Schedule (tentative)

• Matrix Algebra: Addition, Multiplication, Transpose, Inverses (1 week)
• Linear systems: Gaussian Elimination, Reduced row echelon form, Rank, Consistency (2 weeks)
• Test 1
• Determinants: Definition and Properties (1.5 week)
• Euclidean Vector spaces R^n: Span, independence, bases, dimension (1.5 week)
• Eigenvalues and eigenvectors; Diagonalization (1 week)

Please plan accordingly and contact Dr. Alina Duca (anduca@ncsu.edu) if you have any questions.