Class Information:
Course name: Abstract Linear Algebra (MATH 416 Honors)
Offering: Fall 2025
Instructor: Theshani Nuradha
Email: nuradha@illinois.edu (Please include MATH 416 in the subject line of the email)
Grader: Xinran Yu (xinran4@illinois.edu) (Please contact Xinran over Canvas or through email for grading-related queries with MATH 416 in the subject line for the latter)
Class Hours: MWF 13:00-13:50 (IHAB-140, Henry Administration Building)
Office Hours: Wednesday 5:30 PM-6:20PM- Bevier Hall 108
We will use Canvas for all course-related announcements and for submitting homework sheets and in-class activity sheets. Please make sure that you have access to the Canvas course website; otherwise, please contact me.
Syllabus: This is a rigorous proof-oriented course in linear algebra. We will cover the following topics during the class
Solving systems of linear equations, row reduction, and row echelon form
Complex numbers, vector spaces, subspaces
Span and linear independence, bases, dimension of vector spaces
Linear maps, null space and range, matrices, isomorphic vector spaces, isomorphism theorem
Invariant subspaces, eigenvalues, eigenvectors, upper-triangular matrices
Inner products, norms, orthonormal bases, orthogonal complements
Operators on inner product spaces, self-adjoint and normal operators, spectral theorem, isometries, singular value decomposition
Generalized eigenspaces, multiplicity of eigenvalues, characteristic and minimal polynomial, Jordan normal form
Trace and determinant
Textbooks:
Linear Algebra Done Right, Fourth edition by Sheldon Axler
A First Course in Linear Algebra, Version 3.50 by Robert A. Beezer
Class Evaluation and Grading Policy:
Homework (30%)- There will be weekly homework sheets, which are due every Wednesday at 11:59 PM after the first week of classes, except during exam weeks. The lowest two homework scores will be dropped. It is strongly encouraged to collaborate on solving problems and acknowledge those discussions at the end of the solution that you upload to the Canvas.
In-class quizzes, activities, and class participation (20%)- We will have in-class quizzes and group activities during class time. Specific instructions will be given during the class. For the complete learning experience, it is ideal to participate actively in these activities during the allocated time. Five of the lowest scores will be dropped.
If you cannot make it to a class due to an unforeseen circumstance, please contact me for further arrangements.
Midterms (30%)- There will be three midterms. Exams will be held during the class time (50 mins). No conflict exams or make-up exams will be given. Instead, the lowest midterm score will be dropped.
This is the schedule for the midterms (unlikely to change):
Midterm 1- September 24th
Midterm 2- October 29th
Midterm 3- November 19th
Comprehensive Final (20%) - Allocated time 7:00 pm-10:00 pm, December 17th (Room -TBA, Check Course Explorer around October 15th). The final will most likely be a two-hour exam.
Accommodations and Feedback:
Please let me know if there are any accommodations that I could provide to improve your learning experience. I will always be open to feedback and suggestions from the students! This will be an experience for me and the students to learn from each other.
If there are any approved requests by the Disability Resources and Educational Services (DRES), please send them to nuradha@illinois.edu, in the first week of your class attendance.