Fall 2026 - MATH 240 D100
Algebra I: Linear Algebra (3)
Class Number: 4480
Delivery Method: In Person
Overview
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Course Times + Location:
Sep 9 – Dec 6, 2026: Mon, Wed, Fri, 11:30 a.m.–12:20 p.m.
Burnaby
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Instructor:
Nilima Nigam
nna29@sfu.ca
1 778 782-4258
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Prerequisites:
MATH 150 or 151 or MACM 101, with a minimum grade of C-; or MATH 154 or 157, both with a grade of at least B. Students are advised to have taken MATH 141.
Description
CALENDAR DESCRIPTION:
Linear equations, matrices, determinants. Real and abstract vector spaces, subspaces and linear transformations; basis and change of basis. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. Applications. Subject is presented with an abstract emphasis and includes proofs of the basic theorems. Students with credit for MATH 232 cannot take this course for further credit.
COURSE DETAILS:
Linear Equations
- Systems of Linear Equations, Row Reduction and Echelon Form
- Vectors, Vector Equations, Matrices
- The Matrix Equation Ax=b
- Solution Sets of Linear Systems
- Matrix Inverse
- Linear Independence, Rank and Dimension
- Introduction to Linear Transformations
- The Matrix of a Linear Transformation
- Vector Spaces and Subspaces
- Null Spaces, Column Spaces, and Linear Transformations
- Linearly Independent Sets; Bases for Subspaces
- Coordinate Systems
- The Dimension of a Vector Space
- Change of Basis
- The Complex Plane, Complex Conjugate, and Magnitude
- Polar Form, De Moivre's Formula and Euler's Formula
- Roots of Quadratic Polynomials
- Complex Eigenvalues
- Computing Eigenpairs
- Diagonalization
- Eigenvectors and Linear Transformations
- Application: The Leslie Age Distribution model
- Inner Product, Length and Orthogonality
- Orthogonal Sets
- Orthogonal Projections
- The Gram-Schmidt Process
- Application: Least Squares Problems
- LU, QR, SVD
- Determinants and their Properties
Grading
- Quizzes (5 quizzes) LOWEST WILL BE DROPPED 15%
- Midterm 1 15%
- Midterm 2 15%
- Final Exam 55%
NOTES:
In addition to the above, students will write concept quizzes, Pass/Fail basis, each with 2 retakes [3 quizzes].
Policy on generative AI
The prevalence of powerful new AI-based tools (chatbots and agents) is changing many facets of life. Here’s one sobering opinion: students are uniquely vulnerable to becoming redundant if they don’t train their mathematical brain. Relying on AI chatbots measurably decreases our cognitive abilities. You are here to learn the material; AI will empower you once you have done so.
With this in mind: I expect you to treat the training of your mind as an existentially important activity. Homeworks won’t be graded, and if you get solutions from the web or from AI – there is ample evidence that you will perform poorly on the examinations. The use of AI tools is strictly prohibited on the graded portions of this class.
Materials
REQUIRED READING:
Linear Algebra and Its Applications
6/E
Lay, Steven R.; Lay, David C.; McDonald, Judith; McDonald, Judi J.
Pearson Education
Registrar Notes:
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
At SFU, you are expected to act honestly and responsibly in all your academic work. Cheating, plagiarism, or any other form of academic dishonesty harms your own learning, undermines the efforts of your classmates who pursue their studies honestly, and goes against the core values of the university.
To learn more about the academic disciplinary process and relevant academic supports, visit:
- SFU’s Academic Integrity Policy: S10-01 Policy
- SFU’s Academic Integrity website, which includes helpful videos and tips in plain language: Academic Integrity at SFU
RELIGIOUS ACCOMMODATION
Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.