Overview
An introductory study of linear algebra emphasizing computational fluency, conceptual understanding, and rigorous mathematical communication. Topics include systems of linear equations, Gaussian elimination, matrix operations, inverses, determinants, vectors, vector spaces, subspaces, span, linear independence, bases, dimension, coordinates, rank, null spaces, linear transformations, matrix representations, composition, and change of basis.
The course develops the use of inner products, orthogonality, projections, and least-squares methods for approximation problems, followed by eigenvalues, eigenvectors, diagonalization, and an introduction to singular value decomposition. Applications include computer graphics, data analysis, differential equations, networks, and machine learning, with software and programming exercises supporting computation and interpretation.
Learning Outcomes
- Solve and interpret systems of linear equations using matrix methods and Gaussian elimination.
- Explain and prove fundamental properties of vector spaces, subspaces, span, linear independence, bases, and dimension.
- Determine the rank, nullity, column space, row space, and null space of a matrix.
- Represent, compose, and analyze linear transformations using appropriate bases and matrices.
- Apply inner products, orthogonality, projections, and least-squares methods to solve approximation problems.
- Compute and interpret eigenvalues, eigenvectors, eigenspaces, and diagonalizations where applicable.
- Connect algebraic, geometric, and matrix representations of linear algebraic structures.
- Apply linear algebraic methods to selected problems in graphics, data analysis, differential equations, networks, and machine learning.
- Use mathematical software or programming tools to perform computations, assess results, and communicate reasoning rigorously.
Timetable
| Type | Length | Frequency | Period |
|---|---|---|---|
| Lecture | 2 hours | Weekly | All semester |
| Tutorial | 1 hour | Weekly | All semester |
| Lab | 2 hours | Fortnightly | All semester |
Assessment Schedule
| Type | Description | Weighting |
|---|---|---|
| Assignment | Weekly problem sets (10 × 3%) | 30.00% |
| Deliverable | Computer-based linear algebra applications project | 10.00% |
| Test | Mid-semester test | 20.00% |
| Test | Practical computational test | 10.00% |
| Exam | Final examination | 30.00% |
Prerequisites
- Requirement 4 NCEA Level 2 Mathematics credits, externally assessed
Teaching Staff & Programs
This course is delivered jointly by faculty from the participating programs listed below. In line with the Douchewater Way, the University of Sexology tailors core instruction directly to each cohort's specific discipline — adapting curriculum to program needs rather than forcing students into a one-size-fits-all model. Learn more about our approach at The Douchewater Way.
