Overview
This course develops linear algebra through computational, theoretical, and applied problem-solving. Topics include systems of linear equations, matrices, row reduction, echelon forms, rank, inverse matrices, vector spaces, subspaces, linear combinations, span, linear independence, bases, dimension, coordinates, and the four fundamental subspaces.
Students study linear transformations, matrix representations, kernels, ranges, composition, change of basis, determinants, eigenvalues, eigenvectors, and diagonalization. Applications include dynamical systems, Markov models, network analysis, differential equations, and data analysis. The course also introduces inner products, orthogonality, least-squares approximation, projections, Gram-Schmidt orthogonalization, QR methods, singular value decomposition, and principal component analysis.
Emphasis is placed on interpreting algebraic structures geometrically, translating practical questions into mathematical models, selecting efficient solution methods, evaluating numerical and modeling assumptions, and using computational technology responsibly. Students communicate mathematical reasoning through precise notation, proofs or written justifications, code, visualizations, and explanatory prose.
Learning Outcomes
- Solve and interpret systems of linear equations using row reduction, matrix factorization, and other appropriate methods.
- Perform and justify computations involving matrices, vectors, vector spaces, subspaces, bases, dimension, and the four fundamental subspaces.
- Prove or justify core relationships concerning linear independence, span, rank, nullity, linear transformations, and change of basis.
- Analyze linear transformations through their matrix representations, kernels, ranges, compositions, and coordinate systems.
- Compute and interpret determinants, eigenvalues, eigenvectors, and diagonalizations in mathematical and applied contexts.
- Apply inner products, orthogonal projections, least-squares methods, Gram-Schmidt orthogonalization, and QR methods to overdetermined data.
- Construct and evaluate linear algebra models involving dynamical systems, Markov models, networks, differential equations, or data analysis.
- Assess numerical sensitivity, computational limitations, and the validity of modeling assumptions in exact and approximate calculations.
- Implement and verify linear algebra procedures using appropriate computational tools and interpret the resulting numerical evidence.
- Present mathematical solutions and applied findings using precise notation, logically structured reasoning, and clear explanatory prose.
Timetable
| Type | Length | Frequency | Period |
|---|---|---|---|
| Lecture | 2 hours | Weekly | All semester |
| Tutorial | 2 hours | Weekly | All semester |
| Lab | 2 hours | Fortnightly | All semester |
| Workshop | 2 hours | Fortnightly | All semester |
Assessment Schedule
| Type | Description | Weighting |
|---|---|---|
| Assignment | Weekly problem sets (10 × 3%) | 30.00% |
| Deliverable | Computational laboratory exercises (4 × 5%) | 20.00% |
| Test | Mid-semester test | 15.00% |
| Capstone | Applied linear algebra project | 15.00% |
| Exam | Final examination | 20.00% |
Prerequisites
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.