MTH2025 · Linear algebra (Advanced)

Overview

Vector spaces, linear transformations. Determinants, eigenvalue problems. Inner products, symmetric matrices, quadratic forms. Linear functionals and dual spaces. Matrix decompositions, least squares approximation, power method. Applications to areas such as coding, economics, networks, graph theory, geometry, dynamical systems, Markov chains, differential equations.

Areas of study: Applied mathematics Financial and insurance mathematics Mathematical statistics Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. Apply core concepts of vector spaces and linear transformations to model and solve mathematical problems;
2. Analyse and compute eigenvalues, eigenvectors, and diagonalisation, and interpret their applications;
3. Employ inner product methods, matrix decompositions, and computational tools to address applied problems such as least-squares approximation;
4. Communicate mathematical reasoning clearly and effectively in both written and oral forms;
5. Extend and deepen understanding through rigorous proofs, advanced theoretical concepts, and more complex applications of linear algebra.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12); • One 1-hour workshop and • Six hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.