MTH2021 · Linear algebra with applications

Overview

Vector spaces, linear transformations. Determinants, eigenvalue problems, matrix decompositions. Inner products, least squares approximation. Applications to areas such as coding, economics, graph theory, 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.

Requisites

Learning outcomes

1. Apply basic concepts related to vector spaces, including subspace, span, linear independence and basis;
2. Understand basic properties of linear transformations and identify their kernel and range;
3. Diagonalize real matrices by computing their eigenvalues and finding their eigenspaces;
4. Understand basic concepts related to inner product spaces and apply these to problems such as least-squares data fitting;
5. Apply tools from linear algebra in a wide variety of relevant situations;
6. Recognise and apply relevant numerical methods and demonstrate computational skills in linear algebra;
7. Present clear mathematical arguments in both written and oral forms.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

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