MTH2021 - Linear algebra with applications - 2017

Vector spaces, linear transformations. Determinants, eigenvalue problems. Inner products, symmetric matrices, quadratic forms. LU-decomposition, least squares approximation, power method. Applications to coding, economics, networks, graph theory, geometry, dynamical systems, Markov chains, differential equations.

On completion of this unit students will be able to:

1. Understand 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. Understand and apply relevant numerical methods and demonstrate computational skills in linear algebra;
7. Present clear mathematical arguments in both written and oral forms.

Examination (3 hours): 70% + Assignments and tests: 30%

Three 1-hour lectures and one 2-hour support class per week

See also Unit timetable information

Associate Professor Tim Garoni

Applied mathematics

Financial and insurance mathematics

Mathematical statistics

Mathematics

Pure mathematics

MTH1030, MTH1035, ENG1005 or equivalent

MTH2025