MATH2501 is a Mathematics Level II course. See the course overview below.

Units of credit: 6

Prerequisites: MATH1231 or MATH1241 or MATH1251 or DPST1014

Exclusions: MATH2601, MATH2099

Cycle of offering: Term 2

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

The higher version of this course, MATH2601 Higher Linear Algebra, is offered yearly in Semester 1.

MATH2501 (alternatively MATH2601) is a compulsory course for Mathematics and Statistics majors.

If you are currently enrolled in MATH2501, you can log into UNSW Moodle for this course.

#### Course Aims

This course aims to examine key ideas in linear algebra. Students will improve and develop their analytical thinking skills and their ability to communicate technical arguments clearly. Material on vector spaces and related topics which was introduced in MATH1231, MATH1241 or MATH1251 will be revised and understood in greater depth. We shall introduce more advanced work in this area including applications to geometry, data fitting and differential equations.

#### Course Description

Linear algebra is a key tool in all of mathematics and its applications. For example, the output of many electrical circuits depends linearly on the input (over moderate ranges of input), and successfully correcting the trajectory of a space probe involves repeatedly solving systems of linear equations in hundreds of variables. Linear methods are vital in ecological population models, and in mathematics itself. You have met systems of linear equations and matrices, vector spaces and linear transformations in first year Mathematics courses, without necessarily understanding all the subtleties involved. In MATH2501, you will review the material from first year, so that vector spaces and linear transformations become familiar friends rather than uneasy acquaintances. You will learn about geometric transformations: projections

(which can also be viewed as least squares approximations), rotations and reflections. You will see how to view many linear transformations as being made up of "stretches" in various directions, (the diagonalisation process), and the more general Jordan form. This will allow you to calculate functions of matrices (such as the exponential of a matrix) and hence to solve systems of linear differential equations.