MATH5535 is a Mathematics Special Topics in Pure Mathematics Honours or Master course. In Semester 2, 2016 it will be a course on Lie Groups. See the course overview below.

**Units of credit:** 6

**Prerequisites: **No formal prerequisites, but a knowledge of linear algebra and multivariable calculus will be assumed.

**Cycle of offering: **Course not offered every year.

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

**More information:**

The course outline contains information about course objectives, assessment, course materials and the syllabus.

If you are currently enrolled in MATH5535, you can log into UNSW Moodle for this course.

#### Course Overview

**Lie Groups**

Rotations in R^3 form a group because a given rotation can be undone with another rotation and the composition of two rotations is itself a rotation. However the group properties are only part of the story because rotations can be continuously varied and the group operations are smooth. So the set of rotations is both a group and a smooth manifold, that is, a Lie group. In this course we will see many other Lie groups that occur as the symmetries of objects in mathematics and theoretical physics.

The course will first review some basic differential geometry and in particular, vector fields and tangent spaces, so that the connection with of Lie algebras can be made. Much of the structure of a Lie group can be determined by from its Lie algebra and so we will study the structure theory of Lie algebras that leads to the classification of semi-simple Lie algebras in terms of Dynkin diagrams.