MATH3511 Transformations, Groups and Geometry

MATH3511 is a Mathematics Level III course. See the course overview below.

Units of credit: 6

Prerequisites: MATH1231 OR MATH1241 OR MATH1251

Cycle of offering: Semester 2 in odd years

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 information about the course. (The timetable is only up-to-date if the course is being offered this year.)

If you are currently enrolled in MATH3511, you can log into UNSW Moodle for this course.

Course Overview

A transformation on the plane is a bijection (or permutation) from the plane to itself. We will first study several types of transformations such as translations, reflections, rotations etc. We will also prove some theorems in classical Euclidean geometry and discover surprising properties of triangles and circles. We will then look at symmetries, i.e. transformations of geometric figures which preserve some property (such as distance or angles between lines) and projective geometry, i.e. the study of perspective. Projective transformations can change a conic section of one type to another, e.g. an ellipse to a hyperbola. This leads us then to the study of abstract groups, where we will study the permutation group, subgroups, normal subgroups, direct products, quotient groups and group homomorphisms.