MATH3531 is a Mathematics Level III course. See the course overview below.

Units of credit: 6

Prerequisites: 12 units of credit in Level II Mathematics courses, including MATH2011 or MATH2111 or MATH2510 or MATH2610.

Excluded: MATH3701

Cycle of offering: every even year in Semester 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. (This pdf will usually be updated by the end of the first week of the semester.)

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

The higher version of this course, MATH3701 Higher Topology and Differential Geometry, is offered yearly in Semester2.

If you are currently enrolled in MATH3531, you can log into the My eLearning Vista instance of this course.

Differential Geometry is about how curves and surfaces bend and twist: we investigate those properties of surfaces that do not change under rigid motions. We will learn what it means for a curve or surface to be curved. We will learn what makes a circle (or any other conic section) different from a spiral, for example. We will also see how the way a sphere is curved differs from the way a cylinder is curved, and investigate some of the simpler consequences of curvature.

Combinatorial Topology is about those properties of surfaces that do not change if we are allowed to stretch and distort them continuously, e.g. without tearing. We will learn why a sphere and a torus (doughnut) are fundamentally different, and look at more general surfaces. We will also look at colouring maps (in the sense of countries) on these surfaces, and several interesting general theorems on topological spaces and simultaneous bisection.

Here are pictures of common surfaces which occur in the course:

The Saddle surface
The Torus
The Pseudosphere
The The Helicoid
The Catenoid
Enneper's surface

The animated GIF file helicoid.gif shows the isometric deformation of a helicoid into a catenoid.