# MATH3531 Topology and Differential Geometry

MATH3531 is a Mathematics Level III course. See the course overview below. A higher version of this course is MATH3701.

Units of credit: 6

Prerequisites: 12 units of credit in Level II Math courses including MATH2011 or MATH2111 or MATH2069.

Exclusions: MATH3701, MATH5700

Cycle of offering: Term 3

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

More information: This recent course handout 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 MATH3531, you can log into UNSW Moodle for this course.

#### Course Aims

The principal aim is to develop a working knowledge of the geometry and topology of curves and surfaces.

#### Course Description

This major theme of this course is the study of properties of curves and surfaces that are preserved under changes: differentiable changes in differential geometry and continuous changes intopology. The differential geometry is treated as a continuation of vector calculus studied in earlier courses.

We begin with the study of curves in the plane and analyse what it means to be curved rather than straight, and then cover curves in space and how they curve and twist. We progresses to surfaces and how they bend both internally and externally and look at minimal surfaces and geodesics. We show why a map of the earth must be distorted in our study of Gauss' "Remarkable Theorem" and then cover the Gauss-Bonnet Theorem. In the last section, we cover the Euler characteristic and the platonic solids, Mobius bands and other surfaces and study the elementary combinatorial topology of surfaces. The course culminates in the complete classification of topological surfaces..

Note: Offered in even numbered years only.