## Overview

MATH3531 is a Mathematics Level III course. 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, MATH3700, MATH3760

Cycle of offering: Term 3  (not offered every year)

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

Important additional information as of 2023

#### UNSW Plagiarism Policy

The University requires all students to be aware of its policy on plagiarism.

For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.

If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.

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.