## Overview

MATH3701 is a Mathematics Level III course; it is the higher version of MATH3531 Topology and Differential Geometry.

Units of credit: 6

Prerequisites: 12 units of credit of Level II Mathematics courses with an average mark of 70 or higher, including MATH2111 or MATH2011 (Credit) and MATH2601 or MATH2501 (Credit).

Exclusions: MATH3531

Cycle of offering: Term 3

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 up-to-date timetabling information.

If you are currently enrolled in MATH3701, you can log into UNSW Moodle for this course.

## Course aims

The principal aim of this subject is to introduce students to the topology and differential geometry of curves and surfaces, and to study some of the many applications.

## Course description

Topology and differential geometry both deal with the study of shape: topology from a continuous and differential geometry from a differentiable viewpoint.

This course begins with an introduction to general topology. We then study curves in space and how they bend and twist, and the topology of curves. We then consider surfaces, studying the first and second fundamental forms introduced by Gauss, the various measures of curvature and what they mean for the external and internal appearance and properties of surfaces. We prove the important Gauss-Bonnet theorem and use it to examine topological properties of surfaces, such as the Euler Characteristic. We finish with a look at the hyperbolic plane and a look forward to general Riemannian geometry.