Program Overview

MATH3968: Differential Geometry (Advanced)

Introduction

This unit is an introduction to Differential Geometry, one of the core pillars of modern mathematics. Using ideas from calculus of several variables, we develop the mathematical theory of geometrical objects such as curves, surfaces and their higher-dimensional analogues. Differential geometry also plays an important part in both classical and modern theoretical physics. The unit aims to develop geometrical ideas such as curvature in the context of curves and surfaces in space, leading to the famous Gauss-Bonnet formula relating the curvature and topology of a surface.

Unit Details and Rules

• Managing faculty or University school: Science
• Study level: Undergraduate
• Academic unit: Mathematics and Statistics Academic Operations
• Credit points: 6

Enrolment Rules

• Prerequisites: A mark of 65 or greater in 12 credit points of MATH2XXX units of study
• Corequisites: None
• Prohibitions: MATH4068
• Assumed knowledge: (MATH2921 and MATH2922) or MATH2961

Learning Outcomes

At the completion of this unit, you should be able to:

• LO1. demonstrate knowledge and understanding of fundamental concepts and theorems in differential geometry.
• LO2. apply fundamental theorems and concepts of differential geometry in order to solve geometric problems
• LO3. understand and apply geometric concepts to analyse examples to draw conclusions
• LO4. evaluate geometric quantities such as torsion and curvature
• LO5. synthesise knowledge across a range of topics and write valid mathematical proofs.

Unit Availability

This section lists the session, attendance modes and locations the unit is available in.

• Session: Semester 2 2025, Semester 2 2026, Semester 2 2020, Semester 2 2021, Semester 2 2022, Semester 2 2023, Semester 2 2024
• Mode of attendance (MoA): Normal day
• Location: Camperdown / Darlington, Sydney, Remote
• Outline: Available for some sessions, unavailable for others.