MTH3110 - Differential geometry

Leader: Professor Robert Bartnik

Offered

Clayton Second semester 2008 (Day)

Synopsis

This unit will explore the metric structure of curves and surfaces, primarily in 3-dimensional Euclidean space. Concepts of curvature arise naturally, and the major focus will be on the inter-relationships of various definitions of curvature, such as the normal and binormal curvatures of a curve, and the extrinsic, principal and Gaussian curvatures of a surface. Links will be drawn with many other areas of mathematics, including complex analysis, linear algebra, differential equations, and general relativity.

Objectives

On completion of this unit students will be able to demonstrate: an understanding of the significance of intrinsic measures of curvature, for curves and surfaces in R3; competence in computing curvature and related quantities, by hand and using computer software; an understanding of tensors and their use in geometry; and communication skills and team work as appropriate for the discipline of mathematics

Assessment

Three assignments: 10% each
Final examination: 70%

Contact hours

Three hours of lectures and one hour support class per week

Prerequisites

MTH2010, MTH2021

Prohibitions

MTH3132