Overview

This unit will explore the metric structure of curves and surfaces, primarily in 3-dimensional Euclidean space. The major focus is on the various concepts of curvature and related notions, and the relationships between them. Curvature and torsion of a curve. First and second fundamental forms of a surface. Geodesic and … For more content click the Read More button below.

Offerings

S1-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Associate Professor Daniel Mathews

Unit Coordinator(s)

Associate Professor Daniel Mathews

Notes

This unit shares seminars with MTH3110, but has separate applied classes and assessment.

Learning outcomes

On successful completion of this unit, you should be able to:
1.

Explain the significance of intrinsic measures of curvature, for curves and surfaces in 3-dimensional space;

2.

Perform advanced calculations of curvature and related quantities for curves and surfaces in 3-dimensional spaces;

3.

Explain and apply important concepts about the geometry of curves and surfaces in 3-dimensional space;

4.

Prove important theorems about the geometry of curves and surfaces in 3-dimensional space;

5.

Apply results about differential geometry to write proofs and solve advanced problems about curves and surfaces in 3-dimensional space;

6.

Demonstrate understanding of the links between differential geometry and other areas of mathematics and physics, such as real and complex analysis, linear algebra, differential equations, and general relativity;

7.

Communicate mathematical ideas relating to differential geometry in a clear, precise and rigorous manner;

8.

Develop and present rigorous mathematical proofs.

Teaching approach

Active learning
Problem-based learning

Assessment

1 - Continuous assessment
2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions
Seminars

Workload requirements

Workload

Learning resources

Recommended resources

Availability in areas of study

Mathematics
Pure mathematics