MTH3115 Differential geometry (Advanced)

When you finish this unit, you should be able to:

1. 1

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

2. 2

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

3. 3

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

4. 4

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

5. 5

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

6. 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. 7

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

8. 8

   Develop and present rigorous mathematical proofs.