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Unit of study_

MATH3968: Differential Geometry (Advanced)

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.

Code MATH3968
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
A mark of 65 or greater in 12 credit points of MATH2XXX units of study
Assumed knowledge:
(MATH2921 and MATH2922) or MATH2961

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.