This is a special topics course which introduces students to the key concepts and techniques of Differential Geometry. Possible topics include:

Surfaces in Euclidean space, general differentiable manifolds, tangent spaces and vector fields, differential forms, Riemannian manifolds, Gauss-Bonnet theorem.

Note: This is an Honours Pathway course. It emphasises mathematical rigour and proof and develops the fundamental ideas of differential geometry from an abstract viewpoint.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the concepts and language of differential geometry and its role in modern mathematics
2. Analyse and solve complex problems using appropriate techniques from differential geometry with mathematical rigour
3. Apply problem-solving with differential geometry to diverse situations in physics, engineering or other mathematical contexts

4 written assignments involving problem-solving, proofs of theorems and extension of theory (25% each; LO 1, 2, 3)

36 lectures and tutorials by arrangement.

A mark of 60 or more in MATH2320 or a mark of 60 or more in MATH3116.

with MATH3027.