Differential Geometry (Advanced) (MATH3968)

UNIT OF STUDY

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 course 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.

Further unit of study information

Classes

Three 1 hour lectures and one 1 hour tutorial per week.

Assessment

One 2 hour exam and 2 assignments (100%)

Faculty/department permission required?

No

Unit of study rules

Prerequisites and assumed knowledge

Credit average or greater in 12 credit points of Intermediate Mathematics, including MATH2961, Credit average or greater in 12 credit points of Intermediate Mathematics, including MATH2961, Credit average or greater in 12 credit points of Intermediate Mathematics, including MATH2961

At least 6 credit points of Intermediate Advanced Mathematics or Senior Advanced Mathematics units

Prohibitions

MATH3903, MATH3903, MATH3903

Study this unit outside a degree

Non-award/non-degree study

If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student.

Cross-institutional study

If you are from another Australian tertiary institution you may be permitted to underake cross-institutional study in one or more units of study at the University of Sydney.