MATH3701 Higher Topology and Differential Geometry

MATH3701 is a Mathematics Level III course; it is the higher version of MATH3531 Topology and Differential Geometry. See the course overview below.

Units of credit: 6

Prerequisites: 12 units of credit of Level II Mathematics courses with an average mark of 70 or higher, including MATH2111 or MATH2011 (Credit) and MATH2601 or MATH2501 (Credit), or permission from Head of Department.

Exclusions: MATH3531

Cycle of offering: Term 3 

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH3701, you can log into UNSW Moodle for this course.

Course Aims

The principal aim of this subject is to introduce students to the topology and differential geometry of curves and surfaces, and to study some of the many applications.

Course Description

Topology and differential geometry both deal with the study of shape: topology from a continuous and differential geometry from a differentiable viewpoint.
This course begins with an introduction to general topology. We then study curves in space and how they bend and twist, and the topology of curves. We then consider surfaces, studying the first and second fundamental forms introduced by Gauss, the various measures of curvature and what they mean for the external and internal appearance and properties of surfaces. We prove the important Gauss-Bonnet theorem and use it to examine topological properties of surfaces, such as the Euler Characteristic. We finish with a look at the hyperbolic plane and a look forward to general Riemannian geometry.