Course

Higher Topology and Differential Geometry - MATH3701

Faculty: Faculty of Science

School: School of Mathematics and Statistics

Course Outline: http://www.maths.unsw.edu.au/

Campus: Kensington Campus

Career: Undergraduate

Units of Credit: 6

EFTSL: 0.12500 (more info)

Indicative Contact Hours per Week: 4

Enrolment Requirements:

Prerequisite: 12 UOC of Level 2 Mathematics with an average mark of at least 70, including MATH2111 or MATH2011 (CR) or MATH2510 (CR) and MATH2601 or MATH2501 (CR), or permission from Head of Department.

Excluded: MATH3531

CSS Contribution Charge: 2 (more info)

Tuition Fee: See Tuition Fee Schedule

Further Information: See Class Timetable

View course information for previous years.

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.


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