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Higher Topology and Differential Geometry - MATH3701
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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, MATH3700, MATH3760
 
 
Fee Band: 5 (more info)
 
 
Further Information: See Class Timetable
 
  

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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© The University of New South Wales (CRICOS Provider No.: 00098G), 2004-2011. The information contained in this Handbook is indicative only. While every effort is made to keep this information up-to-date, the University reserves the right to discontinue or vary arrangements, programs and courses at any time without notice and at its discretion. While the University will try to avoid or minimise any inconvenience, changes may also be made to programs, courses and staff after enrolment. The University may also set limits on the number of students in a course.