Overview
MATH5700 is an honours and postgraduate coursework mathematics course. See theÌýcourse overviewÌýbelow.
Units of credit:Ìý6
Exclusions: MATH3531, and MATH3701 (MATH5700 jointly taught with MATH3701)
Course offering:ÌýTerm 3Ìý Ìý
Graduate attributes:
This course provides a good understanding of basic topological properties. These include, constructions and reasoning in three dimensional space and classical curves and surfaces. You will understand the meaning of curvature for curves and surfaces, and appreciate the connections between topology and differential geometry for surfaces.
On completion you will know how to compute the fundamental group for a range of topological spaces and understand the importance of homotopy relation. You will know how to differentiate between two manifolds using algebraic topology tools and differential geometry tools. You will gain an appreciation for the importance of quadrics to approximate surfaces at a point, and be able to make explicit computations for a wide variety of examples. This includes, computing Frenet frames for curves, and first and second fundamental forms for many surfaces. Algebraic surfaces and surfaces of revolution will provide a good source of examples. You will understand the idea of a developable surface and its applications.
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The above outcomes are related to research, inquiry and analytical thinking abilities, communication, and information literacy.
More information:ÌýÌýThe Course outline will be made available closer to the start of term - please visit this website: www.unsw.edu.au/course-outlinesÌý
Important additional information as of 2023
UNSW Plagiarism Policy
The University requires all students to be aware of itsÌý.
For courses convened by theÌýSchool of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.
If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.
TheÌýcontains information about the course. The timetable is only up-to-date if the course is being offered this year.
If you are currently enrolled in MATH5700, you can log intoÌýÌýfor this course.
Course overview
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.