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MATH306 Geometry of Curves and Surfaces

An introduction to differential geometry with a focus on the structure of two-dimensional surfaces.

This paper provides the necessary tools to describe two-dimensional surfaces in many applications, such as modelling air flow around cars, architecture, etc.

Paper title Geometry of Curves and Surfaces
Paper code MATH306
Subject Mathematics
EFTS 0.1500
Points 18 points
Teaching period Second Semester
Domestic Tuition Fees (NZD) $904.05
International Tuition Fees (NZD) $3,954.75

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MATH 202 and MATH 203
Schedule C
Arts and Music, Science
This paper is particularly relevant to Mathematics and Physics majors.
Teaching staff

Professor Jörg Frauendiener

Paper Structure
Main topics:
  • Curves in the plane and in space (parametrised curves, arc length, Frenet-Serret equations)
  • Regular surfaces (regular values, functions on surfaces, first and second fundamental forms)
  • Intrinsic geometry of surfaces (the Gauss theorem, parallel transport and geodesics, Gauss Bonnet and applications)
Teaching Arrangements
Three lectures and one tutorial per week.
Andrew Pressley, Elementary Differential Geometry, Springer Verlag (this book is freely downloadable in electronic form from Springer Verlag).
Course outline
View course outline for MATH 306
Graduate Attributes Emphasised
Critical thinking.
View more information about Otago's graduate attributes.
Learning Outcomes
  • Demonstrate in-depth understanding of geometric concepts
  • Capability to apply them in real-world problems

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Second Semester

Teaching method
This paper is taught On Campus
Learning management system


Stream Days Times Weeks
L1 Monday 09:00-09:50 28-34, 36-41
Wednesday 09:00-09:50 28-34, 36-41
Friday 09:00-09:50 28-34, 36-41


Stream Days Times Weeks
T1 Monday 15:00-15:50 29-34, 36-41