Geometry of Curves and Surfaces

University of Otago

Course Description

  • Course Name

    Geometry of Curves and Surfaces

  • Host University

    University of Otago

  • Location

    Dunedin, New Zealand

  • Area of Study

    Geometry, Mathematics

  • Language Level

    Taught In English

  • Prerequisites

    MATH 202 and MATH 203

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • Credit Points

    18
  • Recommended U.S. Semester Credits
    3 - 4
  • Recommended U.S. Quarter Units
    4 - 6
  • Overview

    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.

    Course 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)

    Learning Outcomes

    • Demonstrate in-depth understanding of geometric concepts
    • Capability to apply them in real-world problems

Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Availability of courses is based on enrollment numbers. All students should seek pre-approval for alternate courses in the event of last minute class cancellations

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.