Geometry Of Surfaces

King's College London

Course Description

  • Course Name

    Geometry Of Surfaces

  • Host University

    King's College London

  • Location

    London, England

  • Area of Study

    Geometry, Mathematics

  • Language Level

    Taught In English

  • 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

  • UK Credits

    15
  • Recommended U.S. Semester Credits
    4
  • Recommended U.S. Quarter Units
    6
  • Overview

    Geometry Of Surfaces
    Module code: 5CCM223A
    Semester: Semester 2 (spring)
    Module description:
    Aims and objectives:
    This module will apply the methods of calculus to the geometry of curves and surfaces in three-dimensional space. The most important idea is that of the curvature of a curve or a surface. The module should prepare you for more advanced modules in geometry, as well as courses in mathematical physics such as relativity.
    Pre-requisites 4CCM111A Calculus I, 4CCM112A Calculus II, 4CCM113A Linear Methods.
    Syllabus:
    Definition of a curve, arc length, curvature and torsion of a curve, Frenet-Serret equations. Definition of a surface patch, first fundamental form, isometries, conformal maps, area of a surface. Second fundamental form of a surface, gaussian, mean and principal curvatures. Gauss map. Theorema Egregium. Geodesics. Gauss-Bonnet theorem.
    Books:
    http://myreadinglists.kcl.ac.uk/search.html?q=ccm223
    Credit level: 5
    Credit value: 15
    Assessment: written examination/s
    One 2-hour written examination. Exercise sheets will be given out each week. Solutions handed in will be marked and difficulties discussed in the tutorial.

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.

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.