Groups and Symmetries

King's College London

Course Description

  • Course Name

    Groups and Symmetries

  • Host University

    King's College London

  • Location

    London, England

  • Area of Study

    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

    Module description:

    Aims and objectives:
    To provide an understanding of group theory and some of its applications.

    Syllabus:
    General group theory: Definitions of a group, cyclic groups, coset spaces, conjugacy classes, normal subgroups,
    quotient groups, dihedral groups, isomorphism theorems, group of automorphisms. Direct products and semi-direct
    products.
    Classical groups: GL(n,R), U(n), SU(n), 0(n), S0(n) and the various relations between them; centres of classical
    groups; 0(n) = Z2 x S0(n), n odd; the semi-direct product relation for n even; scalar product and 0(n), U(n);
    parametrization of S0(2) and S0(3), rotations in R2 and R3; S0(3) = SU(2)/Z2; Euclidean group, Lorentz group.
    Applications to symmetries of geometrical objects, vector fields and equations.
    Books:
    http://myreadinglists.kcl.ac.uk/search.html?q=ccm232

    Assessment: written examination/s

Course Disclaimer

Courses and course hours of instruction are subject to change.

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

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