Rings, Fields and Galois Theory (Advanced)

University of Sydney

Course Description

  • Course Name

    Rings, Fields and Galois Theory (Advanced)

  • Host University

    University of Sydney

  • Location

    Sydney, Australia

  • Area of Study

    Algebra, Calculus, Geometry, Mathematics

  • Language Level

    Taught In English

  • Prerequisites

    Credit average or greater in 12 credit points of Intermediate Mathematics
    MATH2961

  • 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

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

    This unit of study investigates the modern mathematical theory that was originally developed for the purpose of studying polynomial equations. The philosophy is that it should be possible to factorize any polynomial into a product of linear factors by working over a "large enough" field (such as the field of all complex numbers). Viewed like this, the problem of solving polynomial equations leads naturally to the problem of understanding extensions of fields. This in turn leads into the area of mathematics known as Galois theory.
    The basic theoretical tool needed for this program is the concept of a ring, which generalizes the concept of a field. The course begins with examples of rings, and associated concepts such as subrings, ring homomorphisms, ideals and quotient rings. These tools are then applied to study quotient rings of polynomial rings. The final part of the course deals with the basics of Galois theory, which gives a way of understanding field extensions.

Course Disclaimer

Courses and course hours of instruction are subject to change.

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.