MATH411-22S1 (C) Semester One 2022

Topics in Algebra

15 points

Details:
Start Date: Monday, 21 February 2022
End Date: Sunday, 26 June 2022
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 6 March 2022
  • Without academic penalty (including no fee refund): Sunday, 15 May 2022

Description

Topics in Algebra

The focus of this course is Galois theory, which provides a beautiful connection between field theory and group theory. It can be used to reduce certain problems about fields to group theory which is, in some sense, simpler and better understood. Topics in the theory of finite groups will be covered as needed. Goals of the course include proofs of the Abel-Ruffini Theorem (concerning insolubility of a general quintic equation by radicals) and the Fundamental Theorem of Algebra. Useful prerequisites are MATH240 or MATH321, and ideally both.

Learning Outcomes

  • Develop familiarity with basic concepts in group theory, including group actions
  • Understand the main theorems of Galois theory
  • Apply results from the theory of groups to study field extensions
  • Understand classical applications of Galois theory such as the insolubility of the general quintic polynomial
  • Develop problem solving skills
  • Develop written and oral communication skills, emphasising the ability to explain what the mathematics means

Prerequisites

Subject to approval of the Head of School.

Course Coordinator / Lecturer

Brendan Creutz

Lecturer

Felipe Voloch

Indicative Fees

Domestic fee $1,017.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH411 Occurrences

  • MATH411-22S1 (C) Semester One 2022
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