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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 MATH220 or MATH321, and ideally both.
Develop familiarity with basic concepts in group theory, including group actionsUnderstand the main theorems of Galois theoryApply results from the theory of groups to study field extensions Understand classical applications of Galois theory such as the insolubility of the general quintic polynomialDevelop problem solving skillsDevelop written and oral communication skills, emphasising the ability to explain what the mathematics means
Subject to approval of the Head of School.
Students must attend one activity from each section.
Felipe Voloch
Brendan Creutz
Library portalLearn Postgraduate
Domestic fee $1,138.00
International Postgraduate fees
* 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 .