MATH5725 Galois Theory

MATH5725 is a Honours and Postgraduate Coursework Mathematics course. See the course overview below.

Units of credit: 6

Prerequisites: No

Cycle of offering: Variable

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: 

This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus. 

The Online Handbook entry contains information about the course. (The timetable is only up-to-date if the course is being offered this year.)

If you are currently enrolled in MATH5725, you can log into UNSW Moodle for this course.

Course Overview

The theory of fields holds the key to questions which have frustrated mathematicians for hundreds of years, including the impossibility of squaring a circle or trisecting an angle with ruler and compass, or finding a formula for solving quintic equations. The key to their study involves the Galois group which, loosely speaking, captures the symmetry of the field. Topics covered will include: fields, Eisenstein criterion, field extensions, algebraic extensions, groups of field automorphisms, normal and separable extensions, finite fields, Galois correspondence, solvable groups, solving equations by radicals, ruler and compass constructions, Kummer extensions, Artin-Schreier extensions.