MATH5725 is an honours and postgraduate coursework mathematics course. See the course overview below.

Units of credit: 6

Prerequisites: No formal prerequisites

Cycle of offering: Variable

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

More information:  The Course outline will be made available closer to the start of term - please visit this website: www.unsw.edu.au/course-outlines

The course outline contains information about course objectives, assessments, course materials and the syllabus. 

Important additional information as of 2023

UNSW Plagiarism Policy

The University requires all students to be aware of its policy on plagiarism.

For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.

If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.

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.