Overview
MATH5725 is an honours and postgraduate coursework mathematics course. See the聽course overview聽below.
Units of credit:听6
Prerequisites:聽No formal prerequisites
Cycle of offering:聽Variable
Graduate attributes:聽The course will enhance your research, inquiry and analytical thinking abilities.
More information:聽聽The Course outline will be made available closer to the start of term - please visit this website:聽www.unsw.edu.au/course-outlines
The course outline contains information about course objectives, assessments, course materials and the syllabus.聽
Important additional information as of 2023
UNSW Plagiarism Policy
The University requires all students to be aware of its聽.
For courses convened by the聽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.
罢丑别听聽contains聽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聽聽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.