Unit of study_

# Rings, Fields and Galois Theory (Adv) - MATH3962

Year - 2018

This unit of study investigates the modern mathematical theory that was originally developed for the purpose of studying polynomial equations. The philosophy is that it should be possible to factorize any polynomial into a product of linear factors by working over a "large enough" field (such as the field of all complex numbers). Viewed like this, the problem of solving polynomial equations leads naturally to the problem of understanding extensions of fields. This in turn leads into the area of mathematics known as Galois theory. The basic theoretical tool needed for this program is the concept of a ring, which generalizes the concept of a field. The course begins with examples of rings, and associated concepts such as subrings, ring homomorphisms, ideals and quotient rings. These tools are then applied to study quotient rings of polynomial rings. The final part of the course deals with the basics of Galois theory, which gives a way of understanding field extensions.

Classes
Three 1 hour lectures and one 1 hour tutorial per week.

Assessment
One 2 hour exam, homework assignments (100%)

Students are advised to take MATH2968 before attempting this unit.

Assumed knowledge
MATH2922 or MATH2961

Pre-requisites

Credit average or greater in 12 credit points of Intermediate Mathematics

Prohibitions

MATH3062 or MATH3902 or MATH3002

### Details

Faculty: Science

Semester 1

05 Mar 2018

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Mar 2018
Unit of study level: Senior
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Location
Camperdown
More details
HECS Band: 2
##### Courses that offer this unit

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