Skip to main content
Unit of study_

Rings, Fields and Galois Theory (Adv) - MATH3962

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
3x1-hr lectures; 1x1-hr tutorial/wk

Assessment
2 x assignments (20%); tutorial participation (10%); final exam (70%)

Additional information
Students are advised to take MATH2968 before attempting this unit.

Assumed knowledge
MATH2922 or MATH2961

Pre-requisites

MATH2961 or MATH2922 or a mark of 65 or greater in (MATH2061 or MATH2022)

Prohibitions

MATH3062 or MATH4062

Details

Faculty: Science

Semester 1

25 Feb 2019

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Mar 2019
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
Unit of Study coordinator: Florica Cirstea
HECS Band: 2
Courses that offer this unit

Non-award/non-degree study If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student. Cross-institutional study If you are from another Australian tertiary institution you may be permitted to undertake cross-institutional study in one or more units of study at the University of Sydney.

To help you understand common terms that we use at the University, we offer an online glossary.