RINGS AND FIELDS

Course Code

MX 3531

Credit Points

15

Course Coordinator

Dr D Quinn

Pre-requisites

MX 3020

Overview

• Basic concepts and examples. Ideals, factor rings, isomorphism theorems.


• Rings of polynomials.


• Field of fractions of a domain.


• Unique Factorization Domains, Principal Ideal Domains, Euclidean Domains.


• Passage from R to R[X]. Gauss's Theorem. Eisenstein's criterion.


• Fields : characteristic, prime subfield.


• Finite fields, construction.


• Algebraic and transcendental elements, algebraic closure.

Structure

2 one-hour lectures and 1 one-hour tutorial per week.

Assessment

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour examination (maximum of 100% resit and 80% resit with 20% in-course assessment).
Only the marks obtained on first sitting can be used for Honours classification.

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials.

Students will be invited to contact Course Coordinators for feedback on the final examination.