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2007/08 Undergraduate Module Catalogue

MATH2032 Ring, Polynomials and Fields

10 creditsClass Size: 200

Module manager: Professor W. Crawley-Boevey
Email: w.crawley-boevey@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2007/08

Pre-requisite qualifications

Plus either MATH1015 or MATH1060.

Pre-requisites

MATH1022	Introductory Group Theory
MATH1200	Numbers and Proofs

This module is approved as an Elective

Module summary

Prerequisites: MATH1022 plus MATH1015 or MATH1060. A ring is an algebraic system in which addition, subtraction and multiplication may be performed. Integers, polynomials and matrices all provide examples of rings, so this notion covers an important range of mathematical structures. They are studied in this module. The ideas are used to prove the theorem that there is no straight-edge and compass construction for trisecting a general angle.See the schools website or contact: a.slomson@leeds.ac.uk for more information.

Objectives

By the end of this module students should be able to: a) State the axioms of a ring and deduce directly from them basic properties; b) identify units and irreducibles in various examples, using appropriate tests; c) demonstrate understanding of unique factorisation or the lack of it; d) state the axioms of a field and deduce properties of extension fields; e) use minimal polynomials and the tower law when dealing with extension fields; f) apply the theory of fields to solve problems about ruler and compass constructions.

Syllabus

Basic theory of rings, especially integers and quadratic extensions, and polynomials over Z or over a field. Irreducible elements and factorisation. Basic theory of finite field extensions with application to ruler and compass constructability.

Teaching methods

Delivery type	Number	Length hours	Student hours
Example Class	11	1.00	11.00
Lecture	22	1.00	22.00
Private study hours			67.00
Total Contact hours			33.00
Total hours (100hr per 10 credits)			100.00

Opportunities for Formative Feedback

Example sheets.

Methods of assessment

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 00 mins	100.00
Total percentage (Assessment Exams)		100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 01/04/2008

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