MATH321-20S1 (C) Semester One 2020

# Rings and Fields

15 points

Details:
 Start Date: Monday, 17 February 2020 End Date: Sunday, 21 June 2020
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 28 February 2020
• Without academic penalty (including no fee refund): Friday, 29 May 2020

## Description

An introduction to fields and rings, including applications to coding theory and the impossibility of constructions such as ‘squaring the circle’.

This course formally introduces rings and fields, which have been encountered at 100- and 200-level in special situations, and investigates their algebraic structure. It gives a deeper understanding of these algebraic concepts and thus provides a thorough grounding in the algebraic theory which underpins modern applications like cryptography, error-correcting codes, number theory or finite mathematics. If you are interested in any of these subjects or if you want to see how algebraic theory can be applied to solve certain geometric construction problems or prove their impossibility, then this is the course to take.

The topics covered by this course are:

• fundamentals of ring theory: subrings, ideals, factor rings, ring homomorphisms;
• special rings: integral domains and polynomial rings and factorizations of elements therein;
• fundamentals of field theory: field extensions, constructions of fields, in particular finite fields, and their uses, like the impossibility of certain geometric constructions such as trisecting the angle.

## Learning Outcomes

• Students successfully completing this course should:

• understand a range of basic algebraic concepts.
• have developed a high level of competence at core algebraic skills.
• be able to confidently apply algebraic concepts in practical settings.
• be able to present clear and logical mathematical arguments.

## Pre-requisites

One of MATH203, MATH220, MATH240, or
EMTH211, and a further 15 points from MATH201-294.

MATH439, MATH311

## Timetable 2020

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Tuesday 11:00 - 12:00 - (24/3, 21/4)Online Delivery (28/4-26/5)Jack Erskine 445 (18/2-17/3) 17 Feb - 29 Mar 20 Apr - 31 May Lecture B 01 Monday 13:00 - 14:00 - (23/3, 20/4)Online Delivery (4/5-25/5)Jack Erskine 446 (17/2-16/3) 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May Tutorial A 01 Thursday 15:00 - 16:00 Online Delivery 17 Feb - 22 Mar

## Assessment

To obtain a pass (C- or better), you must obtain at least 40% in the exam.

## Textbooks / Resources

Recommended text:
J.A. Gallian: Contemporary Abstract Algebra, Houghton Mifflin, 8th ed or later.
Earlier editions of the text are also suitable.

## Indicative Fees

Domestic fee \$780.00

International fee \$4,250.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

## All MATH321 Occurrences

• MATH321-20S1 (C) Semester One 2020