SETS AND ALGEBRAIC STRUCTURES

Course Code

MA 2004

Credit Points

15

Course Coordinator

Dr R Hepworth

Pre-requisites

MA 1006 or, with the permission of the Head of Mathematical Sciences, MA 1507.

Overview

This course provides an introduction to algebraic structures and elementary number theory.

The course includes a discussion of:

• Sets (notation, functions, injections, surjections, bijections)


• Countability of the rational numbers and uncountability of the real numbers


• The integers and factorisation


• Prime numbers, Euclidean algorithm, uniqueness of factorisation


• The integers modulo n


• Equivalence relations


• Permutations


• Group axioms


• The symmetric group


• Lagrange's Theorem


• Fermat's Little Theorem


• Definition of commutative ring and of a field with examples, especially polynomial rings


• Vector spaces and linear transformations.

Structure

3 one-hour lectures and 1 tutorial per week (to be arranged).

Assessment

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

Resit: 1 two-hour written examination paper, maximum resit (100%) and resit (80%) with in-course assessment (20%).

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 Coordinator for feedback on the final examination.