Algebra

Module Identifier: MA10510
Module Title: Algebra
Academic Year: 2026/2027
Semester: Semester 1
Co-ordinator: Dr Gwion Evans
Reading List: View on Aspire
Pre-Requisite: A-level Mathematics or equivalent.
Co-Requisite: MP10610 or MT10610
Exclusive (Any Acad Year): MT10510
Other Staff: Dr Kim Kenobi; Dr Alexander Pitchford; Dr Gwion Evans; Dr Adil Mughal; Professor Simon Cox; Dr Adam Vellender; Dr Jukka Kiukas; Dr Robert Douglas

Assessment

Assessment Type	Assessment details	Proportion
Semester Assessment	Coursework: Mark based on engagement, participation and submitted assignments	20%
Semester Exam	Written Examination: 2 Hours	80%
Supplementary Assessment	Blackboard Test:	20%
Supplementary Exam	Supplementary Exam: 2 Hours	80%

Learning Outcomes

On successful completion of this module students should be able to:

Use the notation for sets and mappings
Construct proofs using the Principle of Mathematical Induction
Apply the Binominal Theorem for an integer exponent in various situations
Obtain the sums of arithmetic and geometric series
Manipulate complex numbers and use DeMoivre's Theorem
Use the Division Algorithm for polynominals
Derive inequalities involving the roots of a polynominal and its coeffcients

Brief description

This module covers the algebra which is fundamental to the development of Mathematics

Aims

To introduce the students to the ideas of algebra through the study of complex numbers and polynominals.

Content

1. SETS AND MAPPINGS: Introduction to number systems and mappings;

2. FINITE SUMS: The Binominal Theorem, arithmatic and geometric series, the principle of mathematical induction;

3. COMPLEX NUMBERS: Geometric interpretation, DeMoivre's Theorem;

4. POLYNOMINALS: The Division Algorithm and Remainder Theorem. Symmetric functions. Relations between roots of a polynominal and its coefficients;

Module skills

Skills type	Skills details
Application of Number	required throughout the course.
Communication	Written answers to exercises must be clear and well structured.
Improving own Learning and Performance	Students are expected to develop their own approach to time-management regarding the completion of assignments on time and preparation between lectures.
Information Technology	Via STACK and Blackboard.
Personal Development and Career planning	Completion of task (assignments) to set deadlines will aid personal development.
Problem solving	The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Subject Specific Skills	Broadens exposure of students to topics in mathematics.
Team work	Students will be encouraged to work together on questions during tutorials.

Notes

This module is at CQFW Level 4