# Gwybodaeth Modiwlau

Module Identifier
MA10510
Module Title
Algebra
2021/2022
Co-ordinator
Semester
Semester 1
Co-Requisite
MP10610 or MT10610 or MA10610
Mutually Exclusive
Pre-Requisite
A-level Mathematics or equivalent.
Other Staff

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Assessment Four assignments, participation  20%
Semester Exam 2 Hours   (Written Examination)  80%
Supplementary Exam 2 Hours   (Written Examination)  100%

### Learning Outcomes

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

1. use the notation for sets and mappings
2. construct proofs using the Principle of Mathematical Induction
3. apply the Binominal Theorem for an integer exponent in various situations
4. obtain the sums of arithmetic and geometric series
5. manipulate complex numbers and use DeMoivre's Theorem
6. use the Division Algorithm for polynominals
7. derive inequalities involving the roots of a polynominal and its coeffcients

### 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;

### 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.

### 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.
Research 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