MAT-10038 - Algebra I
Lecture Time: See Timetable...
Level: Level 4
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2023/24

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

None

Barred Combinations

None

Description for 2023/24

This module is intended to help students with the transition from the methods based approach of A level mathematics to the higher levels of understanding and rigour expected at degree level. It begins by discussing mathematical statements and the meaning and basic strategies of proof. This is followed by a short exposition of naive set theory and by a careful treatment of the notion of a function. The remainder of the module covers the algebraic development of number systems and their properties. The module ends with a brief discussion of the properties of polynomials, including the Fundamental Theorem of Algebra.

Aims
The aim of the module is to provide students with an introduction to pure mathematics, through the study of techniques of proof, sets and functions, real and complex numbers, factorisation of the integers, modular arithmetic and polynomials.

Intended Learning Outcomes

state clearly the key definitions and theorems of algebra, including those related to sets and functions, real and complex numbers, factorisation and divisiblity, modular arithmetic and polynomials: 1,2,3
use the basic concepts and theory to develop mathematical and logical arguments: 1,2
use the basic concepts and theory to make judgements and to evaluate different approaches to solving problems: 2
derive and apply the key theorems of algebra, including those related to sets and functions, real and complex numbers, factorisation and divisibility, modular arithmetic and polynomials: 3

Study hours

36 hours lectures
12 hours Examples Classes
20 hours coursework preparation
82 hours private study

School Rules

None

Description of Module Assessment

1: Assignment weighted 20%
A take-home, written assignment.
A take-home, written assignment. This consists of a set of questions with pre-allocated space for written solutions. Students should expect to spend 10 hours on this assignment.

2: Coursework weighted 20%
A take-home, written assignment.
A take-home, written coursework. This consists of a set of questions with pre-allocated space for written solutions. Students should expect to spend 10 hours on this assignment.

3: Exam weighted 60%
Unseen, two hour examination
A closed book examination based on material covered over the semester.