MAT-20035 - Exploring Algebra and Analysis
Coordinator: Paul J Truman Room: MAC2.16 Tel: +44 1782 7 33246
Lecture Time: See Timetable...
Level: Level 5
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2021/22

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

MAT-10046 Calculus,
MAT-10047 Algebra.

Barred Combinations

None.

Description for 2021/22

Algebra and Analysis are two of the main branches of Pure Mathematics.
Linear Algebra generalizes the vector and matrix algebra encountered at level 4. The module will study abstract vector spaces, especially focussing on the role of bases in describing elements.
Mathematical Analysis can be described as the study of the infinitely small and infinitely large. This branch of mathematics arose out of the need to place Calculus on a secure theoretical footing. The module will give rigorous proofs a number of results from Calculus.
Each topic will be introduced via guided investigations, followed by lectures to develop the formal theory. The concepts and styles of thinking developed in this module will stand students in good stead for other level 5 and 6 modules.

Aims
This module will give students a grounding in Linear Algebra and Real Analysis, two of the major branches of Pure Mathematics. Topics will be introduced via guided investigations and developed more formally via lectures. In this way students will gain insight into the different styles of thinking required for each of these branches.

Intended Learning Outcomes

make judgements and evaluate different approaches to problem solving
: 1,2
apply appropriate concepts and theory to develop logical arguments: 1,2
state and apply definitions and theorems of linear algebra related to linearly independent sets, spanning sets, and bases: 1,2
state and apply definitions and theorems of real analysis related to sequences of real numbers: 2
apply knowledge of linearly independent sets, spanning sets, bases, sequences of real numbers to prove theorems and solve theoretical problems: 2

Study hours

48 hours of lectures/investigation sessions
100 hours independent study
2 hours unseen examination

School Rules

None.

Description of Module Assessment

1: Assignment weighted 20%
Linear Algebra Assignment
An assignment comprising approximately 5 questions design to examine students' progress towards the ILOs concerning linear algebra. Solutions will be uploaded to the KLE. Students should expect to spend 10 hours on the assessment.

2: Open Book Examination weighted 80%
2-hour unseen online examination
The examination paper will consist of no less than five and not more than eight questions all of which are compulsory. The examination will be online and open book. A well-prepared student should expect to complete the assessment in two hours.