MAT-20035 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

Programme/Approved Electives for 2024/25

Available as a Free Standing Elective

Co-requisites

None

Prerequisites

MAT-10046 Calculus,
MAT-10047 Algebra.

Barred Combinations

None.

Description for 2024/25

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.

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
: 1,2,3
apply appropriate concepts and theory to develop logical arguments: 1,2,3
state and apply definitions and theorems of linear algebra related to linearly independent sets, spanning sets, and bases: 1,3
state and apply definitions and theorems of real analysis related to sequences of real numbers: 2,3
apply knowledge of linearly independent sets, spanning sets, bases, sequences of real numbers to prove theorems and solve theoretical problems: 1,3

Study hours

44 hours of lectures/investigation sessions
104 hours independent study
2 hours unseen examination

School Rules

None.

Description of Module Assessment