School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2023/24 Last Updated: 06 December 2023

MAT-20035 - Exploring Algebra and Analysis

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MAT-10046 Calculus,

MAT-10047 Algebra.

MAT-10047 Algebra.

None.

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.

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.

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

: 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

44 hours of lectures/investigation sessions

104 hours independent study

2 hours unseen examination

104 hours independent study

2 hours unseen examination

None.

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.

Analysis Assignment

An assignment comprising approximately 5 questions design to examine students' progress towards the ILOs concerning analysis. Solutions will be uploaded to the KLE. Students should expect to spend 10 hours on the assessment.

2-hour unseen 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 closed book.