Module: Mathematical Methods/Computational Science

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Mathematical Methods/Computational Science
Module Code	CA659 (ITS) / CSC1139 (Banner)
Faculty	Engineering & Computing	School	Computing
Module Co-ordinator	Martin Crane
Module Teachers	-
NFQ level	9	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination
Array

Description

ACTIVE

Learning Outcomes

1. Recognise the different types of Time Series Models and decompose such a series into parts such as Trend, Seasonality and Residual Components
2. Apply ARMA/ ARIMA/ SARIMA models to study suitable choice of coefficients and build ARMA/ ARIMA/ SARIMA models for given datasets
3. Perform basic forecasting using time series models, recognising the limits of these forecasts
4. Assess the advantages and disadvantages of various different types of models for real world problems.
5. Translate real world problem specifications into well-formed mathematical equations.
6. Apply difference and differential equation models to study the stability of real-world systems.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	36	Face-to-Face delivery of material
Tutorial	12	Peer-assisted learning
Directed learning	3	End of Year Recap
Independent Study	48	No Description
Online activity	41	Online recorded lectures as preparation for lectures.
Independent Study	48	Working through Example sheets
Total Workload: 188

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Introduction to Time Series Analysis
- Understand the different types of Time Series Models and decompose a such a series into parts such as Trend, Seasonality and Residual Components - Examine ARMA/ ARIMA models to study suitable choice of coefficients and build ARMA/ ARIMA models for given datasets - Perform basic forecasting using time series models, recognising the limits of these forecasts

Introduction to Discrete Models of Growth and Decay
- Revision of Underpinning Linear Algebra (eigenvalues, eigenvectors and meaning in this area, Stability in Difference Equations) - Simple and Higher-Order Linear Difference Equations - Applications (Fibonacci Series, Leslie Matrices) - Non-linear Growth Models (logistic growth with additions, stability) - Applications of Non-linear Models

Introduction to Continuous Models
- More Mathematical Underpinning - Differential Equations and their Simplification by Non-dimensionalisation, - Stability in Continous models (Jacobians, steady states, Routh-Hurwitz conditions etc) - Linear and Non-Linear continuous models comparing and contrasting with discrete models

Linear and Non-Linear Models of Interaction
- Linear Compartmental Models with examples - Non-Linear: - More Mathematical Underpinning: Phase-Plane Plots - Destructive to one party: Predator-Prey (RH conditions, phase plane analysis) - Mutually Beneficial: Symbiosis (RH conditions, phase plane analysis) - Mutually Destructive: Lanchester models of Guerrilla combat (RH conditions, phase plane analysis) - More models of interaction: SIR, SIRS models of disease (RH conditions, phase plane analysis)

Assessment Breakdown
Continuous Assessment	0%	Examination Weight	100%

Type	Description	% of total	Assessment Date
Course Work Breakdown

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 1

Indicative Reading List

Rob J Hyndman,George Athanasopoulos: 2018, Forecasting: principles and practice, 2, OTexts, 0987507117
Nicholas F. Britton: 2003, Essential Mathematical Biology, Springer Undergraduate Mathematics Series, 978-1852335366
Fulford, Forrester and Jones: 1997, Modelling with Differential and Difference Equations, Cambridge University Press, 052144618X

Other Resources

None

Updated learning outcomes