Mathematics Module Details

First yearSecond yearThird year

First year

Linear Algebra I 
Introduces fundamental algebraic providing core knowledge of linear algebra including matrices and systems of linear equations.

Linear Algebra II 
Introduces basic discrete mathematics with reference to systems of linear equations, vector algebra and complex numbers.

Calculus I 
Introduces the theoretical foundations of Calculus and Mathematical Analysis, including mathematical proof. 

Calculus II 
Further develops elements of Calculus and Mathematical Analysis that can be used to solve real-world problems. The emphasis of this module is on differentiation and integration; practical examples being used to illustrate the utility of the theory.

Statistics I 
Introduces core statistical techniques for data collection,  summary and presentation, and statistical inference including regression and parametric techniques. In the module students will write a statistical report, work in a team and use industry standard software, e.g. Minitab, SAS.

Operational Research I 
Introduces fundamental decision mathematics such as project management techniques (e.g. CPM, PERT) and linear programming. Besides the theory, students will learn how to implement the techniques using appropriate software e.g. Excel. 

Mathematical Modelling with Computers I 
This module provides the students with basic computer science concepts and the implementations of mathematical concepts using computer-aided mathematical modelling.

Mathematical Modelling with Computers II 
Provides the students with an understanding on how computer science relates to mathematics and how mathematical models can be developed, using the algorithms and data structures available in the C++ standard library.

Second year

Applied Mechanics 
The mechanics presented in this module can be split into 3 key areas all concerned with rigid bodies: the simulation of motion, the detection of collisions and the resolution of collisions. Students will be introduced to the mathematical techniques of these models. 

Introduction to CI and Control Systems 
This module introduces the principles of Computational Intelligence and the main techniques applicable to control as well as a variety of real world problems. 

Abstract Algebra I 
In this module a student's knowledge of discrete mathematics and linear algebra is further developed focussing on the abstract algebra approach including algebraic Structures, Group Theory and Vector Spaces.

Abstract Algebra II 
Further advances the student's knowledge of abstract algebra focussing on inner product spaces and linear mapping.

Further Calculus I 
Focuses on multivariate calculus.

Further Calculus II 
Broadens the student's knowledge and understanding focusing on multivariate optimisation and integrability in multidimensional spaces.

Statistics II 
Advances a student's statistical knowledge by focusing on generalised linear models (including factorial design) and multiple regression techniques. Extensive use will be made of industry standard  software, e.g. SAS and the writing of a statistical report.

Operational Research II

Third year

No core modules - students select from a range of optional modules available.

Dissertation 
The final year project provides students with the opportunity to carry out a significant piece of work involving mathematical rigour, critical analysis and reflection to provide an effective solution to a given technical and/or research-based problem. It enables students to apply and integrate previous material covered on the student's course as well as to extend the work covered on the course through research and self-learning. Students will be expected to demonstrate appropriate and proactive project management, and written/verbal presentation skills throughout the period of the project. Their work being assessed by a written dissertation and a verbal presentation and viva.

Data Mining 
Data is collected and stored in all different types of organisations - commercial, governmental, educational. Every day hundreds of terabytes of data are circulated via the Internet. Extraction of meaningful information and hidden patterns from data is critical for many business applications including marketing, fraud, credit risk, etc. Data mining (also known as data analytics or more recently: data science) involves extracting meaningful information and knowledge from vast quantities of data, to help us to make informed decisions. This is a practical module, using industry standard software, e.g. SAS Enterprise Miner, to effectively apply data mining techniques to real-life problems. 

Fuzzy Logic and Knowledge Based Systems 
This module will introduce Fuzzy Logic and explain how to use it in the context of decision making.

Nonlinear Optimisation
This module advances a student's operational research knowledge focussing on Nonlinear Optimisation problems with reference to both analytical and numerical methods for single and multi-objective problems. Use will be made of appropriate industry standard software, e.g. Excel, MATLAB.

Multicriteria Analysis 
Examines the different types of advanced linear programming applications, such as transportation, trans-shipment and assignment problems; revenue management, portfolio models and other asset allocation problems and multicriteria problems. Students will formulate and model the problems mathematically using industry standard software e.g Excel LP Solver and MATLAB.

Non-linear Dynamical Systems 
This module provides the student with knowledge of modern nonlinear dynamical system theory and numerical methods for nonlinear analysis using MATLAB.

Modelling with Ordinary Differential Equations 
In this module students will experience some of the ways in which ordinary differential equations are used by mathematicians, engineers and scientists to model, explain and predict the behaviour of physical and biological systems. This module will draw upon a wide range of applications to demonstrate the modelling processing and solution using differential equations.

Modelling with Partial Differential Equations 
Expands a student's knowledge to partial differential equations, which are used by mathematicians, engineers and scientists to model, explain and predict the behaviour of physical and biological systems. This module will draw upon a wide range of applications to demonstrate the modelling processing and solution using partial differential equations and variational principles.

Statistical Modelling I: Analysis of Time Series Data 
In this module Time series is analysed from two complementary perspectives: the statistical theory and the implementation of the theory using industry standard computer software packages, e.g.) SAS, Minitab.  Taking a practical approach, advanced statistical techniques will be introduced and students will use real problems to analyse time series data, thus building relevant statistical models, which are interpreted, critiqued and used to forecast. Typical assessment will be a presentation and a lab based phase test.

Statistical Modelling II: Analysis of Categorical Data and Multivariate Data 
This module focuses on the theoretical detail and practical application of analysing categorical data and the theoretical detail and practical application of analysing multivariate data. Taking a practical approach, advanced statistical techniques will be introduced and students will use real problems to analyse multivariate and categorical data, thus building relevant statistical models, which are interpreted and critiqued using appropriate industry standard software e.g.) SAS. Typical assessment will be a statistical report.

Rigorous Systems 
For those students interested in more mathematical programming this module looks at formal systems in rigorous software development.

 
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