Mathematics MMath

Compulsory

• MA1632 - Calculus 1
  This module aims to familiarise students with the basic results, techniques and elementary functions of differential and integral calculus, to introduce students to rigorous definitions, arguments and proofs through many simple examples, to develop students’ manipulative skills in performing operations in differential calculus through work on many simple examples, and to illustrate the solution techniques of first order differential equations.
• MA1633 - Calculus 2

  Aims to further develop skills in differential and integral calculus and associated applications. To further develop students’ manipulative skills in performing operations in differential calculus through work on examples, including solution techniques of ordinary differential equations.

• MA1634 - Elements of Applied Mathematics 1
  The first of a sequence of blocks aimed at developing modelling skills. The main aim of this module is for students to develop a facility for mathematical modelling by examining a problem in its original form, extracting the principal features, formulating and solving appropriate mathematical models, and interpreting the results in terms of the original problems.
• MA1635 - Elements of Applied Mathematics 2

  Second of a pair of modules developing modelling skills. Furthering a facility for mathematical modelling by examining a problem in its original form, extracting the principal features, formulating and solving appropriate mathematical models and interpreting the results in terms of the original problems.

• MA1630 - Fundamentals of Mathematics

  Aims to manipulate mathematical expressions accurately, as well as recall and use mathematical formulae in areas of interest for Year 1. To develop skills in handling summation notation. To introduce students to fundamental results in mathematics. To develop an understanding of the need for rigour in definitions and proofs. To introduce the language of formal mathematics, in particular sets and functions.

• MA1631 - Linear Algebra
  This module aims to enable students to understand and become proficient in basic linear algebra and the algebra of complex numbers, to determine the eigenvalues and eigenvectors of matrices and understand their role in the theory of similar matrices and diagonalization, and to see and practice applications of linear algebra.
• MA1636 - Probability and Statistics 1

  Aims to introduce key notions of mathematical probability and develop techniques for calculating with probabilities and expectations: to lay the foundation of subsequent modules in probability and statistics. To obtain a solid grounding in some applications of probability and elementary statistical concepts, with applications. To develop skills in extracting meaning from data, presenting data graphically and summarising results in writing.

Compulsory

• MA2619 - Applied Statistics

  Aims to introduce and consolidate the notions of single and multivariable probability. Introduce statistical tools and explain their use in extracting and/or inferring meaning from data. To introduce sampling and inference, along with confidence intervals and hypothesis tests.

• MA2618 - Calculus 3

  Aims to develop ideas and methods of multivariable calculus, including Taylor series, extrema, the use of Lagrange multipliers, and the integration of functions of several variables. To understand the extension from single variable to several variables of basic concepts such as continuity and differentiability.

• MA2621 - Discrete Mathematics

  Graphs serve as a background for many important problems in real world applications. This gives an understanding of this area of discrete mathematics, and develops a knowledge of graph theory applications. Also, to introduce operational research optimisation modelling and problem solving and, in particular, linear programming (LP) problems. To introduce algorithms for numerical optimisation and the modelling of random events.

• MA2616 - Linear and Abstract Algebra

  Aims to enlarge the set of technical tools of linear algebra and develop its applications to different problems, including construction and analysis of linear models. To introduce basic algebraic structures, concentrating on group theory. To exemplify their power, relevance and importance in real life applications.

• MA2633 - Machine Learning for Artificial Intelligence

  This moduke introduces basic foundational principles of machine learning with mathematical underpinning and software incarnations. To explore the role of Machine Learning (ML) in Artificial Intelligence (AI) and the ethical issues around data and AI. To illustrate the distinctions between regression and classification, between supervised and unsupervised learning, and, between the training, validation and test data sets. To outline the notions of cost and loss, of decision boundaries, and of the bootstrap technique. To work with data, and to illustrate the implementation of a prediction machine based on a clustering or ‘neighbours’ analysis, and to report on that effort.

• MA2615 - Probability and Statistics 2

  Aims to further develop skills in continuous and multivariate probability. To impart an understanding of statistical concepts and applications. To develop skills in extracting meaning from data, using software, and presenting results. To develop the concepts of confidence intervals and hypothesis tests. To apply these concepts in a variety of situations and to interpret the results of these procedures.

• MA2620 - Professional Development and Project Work

  Aims to develop skills required for planning and obtaining employment, whether it is an internship, a placement or a graduate job, in a field related to the student degree programme. To see the development of these skills as a continuing, managed, lifelong process. To apply techniques, methods, algorithms and/or theories to an applied problem cognate to your degree studies.

Compulsory

• MA3621 - Complex Variable Methods and Applications
  This module aims to develop the students' ability to manipulate expressions involving complex quantities and to develop their understanding of analytic functions with representations involving contour integrals and series, and to enable students to evaluate certain definite integrals using contour integration.
• MA3611 - Final Year Project
  This module aims to stimulate independent learning and critical thinking by the student, both as a means for studying their chosen topic and for approaching other real-life problems, to enable the student to plan and execute a major piece of work with limited input from a more experienced worker, and to give the student experience in the written communication of complex ideas and concepts and the presentation of a substantial piece of work.
• MA3620 - Ordinary and Partial Differential Equations
  This module aims to introduce students to the mathematics of differential equations; techniques of analysing such equations, and methods of solving them, exactly or approximately.

Optional

• MA3622 - Practical Machine Learning

  The aim of this module is to develop practical skills in applying selected machine learning techniques to real-world data analytics problems. Focus is placed on artificial neural networks, deep learning, support vector machines and hidden markov models. 

• MA3623 - Experimental Design and Regression Analysis

  To give students an understanding of the principles of the statistical design of experiments through the study of particular design, of sampling theory for finite populations. To develop the student’s knowledge and understanding of the theory and applying this theory to experimental data arising in a wide range of situations, including designed experiments, where factor effects and/or explanatory variables are present. To give students an understanding of, and an ability to use, linear models with random effects and to develop their skills in the analysis and interpretation of the data. 

• MA3624 - Stochastic Models
  This module aims to introduce students to the concept of a stochastic process, so that they may develop an understanding of the theory underlying some of the standard models and acquire knowledge of methods of applying these models to solve problems. Students will further develop their general ability to think abstractly, to generalise, to formulate and structure stochastic problems, and to apply their knowledge of analytical and numerical mathematical techniques to solving a variety of problems in stochastic modelling.
• MA3625 - Mathematical Finance
  This module aims to introduce the students to the main aspects of modern mathematical finance, in particular to the Black-Scholes-Merton theory of option pricing, the ideas of arbitrage pricing, replication and dynamic hedging. It aims to illustrate the necessary ideas from continuous time stochastic process theory by using discrete time models to, in particular, outline the concept of a lognormal random walk.
• MA3627 - Data Mining and AI for Big Data Analytics

  The aim of this module is to develop the reflective and practical understanding necessary to extract value and insight from large heterogeneous data sets. Focus is placed on the analytic methods/techniques/algorithms for generating value and insight from the (real-time) processing of heterogeneous data. Content will cover approaches to data mining alongside machine learning techniques, such as clustering, regression, support vector machines, boosting, decision trees and neural networks.

• MA3628 - Applied Optimisation

  To introduce students to advanced modelling techniques in linear and integer programming (LP/IP) and their investigation using an industrial software package. To introduce students to the concepts of optimum allocation of financial resources under uncertainty. To familiarise the students with the basic issues of financial planning and with the models that provide mathematical descriptions of these investment problems. To introduce financial risk measures and illustrate how they can be incorporated in financial planning models. 

Compulsory

• MA5691 - Advanced Project

  The project will last for two terms. The students have to demonstrate that they are capable of developing a topic in advanced mathematics compatible with Level 5. The advanced major project will favour theoretical depth over quantity of work. Student will have to take charge from the beginning, working mostly independently, using the literature and some advice from their supervisor.

• MA5640 - Research Methods and Case Studies

  The aims of this module are to develop students’ knowledge and critical awareness of a variety of research methods, to encourage students to develop critical thinking skills and transferable skills appropriate to their discipline, to enable students to develop an understanding of the current needs of industry and commerce, and to prepare students for their dissertation. 

Optional

• MA5643 - Advanced Computational Statistics for Data Analytics

  This module aims to introduce the students to a range of computational intensive statistical methods, to further develop their skills in correct interpretation and clear reporting of results, and to enable the students to create algorithms for regression models (parametric regression and nonparametric regression) to cope with massive data. 

• MA5619 - Advanced Mathematical Methods
  This module aims to further the knowledge and understanding of students in mathematical methods that are of interest at Level 5. The main topics will be asymptotic methods and their applications. Those techniques are used in many areas of mathematics of interest at Level 5. Students will also become capable of using computer algebra to carry out some of those calculations.
• MA5661 - Dynamical Systems and ODEs
  This module aims to demonstrate a good understanding of the qualitative approach to differential equations and apply the concepts of phase portraits, flows and fixed points in the context of continuous dynamical systems, to demonstrate a good understanding of the concepts of bifurcation theory and chaos, with applications to realistic systems, and to construct and analyse mathematical models of practical importance.
• MA5663 - Fundamentals of Machine Learning
  This module aims to equip students with the knowledge and ability to use modern regression and classification methods with different types of data, to enable students to apply a range of models and tools to variable selection and model selection.
• MA5664 - Mathematical Biology
  This module aims to discuss the application of mathematics to various biological problems, and to deepen the knowledge and understanding of the mathematical theories associated with difference equations and ordinary and partial differential equations.
• MA5614 - Probability and Stochastics
  This module aims to equip students with the basic measure-theoretic and probabilistic concepts and techniques needed for them to be able to apply the modern mathematical theory of finance, and to enable students to use methods of stochastic calculus based on Brownian motion in such a way that they are able to carry out the necessary mathematical manipulations and calculations required for use and critical assessment of the various financial models introduced in other modules of the programme.
• MA5672 - Random Matrix Theory
  This module aims to master the basic concepts of the modern Random Matrix Theory (RMT).
• MA5646 - Time Series Forecasting and Risk Modelling
  This module aims to equip students with the ability to employ different methods for modelling and forecasting time series data, in particular in the context of financial data and forecasting financial risk, and to enable students to apply a range of models and tools to make financial decisions such as risk assessment.
• MA5620 - Topics in Combinatorics
  This module explores use of generating functions in combinatorics. Generating functions are a bridge between discrete mathematics on the one hand, and continuous analysis and complex variable theory on the other.