Mathematics MMath

Compulsory

• 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.

• Calculus 1

  Aims to familiarise students with the basic results, techniques and elementary functions of differential and integral calculus as well as some simple applications. 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, including solution techniques of first order differential equations

• 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.

• 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.

• Elements of Applied Mathematics 1

  First of a pair of modules developing modelling skills. 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. Problems will be chosen from a wide range of applications.

• Linear Algebra

  Aims to develop understanding and technical skills in linear algebra with a particular focus on systems of linear equations, vector and matrix algebra, eigenvalues and eigenvectors of matrices, and diagonalization.vStudents will practise on large systems of linear equations using software.

• 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

• 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.

• Scientific Computing

  Aims to introduce the need for approximation in mathematics and/or statistics in the context of important pure and/or applied problems that cannot be solved exactly ‘by hand’. To introduce Computer Algebra as a tool for symbolic ‘exact’ computation as well as aid for approximation of otherwise intractable problems. To introduce the concept of simulation and its use in modelling.

• 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.

• 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.

• 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.

• 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.

Optional

• 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.

• Statistical Programming for Data Analytics

  Aims to develop the capacity to use a statistics programming language to perform computational statistics along with a variety of computational statistics methods to tackle mathematical and statistical tasks. In particular, to study some simple mathematical and statistical models, fit these statistical models to real data, make predictions from the models, and report the results.

Compulsory

• 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.
• 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.

Optional

• Encryption and Data Compression
  This module aims to familiarise students with techniques widely used in data encryption and compression, and to study mathematical and algorithmic issues and their implications for encryption and compression in practice.
• Numerical Methods for Differential Equations
  This module aims to introduce numerical methods used to solve problems in financial mathematics, in particular option pricing, and implement them. Most examples treated will be taken from finance, but the module will be suitable for students mostly interested in advanced numerical methods, in particular finite differences algorithms used to approximate solutions of PDEs. The Matlab implementations of the algorithms will be an important part of the module.
• 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.
• 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.
• Practical Machine Learning
• Experimental Design and Regression
• Deep Learning

  Within this module, an in-depth introduction will be provided to the area of learning using deep neural networks. A wide variety of the architectures of deep neural networks and their learning methods will be covered, including convolutional networks, recurrent networks, generative models and deep reinforcement learning etc. The main focus of the module is to develop students’ skill in analysing of problem requirements, applying appropriate deep learning methods to real-world problems, and evaluating the effectiveness of the adopted approach.

• Decision Making in the Face of Risk

Compulsory

• 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.
• Computer Intensive Statistical Methods
  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.
• Quantitative Data Analysis
  The aim of this module is to develop knowledge and skills of the quantitative data analysis methods that underpin data science. Content covers a practical understanding of core methods in data science application and research, such as bivariate and multivariate methods, regression and graphical models. A focus is also placed on learning to evaluate the strengths and weaknesses of methods alongside an understanding of how and when to use or combine methods.

Optional

• 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.
• Time Series 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.
• Option Pricing Theory
  This module aims to equip students with the notion of risk-neutral valuation and the relation between physical and risk-neutral probability measures in the Brownian context, and to enable students to price vanilla options and basic barrier options in the geometric Brownian motion model.
• Interest Rate Theory
  The purpose of this module is to equip students with a basic familiarity of fixed-income securities markets and, in particular, with the structures of key financial products traded in such markets. It aims to enable students to value derivatives in a number of basic models for interest rates and discount bonds.
• 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.