Mathematics and Statistics MMath (Hons)

Analysis

aims to provide an understanding of real and complex number systems, and to develop rigorously the calculus of functions of a single variable from basic principles.

Calculus

builds on ideas of differentiation and integration in A level mathematics, beginning with functions of a single variable and moving on to functions of several variables. Topics include methods of solving ordinary and partial differential equations, and an introduction to Fourier Series and Fourier transforms.

Dynamics

develops an understanding of elementary classical Newtonian dynamics as well as an ability to formulate and solve basic problems in dynamics.

Linear Algebra

presents mathematical ideas, techniques in linear algebra and develops geometric intuition and familiarity with vector methods in preparation for more demanding material later in the course.

Probability

introduces mathematics ideas on probability in preparation for more specialised material later in the course. The module presents a mathematical subject of key importance to the real-world (applied) that is based on rigorous mathematical foundations (pure).

Programming

is taught via lectures and practical sessions that introduce basic principles and competence in computer programming. You will also study control structures; floating point arithmetic; and lists, strings and introduction to objects.

Statistics

introduces frequentist and Bayesian statistics and demonstrates the relevance of these principles and procedures to real problems. This module lays the foundations for all subsequent study of statistics.

Analysis in Many Variables

provides an understanding of calculus in more than one dimension, together with an understanding of, and facility with, the methods of vector calculus. It also explores the application of these ideas to a range of forms of integration and to solutions of a range of classical partial differential equations.

Data Science and Statistical Computing

equips you with the skills to import, explore, manipulate, model and visualise real data sets using the statistical programming language R. The module introduces the concepts and mathematics behind sampling. It also covers data protection and governance issues when working with data.

Statistical Inference

introduces the main concepts underlying statistical inference and methods. This module develops the foundations underlying classical statistical techniques, and the basis for the Bayesian approach to statistics. You will also investigate and compare frequentist and Bayesian approaches.

Statistical Modelling

provides a working knowledge of the theory, computation and practice of the linear model. You will cover areas including analysis of variance, model selection, diagnostics and transformation methods.

In recent years optional modules have included: AlgebraComplex AnalysisMathematical PhysicsNumerical AnalysisElementary Number TheoryGeometric TopologyMarkov ChainsMathematical ModellingProbabilitySpecial Relativity and Electromagnetism

In recent years optional modules have included: Advanced Statistical ModellingBayesian Computation and ModellingDecision TheoryMachine Learning and Neural NetworksMathematical FinanceStochastic Processes

Internship Project

The gives you the opportunity to conduct a substantial piece of independent statistics and machine learning work in a real-world context working with a third party, and to write up and present this work. This will further your analytical, collaborative and transferable skills, and your knowledge of the practice of statistics and machine learning, as well as advance your abilities in oral or written communication.

Project

In the final year Project you will investigate a statistical topic of interest or perform an in-depth analysis of a data set using the tools acquired earlier in the course. You then produce a written report and give a short presentation. Subject to availability, you may have the opportunity to perform this project in collaboration with an external organisation. The project develops your research and communication skills which are important for future employment or postgraduate studies.

In recent years optional modules have included: Spatio-Temporal StatisticsDeep Learning and Artificial IntelligenceDiscrete and Continuous ProbabilityHigh-Dimensional Data AnalysisNon-Parametric StatisticsObject-Oriented StatisticsRobust Bayesian AnalysisTopics in ProbabilityUncertainty Quantification