BSc (Hons) — 2025 entry Mathematics with Data Science

Analysis is the branch of mathematics that rigorously studies functions, continuity, differentiability and integration. This module builds on Level 4 Real Analysis 1 (MAT1032) by studying these concepts in a more formal way and hence provides a deeper understanding of these concepts.

Statistics is the science of collecting and analysing data from random events and modelling them using random variables. This module first recaps the properties of a single random variable as seen in Level 4 Probability and Statistics (MAT1033), then builds on this by considering multiple random variables simultaneously. This module also covers the transformation of random variables, as well as applications such as tail probabilities and limit theorems. 

The module provides an introduction to the theory and properties of curves and surfaces in Euclidean space. Basic concepts and tools from a branch of mathematics known as differential geometry are used to study curves and surfaces, and to understand their geometric properties. This module builds on material from MAT1043 Multivariable Calculus and MAT1034 Linear Algebra. The module is recommended for students intending to select the Year 3 modules MAT3009 Manifolds and Topology, and MAT3044 Riemannian Geometry, although it is not a pre-requisite for either module.

This module is an introduction to the theory of complex functions of a complex variable, also known as complex analysis. We will study the continuity and differentiability of complex functions, integration along paths on the complex plane, Taylor and Laurent series expansions of complex functions with isolated singularities, and residue calculus and its applications. Complex analysis and residue calculus are widely used in many branches of Mathematics and Physics. This module builds on material on two-variable calculus introduced in MAT1043 Multivariable Calculus.    

The Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. The classical linear PDEs such as the heat, wave and Laplace equation will be analyzed in detail. Questions of existence and uniqueness of solutions will be addressed and their physical and mathematical meaning emphasized.

This module provides an introduction to abstract algebra, focusing on the theory of algebraic structures called groups and rings. The module builds on preliminary material on groups introduced in MAT1031 Algebra. This module forms the starting point for subsequent algebraic modules, such as MAT3032 Advanced Algebra, MATM035 Representation Theory and MATM011 Lie Algebras.

This module introduces students to inviscid fluid flows including surface waves. By the end of the module, students should be able to recognise dominant features of fluid motion, and to derive some simple solutions of the equations of motion. Students should also have an appreciation of the force balances that produce various classes of flows.

The module introduces the subject of (infinite dimensional) function spaces and shows how they are structured by metric, norm or inner product. The course naturally extends ideas contained in Real Analysis 1 and 2, and it sets in a wider context the orthogonal decompositions seen in the Fourier analysis part of MAT2011: Linear PDEs.

This module introduces fundamental concepts in analytical dynamics and illustrates their application to real-world problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and symplectic manifolds. The module also leads to a deeper understanding of the role of symmetries and conservation laws in dynamical systems. This module builds on material from MAT1036 Classical Dynamics and lays the foundations for MAT3039 Quantum Mechanics.

This module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity and connectedness. After introducing these key ideas, with appropriate examples, smooth manifolds are introduced. Differential forms and cohomology are developed, which enables the classification of manifolds using topologically invariant numbers. MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.

Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give an oral presentation on their work.

This module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced. This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras

This module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.

Motivated by problems in meteorology and oceanography, this module applies a range of mathematical techniques to the characteristion of fluid flows. Geometry, vector calculus, differential equations, symmetry, dynamical systems theory, and analysis are all combined with fluid motion to produce a deeper understanding of atmosphere and ocean dynamics.

Understanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.

The first half of this module covers various applications of statistical physics to model share prices and financial markets. This mathematics is then applied to calculating prices for some examples of financial derivatives. The second half of the module then focusses on optimization problems with examples including logistics, aerospace, traffic control and finance (which includes pricing, risk managements and portfolio optimizations in financial markets). There is a particular focus on the role of quantum optimization and the use of quantum computer algorithms in finance.

Partial differential equations (PDEs) are used to model many physical, engineering and biological processes.  Some of these systems exhibit exact analytical solutions, but in the majority of cases the PDEs cannot be solved by hand. In these cases we need to utilize computational techniques to form approximate solutions to these PDEs in order to allow understanding and interpretation of the PDE’s behaviour.

Fundamental topics in the design and analysis of experiments are introduced in this module. For a variety of statistical models, the structure of the model and applications are covered. Particular attention is given to practical issues. Statistical software is used to ensure that the emphasis is on methodological considerations rather than on calculation.   There are no pre-requisites for the module but students who have not taken MAT2002 General Linear Models will need to do some initial reading.

Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies, and give an oral presentation on their work.   

This module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.

This module introduces the ideas of viscous fluid flows which build on the ideas some students would have seen in MAT2050: Inviscid Fluid Dynamics. By the end of the module, students should be familiar with the Navier-Stokes equations, and should be able to solve these equations in various simplified situations as well as in a variety of geometries.

Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.

Riemannian geometry is the study of geometric properties of spaces, called manifolds, typically in higher dimensions, which are described smoothly by sets of well-defined co-ordinates. The emphasis is on how mathematically to understand the notion of distance via a metric on such spaces, and how this is used to investigate key associated geometric concepts. Students are introduced to the key concepts of manifolds and metrics, with illustrative examples such as spheres, hyperbolic spaces and Lie groups. The module continues with geodesics, isometries, covariant derivatives, the Levi Civita connection, and concludes with curvature and its properties. Modules in Curves and Surfaces and in Manifolds and Topology contain related material.

This module introduces the topic of Game Theory and various mathematical techniques used in the analysis of games. Classic examples of games are introduced including those with application in economics and biology. The theoretical backbone is a combination of Calculus, Linear Algebra, Ordinary Differential Equations and, in the case of mixed strategies for games, Probability.

Data science is the study of data to extract meaningful and actionable insights at all levels of society such as dynamical systems and social media networks. This module introduces the role of data in society and provides students with the underpinning mathematics that drives data methodology and algorithms. This module then covers wide-ranging topics with a focus on the Surrey brand of data, as research into data is part of the department research agenda. 

Time series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.

The module will introduce students to key concepts in education as well as the tools and strategies for effective public engagement in their discipline areas and for different audiences. Students will gain practical experience by planning, implementing, and evaluating an education or public engagement-based activity. Opportunities will also exist for classroom (e.g. school; early-year University) teaching experience and / or involvement in external exhibitions. The projects will be related to current Faculty, department and / or outreach needs thus leading to informed student partnership activities.

Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give oral presentations on their work.

Analysis is the branch of mathematics that rigorously studies functions, continuity, differentiability and integration. This module builds on Level 4 Real Analysis 1 (MAT1032) by studying these concepts in a more formal way and hence provides a deeper understanding of these concepts.

Statistics is the science of collecting and analysing data from random events and modelling them using random variables. This module first recaps the properties of a single random variable as seen in Level 4 Probability and Statistics (MAT1033), then builds on this by considering multiple random variables simultaneously. This module also covers the transformation of random variables, as well as applications such as tail probabilities and limit theorems. 

The module provides an introduction to the theory and properties of curves and surfaces in Euclidean space. Basic concepts and tools from a branch of mathematics known as differential geometry are used to study curves and surfaces, and to understand their geometric properties. This module builds on material from MAT1043 Multivariable Calculus and MAT1034 Linear Algebra. The module is recommended for students intending to select the Year 3 modules MAT3009 Manifolds and Topology, and MAT3044 Riemannian Geometry, although it is not a pre-requisite for either module.

This module is an introduction to the theory of complex functions of a complex variable, also known as complex analysis. We will study the continuity and differentiability of complex functions, integration along paths on the complex plane, Taylor and Laurent series expansions of complex functions with isolated singularities, and residue calculus and its applications. Complex analysis and residue calculus are widely used in many branches of Mathematics and Physics. This module builds on material on two-variable calculus introduced in MAT1043 Multivariable Calculus.    

The Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. The classical linear PDEs such as the heat, wave and Laplace equation will be analyzed in detail. Questions of existence and uniqueness of solutions will be addressed and their physical and mathematical meaning emphasized.

This module provides an introduction to abstract algebra, focusing on the theory of algebraic structures called groups and rings. The module builds on preliminary material on groups introduced in MAT1031 Algebra. This module forms the starting point for subsequent algebraic modules, such as MAT3032 Advanced Algebra, MATM035 Representation Theory and MATM011 Lie Algebras.

This module introduces students to inviscid fluid flows including surface waves. By the end of the module, students should be able to recognise dominant features of fluid motion, and to derive some simple solutions of the equations of motion. Students should also have an appreciation of the force balances that produce various classes of flows.

The module introduces the subject of (infinite dimensional) function spaces and shows how they are structured by metric, norm or inner product. The course naturally extends ideas contained in Real Analysis 1 and 2, and it sets in a wider context the orthogonal decompositions seen in the Fourier analysis part of MAT2011: Linear PDEs.

This module introduces fundamental concepts in analytical dynamics and illustrates their application to real-world problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and symplectic manifolds. The module also leads to a deeper understanding of the role of symmetries and conservation laws in dynamical systems. This module builds on material from MAT1036 Classical Dynamics and lays the foundations for MAT3039 Quantum Mechanics.

This module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity and connectedness. After introducing these key ideas, with appropriate examples, smooth manifolds are introduced. Differential forms and cohomology are developed, which enables the classification of manifolds using topologically invariant numbers. MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.

Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give an oral presentation on their work.

This module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced. This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras

This module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.

Motivated by problems in meteorology and oceanography, this module applies a range of mathematical techniques to the characteristion of fluid flows. Geometry, vector calculus, differential equations, symmetry, dynamical systems theory, and analysis are all combined with fluid motion to produce a deeper understanding of atmosphere and ocean dynamics.

Understanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.

The first half of this module covers various applications of statistical physics to model share prices and financial markets. This mathematics is then applied to calculating prices for some examples of financial derivatives. The second half of the module then focusses on optimization problems with examples including logistics, aerospace, traffic control and finance (which includes pricing, risk managements and portfolio optimizations in financial markets). There is a particular focus on the role of quantum optimization and the use of quantum computer algorithms in finance.

Partial differential equations (PDEs) are used to model many physical, engineering and biological processes.  Some of these systems exhibit exact analytical solutions, but in the majority of cases the PDEs cannot be solved by hand. In these cases we need to utilize computational techniques to form approximate solutions to these PDEs in order to allow understanding and interpretation of the PDE’s behaviour.

Fundamental topics in the design and analysis of experiments are introduced in this module. For a variety of statistical models, the structure of the model and applications are covered. Particular attention is given to practical issues. Statistical software is used to ensure that the emphasis is on methodological considerations rather than on calculation.   There are no pre-requisites for the module but students who have not taken MAT2002 General Linear Models will need to do some initial reading.

Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies, and give an oral presentation on their work.   

This module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.

This module introduces the ideas of viscous fluid flows which build on the ideas some students would have seen in MAT2050: Inviscid Fluid Dynamics. By the end of the module, students should be familiar with the Navier-Stokes equations, and should be able to solve these equations in various simplified situations as well as in a variety of geometries.

Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.

Riemannian geometry is the study of geometric properties of spaces, called manifolds, typically in higher dimensions, which are described smoothly by sets of well-defined co-ordinates. The emphasis is on how mathematically to understand the notion of distance via a metric on such spaces, and how this is used to investigate key associated geometric concepts. Students are introduced to the key concepts of manifolds and metrics, with illustrative examples such as spheres, hyperbolic spaces and Lie groups. The module continues with geodesics, isometries, covariant derivatives, the Levi Civita connection, and concludes with curvature and its properties. Modules in Curves and Surfaces and in Manifolds and Topology contain related material.

This module introduces the topic of Game Theory and various mathematical techniques used in the analysis of games. Classic examples of games are introduced including those with application in economics and biology. The theoretical backbone is a combination of Calculus, Linear Algebra, Ordinary Differential Equations and, in the case of mixed strategies for games, Probability.

Data science is the study of data to extract meaningful and actionable insights at all levels of society such as dynamical systems and social media networks. This module introduces the role of data in society and provides students with the underpinning mathematics that drives data methodology and algorithms. This module then covers wide-ranging topics with a focus on the Surrey brand of data, as research into data is part of the department research agenda. 

Time series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.

The module will introduce students to key concepts in education as well as the tools and strategies for effective public engagement in their discipline areas and for different audiences. Students will gain practical experience by planning, implementing, and evaluating an education or public engagement-based activity. Opportunities will also exist for classroom (e.g. school; early-year University) teaching experience and / or involvement in external exhibitions. The projects will be related to current Faculty, department and / or outreach needs thus leading to informed student partnership activities.

Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give oral presentations on their work.