MMath Mathematics with a Placement Year

Compulsory modules

Real Analysis I

Explore mathematical analysis concepts including inequalities, sequences, series and functions.

Calculus

Extend your existing knowledge of calculus into two or more dimensions, exploring techniques of ordinary differential equations of the first and second order and learning how programming has mathematical applications.

Foundations of Mathematics 

Gain a solid introduction to fundamental topics in mathematics and develop the necessary skills to study mathematics at university-level. You’ll focus on the concept of sets, functions and various familiar number systems, as well as the importance of proofs and how to construct them.

Linear Algebra 

Learn how to solve systems of linear equations, determine eigenvalues and eigenvectors, and develop the algebra of matrices which are used as a stepping-stone to the more general theory of liner and inner-product spaces.

Mathematical Communication

Discover the importance of expressing mathematical concepts and results clearly, logically and concisely and how to implement basic problem-solving strategies such as data visualisation, pattern exploration and programming.

Probability and Statistics 

Understand probability and probability distributions, results and techniques for statistical reference and data science, and regression and hypothesis testing. 

These are the modules we currently offer for 2024/25 entry. They may be subject to change as we regularly review our module offerings to ensure they're informed by the latest teaching and research methods.

Please note that the University cannot guarantee that all optional modules will be available to all students who may wish to take them.

You can also register your details with us to receive information about your course of interest and study and life at the University of Reading.

Compulsory modules

Differential Equations 

Build on your knowledge of ordinary differential equations and explore partial differential equations and their applications. You’ll explore non-constant coefficients, integral and series solutions, Fourier series, the theory of boundary value problems, diffusion equations, wave equations and Laplace’s equation.

Algebra 

Understand the concepts of abstract algebra, including groups, rings and fields and the connections between them.

Mathematical Modelling and Professional Skills

Develop your problem-solving and independent research skills by applying mathematical modelling techniques to solve real-world problems across a broad range of scientific, engineering and economical areas. You’ll also expand your team-working, presentation, career management, technical, verbal and written communication skills.

Optional modules

Real Analysis II

Expand your understanding analysis to cover continuity of functions, integration and differentiation.

Mathematical Methods and Physical Applications 

Discover how vector calculus and variational principles are applied to various areas of physics, such as classical mechanics, elements of electromagnetism and diffusion.

Numerical Analysis I

Describe, analyse and implement numerical methods for problems in continuous mathematics, including solution of linear equations and nonlinear scalar equations, interpolation, scalar optimisation and solution of ordinary differential equations.

Linear Models and Data Analysis 

Gain understanding of the most common models, including multiple linear regression and completely randomised designs, and explore the key principles of planned experiments. Learn how models are applied to practical problems and gain experience of real-life data analysis.

Probability and Statistical Theory

Uncover the interplay between probability theory and fundamental areas of mathematics, and formulate general real or abstract problems in a probabilistic model.

These are the modules we currently offer for 2024/25 entry. They may be subject to change as we regularly review our module offerings to ensure they're informed by the latest teaching and research methods.

Please note that the University cannot guarantee that all optional modules will be available to all students who may wish to take them.

You can also register your details with us to receive information about your course of interest and study and life at the University of Reading.

Placement Year

Compulsory modules

Portfolio of Projects

Conduct a series of projects on mathematical or statistical topics and develop your technical and professional skills.

Optional modules

Complex Analysis

Gain an introduction to complex analysis and how its functions can be represented, exploring aspects such as power series, exponential functions, trigonometric functions and hyperbolic functions. 

Metric Spaces and Functional Analysis 

Study analysis from a more general perspective based on the concepts of distance, including Normed, metric spaces, the concepts of convergence, continuity, compactness and completeness.

Number Theory and Cryptography

Explore a range of topics within number theory and cryptography, including the RSA cryptosystem and error correcting codes.

Probability and Measures

Explore measure theory, integration and measure theoretic probability.

Asymptotic Methods

Discover the basic ideas of asymptotic analysis and further develop your skills in solving a range of problems involving nonlinear equations, integrals and differential equations.

Applied Stochastic Processes

Learn how to solve problems using stochastic processes and concepts from a variety of applications, including molecular motion, population dynamics, weather and finances.

Dynamical Systems and Applications 

Analyse dynamical systems and their applications to real-world problems. You’ll explore systems of linear and nonlinear differential equations, and understand how they’re applied to biological issues such as population growth, cell systems, and the spread of infectious diseases.

Partial Differential Equations and Applications 

Examine partial differential equations and how they appear in practical applications and natural phenomena, in particular fluid mechanics, water waves and wave scattering theory.

Mathematical Physics 

Explore the core topics of mathematical physics, in particular Hamiltonian formulation of classical mechanics, quantum mechanics and statistical mechanics.

Numerical Analysis II

Motivate, develop and analyse a range of algorithms for the approximate solution of problems of continuous mathematics and techniques in numerical linear algebra.

Advanced Statistical Modelling

Develop an understanding of situations in which different models are likely to be appropriate, learning more about generalised linear models, repeated measurement data, and traditional and modern approaches to data analysis.

Methods of Machine Learning

Gain familiarity with the range of methods used in statistical machine learning and demonstrate how these are used in research and industry. You’ll have the opportunity to implement machine learning methods using statistical software and interpret and communicate your findings.

Summer Placement

Gain experience applying for, and completing, a summer work placement or internship with an employer.

Peer Assisted Learning

Gain a deeper understanding of your own learning and that of your peers through a series of weekly sessions. You’ll develop your coaching, organisational, presentation and communication skills by leading peer study groups and can be excellent experience if you’re considering postgraduate teacher training.

These are the modules we currently offer for 2024/25 entry. They may be subject to change as we regularly review our module offerings to ensure they're informed by the latest teaching and research methods.

Please note that the University cannot guarantee that all optional modules will be available to all students who may wish to take them.

You can also register your details with us to receive information about your course of interest and study and life at the University of Reading.

Compulsory modules

Part 4 Project

Develop an independent project in an area of mathematics of your choice, and present your findings in the form of a presentation or dissertation.

Optional modules

The selection of modules available to you in Year 5 will be influenced by the modules you choose to study in Year 4 as you will not repeat topics. The modules you'll study in Year 5 are master's-level and are designed to build on your knowledge and skills, enabling you to develop a deeper perspective on mathematics content.

Complex Analysis

Gain an introduction to complex analysis and how its functions can be represented, exploring aspects such as power series, exponential functions, trigonometric functions and hyperbolic functions. 

Number Theory and Cryptography

Explore a range of topics within number theory and cryptography, including the RSA cryptosystem and error correcting codes.

Probability and Measures

Explore measure theory, integration and measure theoretic probability.

Asymptotic Methods

Discover the basic ideas of asymptotic analysis and further develop your skills in solving a range of problems involving nonlinear equations, integrals and differential equations.

Applied Stochastic Processes

Learn how to solve problems using stochastic processes and concepts from a variety of applications, including molecular motion, population dynamics, weather and finances.

Dynamical Systems and Applications 

Analyse dynamical systems and their applications to real-world problems. You’ll explore systems of linear and nonlinear differential equations, and understand how they’re applied to biological issues such as population growth, cell systems, and the spread of infectious diseases.

Partial Differential Equations and Applications 

Examine partial differential equations and how they appear in practical applications and natural phenomena, in particular fluid mechanics, water waves and wave scattering theory.

Mathematical Physics 

Explore the core topics of mathematical physics, in particular Hamiltonian formulation of classical mechanics, quantum mechanics and statistical mechanics.

Numerical Analysis II

Motivate, develop and analyse a range of algorithms for the approximate solution of problems of continuous mathematics and techniques in numerical linear algebra.

Methods of Machine Learning

Gain familiarity with the range of methods used in statistical machine learning and demonstrate how these are used in research and industry. You’ll have the opportunity to implement machine learning methods using statistical software and interpret and communicate your findings.

These are the modules we currently offer for 2024/25 entry. They may be subject to change as we regularly review our module offerings to ensure they're informed by the latest teaching and research methods.

Please note that the University cannot guarantee that all optional modules will be available to all students who may wish to take them.

You can also register your details with us to receive information about your course of interest and study and life at the University of Reading.