- Year 1
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In the first year you’ll study the same modules as students on BSc (Hons) Mathematics. This gives you both the expertise required to be confident in the classroom and also flexibility in your future career choices. Modules include calculus, linear algebra, numerical methods and probability. There is also a module on proof and reasoning that includes more surprising material such as the mathematics of cryptography. You'll also use professional software. The flexibility of the course allows you to change to other mathematics degrees at the end of the first and second years.
Core modules
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BPIE113 Stage 1 Mathematics Placement Preparation
The route to graduate-level employment is found easier with experience. These sessions are designed to assist students in their search for a year-long placement and in their preparation for the placement itself. Such placements are optional but strongly recommended.
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MATH1601 Mathematical Reasoning
This module introduces the basic reasoning skills needed to develop and apply mathematical ideas. Clear logical thinking is central to the understanding of mathematics. The module explores fundamental properties of prime numbers, their random generation and use in modern cryptography.
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MATH1602 Calculus and Analysis
This module covers key topics in calculus and analysis and prepares students for the rest of their degree. It has an emphasis on proof and rigour and introduces some multi-dimensional calculus together with the reasoning skills needed for the development of modern mathematics. Analysis is the rigorous underpinning of calculus and these key ideas are developed and applied to limits of sequences, series and functions.
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MATH1603 Linear Algebra and Complex Numbers
This module explores the concepts and applications of vectors, matrices and complex numbers. The deep connection between algebra and geometry is explored. The techniques that are presented in this module are at the foundation of many areas of mathematics, statistics, physics, and several other applications.
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MATH1605 Probability with Applications
An understanding of uncertainty and random phenomena is becoming increasingly important nowadays in daily life and for a variety of fields. The aim of this module in probability is to develop the concept of chance in a mathematical framework. Random variables are also introduced, with examples involving most of the common distributions and the concepts of expectation and variance of a random variable.
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MATH1610 Numerical and Computational Methods
This module provides an introduction to appropriate mathematical software, computational mathematics and creating simple computer programs. Students will use mathematical software interactively and also write programs in an appropriate computer language. The elementary numerical methods which underlie industrial and scientific applications will be studied.
Optional modules
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MATH1611 Geometry and Group Theory
This module will introduce the foundations of group theory, elementary geometric topology, and Euclidean geometry.
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MATH1612 Big Data Analytics for Finance and Social Media
Vast quantities of data are available from many sources including finance and social media. Students will gain experience of mathematical, statistical and computational tools to understand and report the messages underlying data from sources such as stock market trading and Facebook. They will meet a mathematical model for relative returns, Value at Risk, basic option pricing and high-performance computing techniques.
- Year 2
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In Year 2 you'll study a range of modules from real and complex analysis to differential equations giving you further high level mathematical and statistical skills. You’ll also have the opportunity to work with school children as part of our programme of mathematics enrichment activities, or help first year students through our peer assisted learning scheme.
Core modules
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BPIE213 Stage 2 Mathematics Placement Preparation
These sessions are designed to help students obtain a year-long placement in the third year of their programme. Students are assisted both in their search for a placement and in their preparation for the placement itself.
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MATH2601 Advanced Calculus
In this module the geometrical and dynamical concepts needed to describe higher-dimensional objects are introduced. This includes vector calculus techniques and new forms of integration such as line integration. Students also explore the relations between integration and differentiation in higher dimensional hyperspaces. This knowledge is applied to various real world problems.
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MATH2602 Statistical Inference and Regression
The module provides a mathematical treatment of statistical inference, including confidence intervals and hypothesis testing. Methods of estimation are explored, focusing on maximum likelihood estimation. The module also demonstrates the underlying mathematical theory of the general linear model, through a variety of applications, using professional software.
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MATH2603 Ordinary Differential Equations
The module aims to provide an introduction to different types of ordinary differential equations and the analytical and numerical methods needed to obtain their solutions. Extensive use is made of computational mathematics packages. Applications to mechanical and chemical systems are considered as well as the chaotic behaviour seen in climate models.
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MATH2604 Mathematical Methods and Applications
Vector calculus is extended to higher dimensions and applied to a range of important scientific problems primarily from classical mechanics and cosmology. Differential and integral calculus is applied to the solution of differential equations and the orthogonal functions bases are constructed. The crucial mathematical concepts of integral transforms (Fourier and Laplace) and Fourier series are introduced.
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MATH2605 Operational Research and Monte Carlo Methods
This module gives students the opportunity to work on open-ended case studies in operational research (OR) and Monte Carlo methods, both of which are important methods in, for example, industry and finance. It allows students to work on their own and in teams to develop specific skills in OR and programming as well as refining their presentation and communication skills. The skills in computational simulation developed in this module have many applications.
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MATH2606 Real and Complex Analysis
This module deepens the student’s understanding of real analysis and introduces complex analysis. The important distinction between real and complex analysis is explored and the utility of the complex framework is demonstrated. The central role of power series and their convergence properties are studied in depth. Applications include the evaluation of improper integrals and the construction of harmonic functions.
- Optional placement year
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An optional placement in Year 3 to gain valuable paid professional experience and help make your CV stand out. You will be better able to advise your future students on careers.
Optional modules
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BPIE331 Mathematics and Statistics Placement
A 48-week period of professional training is spent as the third year of a sandwich programme while undertaking an approved placement with a suitable company. This provides an opportunity for the student to gain experience of how mathematics is used in a working environment, to consolidate their previous study and to prepare for the final year and employment after graduation. Recent placement providers include GSK, the Office for National Statistics, NATS (air traffic control) and VW Group.
- Final year
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In the final year you'll carry out a year long placement module offering you experience working alongside a mathematics teacher in a primary or secondary school for one morning a week over two terms. Together with our tutorial system, the school placement will strengthen your oral and written communications skills and greatly enhance your employability. You'll also carry out an individual mathematics education project on a topic of your choice. The placement and project combination gives you an ideal start for PGCE teacher training. The degree also gives you excellent prospects in other mathematical careers through a wide choice of final year modules.
Core modules
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MATH3603 Professional Experience in Mathematics Education
This module provides an opportunity for final year students to gain experience in teaching and to develop their key educational skills by working in a school environment for one morning a week over two semesters.
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MATH3619 Education Project
Students have the opportunity to study an area of mathematics education in a final year project. Students work individually and independently, with help and advice from a supervisor, on the chosen topic. The project is assessed through contributions to group discussions and the preparation of a dissertation.
Optional modules
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MATH3604 Geometry and Algebra
A review of group theory leads into an exploration of plane affine, hyperbolic, and projective geometries, all from the Kleinian point of view. Then an introduction to rings and fields is given with applications in geometry emphasised. These topics are key ideas in the study of pure mathematics.
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MATH3605 Partial Differential Equations
This module introduces partial differential equations using real-life problems. It provides a variety of analytic and numerical methods for their solution. It includes a wide range of applications including heat diffusion and the Tsunami wave.
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MATH3606 Classical and Quantum Mechanics
All of physics and a large part of applied mathematics is based on classical mechanics and its extension to quantum theory. This module introduces key ideas of these topics to students with a mathematics background. An overarching theme is the key role of symmetry, both for classical motion and quantum behaviour.
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MATH3609 Optimisation, Networks and Graphs
This module introduces the mathematics of continuous and discrete optimisation. It provides the theoretical background and practical algorithmic techniques required to model and solve a diverse range of problems.
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MATH3611 Electrodynamics and Relativity
This module introduces Maxwell's theory of electromagnetism and Einstein's theory of special relativity. It includes a wide range of applications of electromagnetism, the Lorentz transformations and some of the apparent paradoxes of relativity together with their resolution. It also explains why E = mc^2.
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MATH3612 Dynamical Systems
This module presents an introduction to the basic concepts and techniques needed to analyse nonlinear dynamical systems modelled by differential equations and difference equations. Both regular and chaotic dynamics are explored.
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MATH3614 Medical Statistics
The content includes the design and analysis of clinical trials, including crossover and sequential designs and an introduction to meta-analysis. Epidemiology is studied, including case-control and cohort studies. Survival analysis is covered in detail. Computer packages are used throughout.
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MATH3623 Financial Statistics
This module introduces students to the concepts and methods of financial time series analysis and modelling and to a variety of financial applications. The module reviews the necessary univariate and multivariate time series models and inferential techniques. Model selection, forecasting and the ‘curse of dimensionality’ problem for high dimensional modelling are treated both analytically and computationally. The R programming language is widely used in this module.
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MATH3629 Fluid Dynamics
Fluid flow problems are at the heart of systems ranging from weather forecasting and climate models to hydroelectricity generation and aerodynamics. They are all formulated mathematically as systems of partial differential equations. These are then solved and the results interpreted for a mixture of theoretical and practical examples of both inviscid and viscous fluid flows. Applications studied include: aeronautics, ocean waves and a variety of industrial topics.
Every undergraduate taught course has a detailed programme specification document describing the course aims, the course structure, the teaching and learning methods, the learning outcomes and the rules of assessment.
The following programme specification represents the latest course structure and may be subject to change:
BSc Mathematics with Education programme specification 1202
The modules shown for this course are those currently being studied by our students, or are proposed new modules. Please note that programme structures and individual modules are subject to amendment from time to time as part of the University’s curriculum enrichment programme and in line with changes in the University’s policies and requirements.
