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This module introduces students to core elements of economic theory which forms the basis of the Macro and Micro modules in the Semester 2 of first year. Understanding a number of concepts, like specialisation, markets, competition, rational behaviour and the structure of the economy are key learning outcomes from this module and prepare students for further study in Economics and related subjects.

This module introduces students to the most important techniques in Calculus. In particular, the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide fundamental tools for quantitative descriptions of the real world across the entirety of applied mathematics. Tools and methods for differentiation and integration will be presented in detail. In addition, simple first and second order ordinary differential equations will be studied. Such equations have important applications for interpreting and understanding the world around us.

This module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.

Probability is a numerical description of random events, and statistics is the science of collecting and analysing data from these random events and modelling them with random variables. Students will be introduced to the basic concepts of probability distributions, hypothesis testing and random variables. These concepts are fundamental in probability and statistics and lay the foundations for Level 5 Mathematical Statistics (MAT2013), Linear Statistical Methods (MAT2053) and Stochastic Processes (MAT2003). Students will also be introduced to programming in the statistical software R, and thus gain employability through enhancing their digital capabilities. 

This module builds on the Introductory Economics module by extending the analyses of microeconomic concepts. In particular, it looks at the firm’s supply decision (involving cost and production), and the effect of market structure on the firm’s demand, studies labour markets and explains the constrained optimisation model of labour supply, introduces students to how to model risk and information problems, and covers aspects of welfare economics and market failure (with an application to the environment). The module uses maths from the Quantitative Methods and Maths for Economics modules to demonstrate the role maths can play in economic theory; and makes use of examples from empirical research, reports and news media to illustrate some of the concepts covered. By doing this, the module provides a firm foundation for more advanced microeconomics as the programme proceeds, and for optional modules that apply microeconomic principles.

This module is an introduction to Linear Algebra, a fundamental mathematical discipline that revolves around the exploration of vector spaces as well as linear maps between these spaces. This often necessitates the solution of systems of linear equations, which are elegantly described by matrices and vectors. Techniques from Linear Algebra find application in numerous disciplines ranging from pure and applied mathematics to many fields of science, engineering, computing and economics. This module builds on MAT1031: Algebra and provides a foundation for a variety of subsequent modules, including MAT2009 Operations Research and Optimisation, MAT2047 Curves and Surfaces, MAT2048 Groups & Rings, MAT3004 Introduction to Function Spaces and MAT3039 Quantum Mechanics.

Programming is a companion to the modern mathematician and provides a means to tackle and provide insight into problems which are insoluble by analytical means alone. This module will first develop core programming capability and knowledge of fundamental aspects of programming, including loops, functions and conditional statements. Building on these foundations, the module will then cover aspects of the analysis and visualisation of data, including linear regression to model and interpret quantitative relationships, and mathematical modelling, equipping students with the ability to analyse data and model real world scenarios. The module also aims to develop professional skills required in the contemporary workplace, such as teamwork, report writing, communication of complex ideas through presentation and the use and critical evaluation of the output of modern AI tools. The different strands of this module combine to ensure students are equipped with a relevant and transferrable set of mathematical, computational and professional skills

This module introduces students to Multivariable Calculus in two and three dimensions, and selected topics such as differential operators and line integrals in Vector Calculus. This extends students’ knowledge developed in MAT1030 Calculus on differentiation and integration of single variable functions to partial differentiation, and double and triple integration of two and three-variable functions. This module provides the necessary ground work for modules such as MAT2047 Curves and Surfaces, MAT2050 Inviscid Fluid Dynamics, and MAT2054 Functions of a Complex Variable.

The module builds on the first year microeconomics modules and serves as a foundation for subsequent study of microeconomic topics within the relevant degree programs such as consumer choice and game theory. The module uses some mathematical techniques (from the Level 4 Mathematics modules) and graphical analysis.

This module builds on the differential equation aspects of the Level 4 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.

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. 

Stochastic processes are a series of random variables. Students will be introduced to both Markov Chains and continuous Markov stochastic processes, where the distributions of future random variables are determined by the value of the most recent random variable. These models are important for modelling things which change over time, such as voting intention or population size. 

This module will build on, and extend, what students have learned in previous microeconomics courses.  We will continue to study how agents make optimising decisions, but here with a focus on how those decisions can be inefficient when there are market failures, as opposed to the perfectly competitive world that students have mostly studied before in, for example, the Microeconomics module in the previous semester. Some prominent real-world examples are environmental externalities, or the provision of public goods. We will also explore common mechanisms that have been developed to try and move decisions to more efficient outcomes; for example taxes, tradable permits, preference revelation mechanisms. We will study how societies, rather than individuals, can make collective decisions over resource allocations when preferences differ across the population – again, particularly relevant in the case of public goods. Some of the topics may have been touched on in level 4, but students will see how learning progresses by looking at topics in more detail and with more rigour. Paralleling this, the learning outcomes in this module will provide a basis upon which to build for some of level 6’s microeconomic-based modules.

When an analytical approach is not known or practical for solving a mathematical problem, which is the case for most real-world problems, a numerical approach can be useful in finding approximate solutions that are as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of systems of linear and nonlinear equations, for finding a function that interpolates or approximates a set of data points, for finding numerical values of derivatives and integrals, and for solving initial value problems. For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also analyse the complexity of numerical methods in order to estimate the computational resources required for achieving a given accuracy. Students will learn and practice implementing some of the methods in Python.

Statistical modelling provides a means of extracting information from data, enabling informed decisions to be made. It is a versatile and powerful tool with widespread applications contributing to advancements in research, business, technology, and society. Students will be introduced to the basic concepts of statistical modelling via linear regression models, which are fundamental in statistics and serve as the basis for more complex modelling techniques. Model fitting, selection and evaluation are covered for: Simple Linear Regression; polynomial regression and multiple regression models. The module concludes with the introduction of simple models in the Design of Experiments, covering the use of  such experiments and the analysis of data arising from them. The statistical software R is fully integrated with the module. Students will reinforce their understanding of concepts of statistical modelling and develop their digital capabilities by using R to conduct analyses of real data sets from business, science and industry.

This module provides a structured introduction to financial and commodity derivatives markets, focusing on the pricing, risk management, and practical application of derivative securities. Instruments such as forwards, futures, options, and swaps are examined. The module adopts a lecture-led approach, where core theoretical concepts are introduced systematically and reinforced through guided examples and applied problem-solving. Students are progressively exposed to increasingly complex financial instruments and market practices, enabling them to develop both analytical rigour and professional awareness. Emphasis is placed on linking theory to real-world applications, including hedging decisions, trading strategies, and risk management practices within firms. The module also considers the broader implications of financial innovation, including lessons from past crises.

The module analyses applications of the theory of finance to corporate policy. Broadly defined, this area comprises all operations directed towards the procurement of funds and their investment in the various types of assets.

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.

This module introduces students to core elements of economic theory which forms the basis of the Macro and Micro modules in the Semester 2 of first year. Understanding a number of concepts, like specialisation, markets, competition, rational behaviour and the structure of the economy are key learning outcomes from this module and prepare students for further study in Economics and related subjects.

This module introduces students to the most important techniques in Calculus. In particular, the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide fundamental tools for quantitative descriptions of the real world across the entirety of applied mathematics. Tools and methods for differentiation and integration will be presented in detail. In addition, simple first and second order ordinary differential equations will be studied. Such equations have important applications for interpreting and understanding the world around us.

This module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.

Probability is a numerical description of random events, and statistics is the science of collecting and analysing data from these random events and modelling them with random variables. Students will be introduced to the basic concepts of probability distributions, hypothesis testing and random variables. These concepts are fundamental in probability and statistics and lay the foundations for Level 5 Mathematical Statistics (MAT2013), Linear Statistical Methods (MAT2053) and Stochastic Processes (MAT2003). Students will also be introduced to programming in the statistical software R, and thus gain employability through enhancing their digital capabilities. 

This module builds on the Introductory Economics module by extending the analyses of microeconomic concepts. In particular, it looks at the firm’s supply decision (involving cost and production), and the effect of market structure on the firm’s demand, studies labour markets and explains the constrained optimisation model of labour supply, introduces students to how to model risk and information problems, and covers aspects of welfare economics and market failure (with an application to the environment). The module uses maths from the Quantitative Methods and Maths for Economics modules to demonstrate the role maths can play in economic theory; and makes use of examples from empirical research, reports and news media to illustrate some of the concepts covered. By doing this, the module provides a firm foundation for more advanced microeconomics as the programme proceeds, and for optional modules that apply microeconomic principles.

This module is an introduction to Linear Algebra, a fundamental mathematical discipline that revolves around the exploration of vector spaces as well as linear maps between these spaces. This often necessitates the solution of systems of linear equations, which are elegantly described by matrices and vectors. Techniques from Linear Algebra find application in numerous disciplines ranging from pure and applied mathematics to many fields of science, engineering, computing and economics. This module builds on MAT1031: Algebra and provides a foundation for a variety of subsequent modules, including MAT2009 Operations Research and Optimisation, MAT2047 Curves and Surfaces, MAT2048 Groups & Rings, MAT3004 Introduction to Function Spaces and MAT3039 Quantum Mechanics.

Programming is a companion to the modern mathematician and provides a means to tackle and provide insight into problems which are insoluble by analytical means alone. This module will first develop core programming capability and knowledge of fundamental aspects of programming, including loops, functions and conditional statements. Building on these foundations, the module will then cover aspects of the analysis and visualisation of data, including linear regression to model and interpret quantitative relationships, and mathematical modelling, equipping students with the ability to analyse data and model real world scenarios. The module also aims to develop professional skills required in the contemporary workplace, such as teamwork, report writing, communication of complex ideas through presentation and the use and critical evaluation of the output of modern AI tools. The different strands of this module combine to ensure students are equipped with a relevant and transferrable set of mathematical, computational and professional skills

This module introduces students to Multivariable Calculus in two and three dimensions, and selected topics such as differential operators and line integrals in Vector Calculus. This extends students’ knowledge developed in MAT1030 Calculus on differentiation and integration of single variable functions to partial differentiation, and double and triple integration of two and three-variable functions. This module provides the necessary ground work for modules such as MAT2047 Curves and Surfaces, MAT2050 Inviscid Fluid Dynamics, and MAT2054 Functions of a Complex Variable.

The module builds on the first year microeconomics modules and serves as a foundation for subsequent study of microeconomic topics within the relevant degree programs such as consumer choice and game theory. The module uses some mathematical techniques (from the Level 4 Mathematics modules) and graphical analysis.

This module builds on the differential equation aspects of the Level 4 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.

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. 

Stochastic processes are a series of random variables. Students will be introduced to both Markov Chains and continuous Markov stochastic processes, where the distributions of future random variables are determined by the value of the most recent random variable. These models are important for modelling things which change over time, such as voting intention or population size. 

This module will build on, and extend, what students have learned in previous microeconomics courses.  We will continue to study how agents make optimising decisions, but here with a focus on how those decisions can be inefficient when there are market failures, as opposed to the perfectly competitive world that students have mostly studied before in, for example, the Microeconomics module in the previous semester. Some prominent real-world examples are environmental externalities, or the provision of public goods. We will also explore common mechanisms that have been developed to try and move decisions to more efficient outcomes; for example taxes, tradable permits, preference revelation mechanisms. We will study how societies, rather than individuals, can make collective decisions over resource allocations when preferences differ across the population – again, particularly relevant in the case of public goods. Some of the topics may have been touched on in level 4, but students will see how learning progresses by looking at topics in more detail and with more rigour. Paralleling this, the learning outcomes in this module will provide a basis upon which to build for some of level 6’s microeconomic-based modules.

When an analytical approach is not known or practical for solving a mathematical problem, which is the case for most real-world problems, a numerical approach can be useful in finding approximate solutions that are as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of systems of linear and nonlinear equations, for finding a function that interpolates or approximates a set of data points, for finding numerical values of derivatives and integrals, and for solving initial value problems. For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also analyse the complexity of numerical methods in order to estimate the computational resources required for achieving a given accuracy. Students will learn and practice implementing some of the methods in Python.

Statistical modelling provides a means of extracting information from data, enabling informed decisions to be made. It is a versatile and powerful tool with widespread applications contributing to advancements in research, business, technology, and society. Students will be introduced to the basic concepts of statistical modelling via linear regression models, which are fundamental in statistics and serve as the basis for more complex modelling techniques. Model fitting, selection and evaluation are covered for: Simple Linear Regression; polynomial regression and multiple regression models. The module concludes with the introduction of simple models in the Design of Experiments, covering the use of  such experiments and the analysis of data arising from them. The statistical software R is fully integrated with the module. Students will reinforce their understanding of concepts of statistical modelling and develop their digital capabilities by using R to conduct analyses of real data sets from business, science and industry.

This module provides a structured introduction to financial and commodity derivatives markets, focusing on the pricing, risk management, and practical application of derivative securities. Instruments such as forwards, futures, options, and swaps are examined. The module adopts a lecture-led approach, where core theoretical concepts are introduced systematically and reinforced through guided examples and applied problem-solving. Students are progressively exposed to increasingly complex financial instruments and market practices, enabling them to develop both analytical rigour and professional awareness. Emphasis is placed on linking theory to real-world applications, including hedging decisions, trading strategies, and risk management practices within firms. The module also considers the broader implications of financial innovation, including lessons from past crises.

The module analyses applications of the theory of finance to corporate policy. Broadly defined, this area comprises all operations directed towards the procurement of funds and their investment in the various types of assets.

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.

Students have the option to undertake a work placement, study exchange abroad, or work/study exchange combination. This module supports students' development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment in diverse global contexts. The module is concerned with Personal and Professional Development towards holistic academic and non-academic learning, and is a process that involves self-reflection, documented via the creation of a personal record, planning and monitoring progress towards the achievement of personal objectives. Development and learning may occur before and during the placement/study exchange, and this is reflected in the assessment model as a progressive process. Additionally, the module aims to enable students to evidence and evaluate their placement/study exchange experiences and transfer that learning to other situations through written and presentation skills.

This mathematics module is designed to reinforce and broaden basic A-Level mathematics material, develop problem solving skills and prepare students for the more advanced mathematical concepts and problem-solving scenarios in the semester 2 modules.The priority is to develop the students’ ability to solve real- world problems in a confident manner.  The concepts delivered on this module reflect the skills and knowledge required to understand the physical around us. This is vital as mathematics plays a critical role in the students’ future employability and achievement on their respective undergraduate choices.

The emphasis of this module is on the development of digital capabilities, academic skills and problem-solving skills. The module will facilitate the development of competency in working with software commonly used to support calculations, analysis and presentation. Microsoft Excel will be used for spreadsheet-based calculations and experimental data analysis. MATLAB will be used as a platform for developing elementary programming skills and applying various processes to novel problem-solving scenarios. The breadth and depth of digital capabilities will be further enhanced by working with HTML, CSS and JavaScript within the GitHub environment to develop a webpage, presenting the student's research project narrative. The project provides students with an opportunity to carry out guided research and prepare an online article on one of many discipline-specific topic choices. Students will develop a wide range of writing, referencing and other important academic skills and learn how to use embedded and/or interactive online content to support the presentation of their online article. Students will also receive an introduction to using AI tools to support their learning, alongside critical discussions on the ethical considerations and academic integrity of utilising AI in a university setting.

The module is designed to develop and extend your critical thinking skills and problem solving skills beyond that which would normally be acquired in an A-level (or comparable level) course. From a theoretical perspective, the module introduces fundamental ideas of proof and abstract mathematical structures, including groups and vector spaces. The practical computing aspect of the module brings together a variety of techniques in data processing, analysis, modelling and probability and statistics so that you may further advance your problem solving skills and apply some of the theory within a variety of interesting and challenging contexts using Microsoft Excel.

This module introduces several principles and processes which underpin most physical science and engineering disciplines, which you are likely to study beyond the Foundation Year. Specifically, you will study topics that include S.I. units and measurement theory, electric and magnetic fields and their interactions, the properties of ideal gases, heat transfer and thermodynamics, fluid statics and dynamics, and engineering instrumentation and measurement. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported by the use of the university’s virtual learning platform.

This module builds on ENG0011 Mathematics A and is designed to reinforce and broaden A-Level statistics and calculus. The students will continue to develop their ability to solve real-world problems in a confident manner.  The concepts delivered on this module reflect the skills and knowledge required to understand the physical world around us. This is vital, as mathematics plays a critical role in the students¿ future employability and achievement on their respective undergraduate courses. On completion of the module students are prepared for the more advanced Mathematical concepts and problem solving scenarios in the first year of their Engineering or Physical Sciences degree.

This module builds further on the mathematical and computing skills that you developed previously. As before, there is a strong emphasis on critical thinking, problem solving and becoming more independent as a learner. A number of advanced topic areas will be introduced in both the mathematics and computing components. These module components are weighted at 65% for mathematics and 35% for computing. There are a total of 11 advanced mathematics lectures with associated tutorials and 11 computer laboratory sessions with associated tutorials. The main topic areas covered by the mathematics component are: vectors, complex numbers, complex analysis, and number theory. Associated geometrical concepts are introduced in all of these topic areas. In the computing component, you will learn to use Python and associated packages as a language for implementing a variety of interesting and challenging processes. An emphasis will be placed on the process of abstraction and implementation, with process design considerations at holistic and atomic levels.

This module introduces several principles and processes which underpin most physical science and engineering disciplines, which you are likely to study beyond the Foundation Year. Specifically, you will study topics that include vectors and scalars, equations of motion under constant acceleration, momentum conservation, simple harmonic motion and wave theory. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported by the use of the university’s virtual learning platform.

This mathematics module is designed to reinforce and broaden basic A-Level mathematics material, develop problem solving skills and prepare students for the more advanced mathematical concepts and problem-solving scenarios in the semester 2 modules.The priority is to develop the students’ ability to solve real- world problems in a confident manner.  The concepts delivered on this module reflect the skills and knowledge required to understand the physical around us. This is vital as mathematics plays a critical role in the students’ future employability and achievement on their respective undergraduate choices.

The emphasis of this module is on the development of digital capabilities, academic skills and problem-solving skills. The module will facilitate the development of competency in working with software commonly used to support calculations, analysis and presentation. Microsoft Excel will be used for spreadsheet-based calculations and experimental data analysis. MATLAB will be used as a platform for developing elementary programming skills and applying various processes to novel problem-solving scenarios. The breadth and depth of digital capabilities will be further enhanced by working with HTML, CSS and JavaScript within the GitHub environment to develop a webpage, presenting the student's research project narrative. The project provides students with an opportunity to carry out guided research and prepare an online article on one of many discipline-specific topic choices. Students will develop a wide range of writing, referencing and other important academic skills and learn how to use embedded and/or interactive online content to support the presentation of their online article. Students will also receive an introduction to using AI tools to support their learning, alongside critical discussions on the ethical considerations and academic integrity of utilising AI in a university setting.

The module is designed to develop and extend your critical thinking skills and problem solving skills beyond that which would normally be acquired in an A-level (or comparable level) course. From a theoretical perspective, the module introduces fundamental ideas of proof and abstract mathematical structures, including groups and vector spaces. The practical computing aspect of the module brings together a variety of techniques in data processing, analysis, modelling and probability and statistics so that you may further advance your problem solving skills and apply some of the theory within a variety of interesting and challenging contexts using Microsoft Excel.

This module introduces several principles and processes which underpin most physical science and engineering disciplines, which you are likely to study beyond the Foundation Year. Specifically, you will study topics that include S.I. units and measurement theory, electric and magnetic fields and their interactions, the properties of ideal gases, heat transfer and thermodynamics, fluid statics and dynamics, and engineering instrumentation and measurement. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported by the use of the university’s virtual learning platform.

This module builds on ENG0011 Mathematics A and is designed to reinforce and broaden A-Level statistics and calculus. The students will continue to develop their ability to solve real-world problems in a confident manner.  The concepts delivered on this module reflect the skills and knowledge required to understand the physical world around us. This is vital, as mathematics plays a critical role in the students¿ future employability and achievement on their respective undergraduate courses. On completion of the module students are prepared for the more advanced Mathematical concepts and problem solving scenarios in the first year of their Engineering or Physical Sciences degree.

This module builds further on the mathematical and computing skills that you developed previously. As before, there is a strong emphasis on critical thinking, problem solving and becoming more independent as a learner. A number of advanced topic areas will be introduced in both the mathematics and computing components. These module components are weighted at 65% for mathematics and 35% for computing. There are a total of 11 advanced mathematics lectures with associated tutorials and 11 computer laboratory sessions with associated tutorials. The main topic areas covered by the mathematics component are: vectors, complex numbers, complex analysis, and number theory. Associated geometrical concepts are introduced in all of these topic areas. In the computing component, you will learn to use Python and associated packages as a language for implementing a variety of interesting and challenging processes. An emphasis will be placed on the process of abstraction and implementation, with process design considerations at holistic and atomic levels.

This module introduces several principles and processes which underpin most physical science and engineering disciplines, which you are likely to study beyond the Foundation Year. Specifically, you will study topics that include vectors and scalars, equations of motion under constant acceleration, momentum conservation, simple harmonic motion and wave theory. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported by the use of the university’s virtual learning platform.