Mathematics BSc (Hons)
Available with:
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Foundation Year
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Course Summary
BSc Mathematics at the University of Chester is a successful course with a very good reputation in the UK mathematics community and has been running for more than 30 years. Our academics have a diverse range of expertise and you will explore both pure and applied mathematics and their computational aspects. This will equip you with highly valued mathematical skills, and develop your creativity and problem-solving ability, which are sought after by leading commercial organisations.
The mathematics degree and learning environment will teach you how to model, solve and analyse real-world problems, using techniques valued by major commercial organisations. This will maximise your future employability.
Staff actively encourage a high level of student involvement in the teaching and learning process. Our small group sizes allow you to have a more personal learning experience where you will get to know your lecturers, allowing you to get help with your studies and have regular mathematical conversations.
Our degree is accredited by the Institute of Mathematics and its Applications (IMA), a professional body of mathematicians. This course will meet the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications, when it is followed by subsequent training and experience in employment to obtain equivalent competencies to those specified by the Quality Assurance Agency (QAA) for taught Master’s degrees.
All mathematics staff are research active and internationally recognised with an extensive network of research collaborations with leading researchers in the UK, Europe and worldwide.
What you'llStudy
Module content:
- Reading and writing critically.
- Constructing and evaluating an argument.
- Note-taking techniques for reading and listening.
- Understanding plagiarism and academic integrity.
- Introduction to reflective practice.
- Preparing for, and delivering, powerpoint presentations.
- Referencing and citation.
- Summarising and paraphrasing written sources.
- Literature searching.
- Report writing.
- The culture and expectations of higher education.
- The assessment process including the role of assessment criteria and feedback.
- The nature of research journal publishing.
Whilst much of the content above is generic, students will be encouraged to situate skills within the context of the undergraduate discipline they are entering, which leads to some variation in emphasis for certain skills.
Module aims:
1.To raise awareness of the range of study skills required for successful higher education studies, including the process of academic writing, reading strategies, seminar skills, organisation of time and materials, planning for and meeting deadlines, understanding and responding to feedback.
2. To introduce students to concepts such as plagiarism, academic integrity and appropriate use of artificial intelligence tools.
3. To facilitate an effective transition into higher education by exploring, and providing guidance in, the key elements of successful undergraduate studentship including students' understanding of taking responsibility for their own learning.
4. To teach students how to undertake a literature, visual or data review for their discipline and be able to differentiate between a valid, reliable source and an unsubstantiated or irrelevant source.
Module content:
- Research and planning skills.
- Becoming familiar with topics that comprise their undergraduate degree subject.
- Developing a knowledge base for a discipline of study.
- Identifying areas of interest.
- Application and development of critical analytical skills.
- Development of self-directed study.
- Use of learning resources.
Module aims:
1. To develop students' skills in planning and writing an essay.
2. To familiarise students with the process of tutor supervision for a written piece of work.
3. To give students an opportunity to focus on a topic within their undergraduate degree subject.
4. To write a piece of work that allows the student to broaden and deepen knowledge on a topic of their choice.
5. To prepare and deliver an academic poster presentation outlining the student's research topic.
Module content:
- Algebraic skills
- Solving equations
- Co-ordinating geometry, including points, lines and areas
- Differentiation
- Integration
- Matrices
- Sequences and series
Module aims:
1. To further develop skill in mathematical application, method and technique.
2. To prepare students with the mathematical skills required for undergraduate degrees in engineering and physical and mathematical sciences.
Module content:
- Background study and basic definitions
- Particles I: The structure and properties of atoms
- Particles II: The sub-atomic regime
- Introduction to quantum phenomena e.g. the photo-electric effect
- Radioactivity
- Nuclear processes
- Electricity and electric circuits
- Electric fields and forces
- Magnetic fields and forces
- Waves I: Mathematical descriptions
- Waves II: Electromagnetic waves
- Waves III: Properties of optics including reflection, refraction and diffraction
- Introduction to thermodynamics
- The laws of gases
Module aims:
1. To provide the students with the knowledge and understanding of the basic principles of particle physics, electricity, magnetism, waves, thermodynamics, and gravitation in preparation for undergraduate study.
2. To develop students’ awareness of the applications of physics in real situations.
3. To develop modelling and problem solving skills as well as communicate effectively using scientific concepts and language.
Module content:
- Working with units and physical quantities
- Trigonometry and basic mathematical concepts
- Coordinates and vectors
- Particle dynamics
- Forces and Newton's laws of motion
- Moments of forces
- Centres of gravity and mass
- Linear and projectile motion
- Circular motion
- Oscillations and simple harmonic motion
- Work, Energy and Power
- Impulse & Momentum
- Newtonian theory of gravity
Module aims:
1. To introduce the relationships between forces, one and two dimensional types of motion, energy and momentum.
2. To develop students' understanding of mathematical modelling of force combinations, non-linear motion and non-uniform motion related to varying forces.
3. To adequately prepare students for the next levels of study on their undergraduate degree with reference to problem solving technique as a key feature of exams.
Module content:
- Understanding the full software development lifecycle from requirements definition to implementation
- Focusing on developing Python programming techniques.
- The use of Artificial Intelligence as an aid to faster and higher quality programming.
- Developing an understanding of different data and collection types.
- Utilising control flow, loops and functions.
- Working with the NumPy and Pandas libraries for Data Science
- Exploring data visualisation with Seaborn and Matplotlib
- Data pre-processing for machine learning
- Building regression models to explore and utilise trends within data
- Using a range of common techniques to measure performance of machine learning models
- Exploring real life uses and practical examples of machine learning
Module aims:
To understand the full software development lifecycle from business requirements definition, to functional specification, programming, quality assurance (testing) and implementation
To develop an understanding of programming in Python and to be able to code to a high degree of fluency independently and with assistance from AI tools where appropriate
To be able to use popular data science libraries in Python in order to be able to process and analyse real world data.
To understand the difference between regression and classification algorithms and be able to utilise their outcomes to make accurate predictions with data sets.
To develop technical skills in the Seaborn graphing library in order to show charts and graphs to visualise data and to show accuracies of models.
In Year 1, you will be exposed to a diverse range of topics, laying a solid foundation to help your transition to being an undergraduate mathematician.
Module content:
This module is designed with student's employability at the forefront, aiming to develop essential transferable skills which employers look for and value in Mathematics graduates. Programming and computational techniques are all pervasive in today's society, from the next generation of quantum-secure algorithms allowing secure communication with your bank, to using mathematical computer simulations to model real-world phenomena.
The module is split into several different parts. We will provide an in-depth introduction to algorithms and the process of translating these into computer programs, using state-of-the-art software tools, such as Python. This will provide you with a solid foundational understanding to tackle any future computational and programming challenges. You will develop important research and writing skills. You will learn to use LaTeX, an industry-standard typesetting system for produce professional scientific documents. Finally, we will also develop and practice key skills for gaining employment, such as CV building, interview techniques, and giving compelling and engaging presentations.
- Comprehension and understanding of mathematical arguments.
- How to write coherent mathematical arguments.
- Introduction to mathematical and scientific typesetting with the LaTeX package and associated editors.
- Incorporating graphs, figures, tables and bibliographic information in reports and articles, using LaTeX.
- Referencing methodologies in the Mathematical Sciences.
- Introduction to online search tools and searching the library catalogue.
- Introduce algorithms and how to translate them into computer programs.
- Introduce students to computer programming software, for example Python.
- Learn about basic programming concepts including algorithms, loops, conditional statements and functions. Also learn about more advanced scientific functions.
- Introduction to numerical algorithms from a variety of mathematical areas.
- Working & communicating as part of a scientific team.
- Oral presentation design and delivery.
- CV building, job applications and interview training.
Module aims:
10.1 Equip students with the necessary technical skills to facilitate communicating Mathematics to both specialist and more general audiences.
10.2 Develop students' skills and confidence in communicating their scientific ideas and outputs both verbally and in writing.
10.3 Introduce students to programming and translating algorithms into computer code.
10.4 Introduce students to the concept of independent learning through research skills and tools.
10.5 Give students the opportunity to appreciate the importance of contributing to a team with a shared goal.
Module content:
In modern life, probability, data and statistics are all around us. Computers allow us to collect ever-growing amounts of data right down to the fine details of our internet use and shopping habits. In order to make any sense of this, we need statistics to be able to analyse the data and look for hidden patterns and trends. Even so, many processes, from die rolls to the movement of the stock exchange are random and we need probability to understand them. The mathematical theory of chance and statistical inference underpins artificial intelligence and is indispensable to empirical deduction. This module introduces students to both the theoretical knowledge and applied skills required for understanding and interrogating data and modelling uncertainty in real-world scenarios.
Topics covered in this module include:
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Introduction to a set-theoretic approach to probability
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Combinatorics
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Conditional probability, independence and Bayes' Theorem
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Discrete and continuous random variables
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Probability distributions, including expectation and variance
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Introduction to commonly used distributions (e.g. Binomial, Poisson, Normal)
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An introduction to joint probability distributions
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Methods of data collection, including ethical considerations
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Introduction to non-parametric and parametric hypothesis testing
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Correlation and Regression
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Forecasting and time-series
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Confidence intervals and uncertainty in data
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An introduction to machine learning and big data
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Introduction to appropriate software tools for data analysis and interpretation
Module aims:
This gives students a solid foundation in introductory data science and probability theory, including ethical considerations, the use of software and an understanding of the concepts of uncertainty, confidence and reliability.
Module content:
This module has two parts: in the first part we introduce basic concepts required throughout mathematics and in the second part, we explore differential equations and their real world applications.
Foundations of Mathematics
This part introduces students to a rigorous mathematical language and notation that are used throughout mathematics, including mathematical logic, set theory, proofs, number systems, functions, elementary number theory, symmetry groups
etc. Through these diverse topics, students will gain a solid understanding of the foundational principles of mathematics, laying the groundwork for more advanced studies in the field. The focus on logical reasoning and mathematical structures prepares students to engage in constructing rigorous mathematical arguments necessary for all university-level mathematics.
Topics may include:
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Introduction to basic language, concepts, methods, and results in Mathematics, aiming to help students transition to university-level mathematics, including learning key independent and group study skills.
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Exploration of mathematical language, logic, and methods of proof, including induction.
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Elementary set theory.
- Functions, including injective, surjective, and bijective functions, as well as inverses.
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Operations, binary operations, equivalence relations and properties of algebraic structures.
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Introduction to groups, permutation groups, and cyclic groups.
- Elementary number theory: congruence, gcd and lcm, Euclidean algorithm, prime numbers, Fundamental Theorem of Arithmetic
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Different types of infinity: countable and uncountable sets.
Differential Equations and their applications
Differential equations play a pivotal role in modelling numerous mathematical, scientific and engineering problems, stretching across celestial motion dynamics, neuron interactions, cancer progression, bridge stability and financial market trends. This module serves as an introduction to the essential theory and numerical methods used in solving ordinary and partial differential equations (ODEs and PDEs) while exploring their varied applications.
In this module, we will review the essential calculus techniques, including methods of differentiation and integration, necessary to solve ODEs. We will introduce ODEs, see their applications to real-world problems and explore techniques for generating both exact and approximate solutions for ODEs. We will also give a brief introduction to PDEs and their applications.
Topics may include:
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Review of trigonometric functions, hyperbolic functions, limits and differentiation.
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Integration, techniques such as integration by parts, partial fractions, and multiple integration.
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Review of sequences and series, covering convergence and divergence.
- Exploration of complex numbers, covering axiomatic foundations, complex conjugates, loci, polar form, De Moivre's Theorem, and roots.
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Notation and classification of ordinary differential equations.
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Linear ODEs and their applications.
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Selective exploration of non-linear ODEs and their applications.
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Introduction to systems of ODEs.
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Numerical integration: Trapezoidal Rule and Simpson’s Rule.
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Numerical solutions for ODEs: Euler method, using computer code in, for example, MATLAB, or Python.
- Partial differentiation, functions of two variables.
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Brief introduction to PDEs and their applications.
Module aims:
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This module aims to introduce students to various basic concepts and language used throughout mathematics. Students will be introduced to the idea of mathematical proof and should be able to form a coherent mathematical argument to either prove or disprove a mathematical conjecture.
- We will introduce students to ordinary differential equations and their applications as mathematical models for various real-world applications. They will learn to solve ordinary differential equations and have an understanding of the ideas of exact and approximate solutions methods.
Module content:
In this module you will have an introduction to both analysis and linear algebra.
Analysis
What is infinity? And how can we talk about a function 'tending to a limit'? Many problems in mathematics can't be solved exactly, but we can find a series of approximations tending to a true solution. However, our intuition can start to go very wrong in these cases as various pathological functions found in the 19th century illustrate. To make sense of this, we need rigorous definitions to enable us to definitively prove results; these can then be applied to accurately solve problems.
Analysis is the rigorous underpinnings and proof of calculus – differentiation and integration. In this module, we begin by laying the foundations for analysis by studying sequences and series. We then use this to explore functions and their continuity and differentiability.
Topics may include:
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Basic properties of the real numbers.
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Sequences and Series.
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Introduction to real valued functions of one variable, including limits.
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Continuous functions and their properties.
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Continuous functions on closed interval: Boundedness Theorem, Extreme Value Theorem, Intermediate Value Theorem.
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Differentiablility and properties of differentiable functions.
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Rolle’s Theorem, Mean Value Theorem.
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L’Hôpital's rule, Taylor’s Theorem.
Linear Algebra
Linear algebra is of fundamental importance throughout science, engineering and computing and it underpins almost all higher mathematics. Its real-world applications are extensive, encompassing error-correcting codes, noise and signal analysis, facial recognition, quantum computer algorithms, search engine ranking, computer game graphics and even providing you personalised suggestions on Netflix.
In this module, we adopt a dual approach, blending theoretical exploration with a computational and practical perspective on linear algebra. On the theoretical side, we will introduce the abstract notion of a vector space and explore linear transformations between them. We will use these theoretical results to tackle various computational questions ranging from solving systems of linear equations to utilising eigenspace structure for quick matrix computation.
Topics may include:
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Introduction to vectors, Euclidean space and matrices.
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Solving systems of linear equations using matrix techniques.
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Matrices and elementary row operations.
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Generalising Euclidean space over the real numbers to vector spaces over fields.
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Linear dependence and independence, bases, dimension, subspaces.
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Linear maps/transformations between vector spaces.
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Kernel, Image and the Rank-Nullity theorem.
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Matrix determinants and inverses.
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Eigenvalues, eigenvectors and diagonalisation.
Module aims:
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This module aims to introduce students to the logically precise formulation and reasoning that is characteristic of university-level mathematics. We will introduce important concepts such as sequences and series, and continuity and differentiability for functions and introduce important results.
- Students should have a good understanding of the concept of a vector space and should be able to identify vector spaces in other areas of mathematics. They should be able to apply fundamental results on bases and linear transformations and solve new problems using them. They should also be able to use matrix techniques to solve systems of linear equations and find the determinant and inverse of a matrix.
In Year 2, you will explore key theoretical results from pure mathematics and important techniques in applied mathematics which are highly valued in a variety of industries.
Module content:
Many optimisation problems in business and industry can be expressed in the form of a linear programming problem. Businesses and industry use linear programming to determine what to make in order to maximise their profits, Amazon use it to schedule your parcels for delivery and it is also used widely in Game Theory: you can use it to beat your friends at rock-paper-scissors and other games!
In this module, we will study the theoretical background behind the linear programming methods, learn how to express real-world questions as linear programming problems and solve them by hand and using computer programs. Topics include:
- Canonical forms of linear programming problems.
- Theoretical considerations: relevant results from set theory and geometry.
- Integer linear programming.
- Solutions of linear programming models: Simplex and dual simplex methods, Pivot algorithm, and computer-based techniques.
- Degeneracy, cycling, duality.
- Use of a mathematical computer software package, for example, Python, Matlab, Excel
etc. - Application to logistics in transportation and assignment problems, VAM and the Hungarian algorithm.
- Game theory: zero-sum matrix games, multi-phase games.
Module aims:
- Express realistic problems in standard forms.
- Solve linear programming problems by hand and using appropriate computer software.
Module content:
Geometry is probably the most accessible branch of mathematics, and can provide an easy route to understanding some of the more complex ideas that mathematics can present. This module intends to introduce students to the major geometrical topics taught at undergraduate level, in a manner that is both accessible and rigorous. The course will consider Euclidean geometry and solid geometry, covering topics such as the equation of lines and planes, inner product, cross product, and triple product. Spherical geometry, featuring concepts including great circles, geodesics, and spherical trigonometry, will be explored for its significant applications in fields like astronomy, navigation and understanding the Earth. Additionally, the study will extend to quadratic curves, quadratic surfaces, and planetary motion. Through this comprehensive study, students will understand the various geometric concepts, laying a foundation that combines accessibility with the necessary mathematical rigour.
Topics in Geometry are drawn from the following:
- Geometry of numbers (including the golden ratio and continued fractions).
- Coordinate geometry: lines, planes and hyperplanes.
- Euclidian geometry.
- Solid geometry: vector products, polyhedra.
- Projective geometry: basic concepts & applications.
- Spherical geometry.
- Use of appropriate software to visualise problems (such as Autograph or Matlab, for example).
- Real-life applications of geometry: examples drawn from a wide range of contexts (e.g. cartography, forensic science, navigation, architecture).
Module aims:
1. Introduce students to underlying geometric theory.
2. Develop confidence and ability in using geometry as a problem-solving tool.
3. Develop further understanding of familiar concepts through their expression as geometric problems and introduce unfamiliar problems in this manner.
4. Develop appreciation of some real-life applications of geometry.
5. Develop skills in communicating mathematical concepts.
Module content:
Stochastic processes serve as essential mathematical models for systems and phenomena exhibiting apparent randomness. Examples encompass diverse scenarios, such as the growth of a bacterial population, fluctuations in electrical current due to thermal noise, or the motion of gas molecules. The applications of stochastic processes span various disciplines, including biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, and financial markets. In order to understand such random behaviour, we introduce and study Markov chains, random walks, Brownian motion and stochastic differential equations. Through these topics, students will not only establish a robust foundation in the principles of stochastic processes but will also gain valuable insights into their diverse applications across numerous domains. The module's goal is to equip students with analytical tools essential for comprehending and modelling complex uncertainties, thereby enhancing their capacity to address real-world challenges in mathematics, statistics, and related fields.
Topics covered include:
- Brief review of Probability Theory via a Measure Theory approach.
- Martingales: Basic definitions, filtrations, stopping times.
- Doob's Martingale inequalities and Convergence Theorem.
- Markov Chains.
- Moment generating functions.
- Characteristic functions.
- Probability generating functions.
Module aims:
- Introduce, through further study of probability theory, fundamental ideas and methods used in Stochastic Analysis and Stochastic Equations.
- Present in full details a variety of exercises involving calculus with stochastic processes.
- To show how stochastic analysis techniques can be used to analyse real problems.
- To introduce students to certain basic applications of stochastic processes to Financial Mathematics.
Module content:
Although geometric intuition allows us to understand some simple calculus (differentiation and integration), when things become more complicated we need a more rigorous foundation. Mathematical analysis provides this framework and indispensable to understanding applied techniques such as numerical methods and solving differential equations. By treating the notions of distance and limit formally, this course develops a rigourous theory of convergence, differentiation and integration of real-valued functions.
Module aims:
- Encourage students to develop systematic skills in handling complicated algebraic manipulations.
- Introduce students to the language and methods of analysis of functions of one variable.
- Introduce concepts leading to fundamental theorems which are widely used throughout applications in mathematics.
Module content:
Linear algebra is of fundamental importance throughout science, engineering and computing and it underpins almost all higher mathematics. Its real-world applications are extensive, encompassing error-correcting codes, noise and signal analysis, facial recognition, quantum computer algorithms, search engine ranking, computer game graphics and even providing you personalised suggestions on Netflix.
In this module, we adopt a dual approach, blending theoretical exploration with a computational and practical approach to linear algebra. On the theoretical side, we will introduce the abstract notion of a vector space and explore linear transformations between them. We will use these theoretical results to tackle various computational questions ranging from solving systems of linear equations to utilising eigenspace structure for quick matrix computation.
Topics covered include:
- Introduction to vectors, Euclidean space and matrices.
- Solving systems of linear equations using matrix techniques.
- Matrices and elementary row operations.
- Generalising Euclidean space over the real numbers to vector spaces over fields.
- Linear dependence and independence, bases, dimension, subspaces.
- Linear maps/transformations between vector spaces.
- Kernel, Image and the Rank-Nullity theorem.
- Matrix determinants and inverses.
- Eigenvalues, eigenvectors and diagonalisation.
Module aims:
- Introduce students to Linear Algebra.
- Understand the use of computers to solve linear algebra problems.
- Develop further understanding of abstract algebraic structures and their relationship to some familiar and unfamiliar mathematical problems.
Module content:
The traditional academic programme structure is not applicable in this experiential learning internship opportunity. The placement content is freely structured and subject to negotiation between the student, the host organisation and the placement supervisor.
A mid placement conference will be used for a mid term assessment and facilitate the student's transition between the placement year and their return to University for their final year. The conference will enable students to share experiences and analyse the range of skills derived from the placement. It will also further develop the construction of their learning logs and portfolio and give opportunities to plan ahead for their final year projects/dissertations.
Module aims:
To provide students with an opportunity for first hand work experience in an industrial setting and to experience a broad range of tasks and responsibilities in different professional areas.
To allow students to apply and enrich their previous theoretical knowledge and understanding of course content through observation and application to tasks, problems and scenarios presented in an industrial environment.
To enable students to recognise the nature of tasks, workloads, management problems and working methods in the working environment.
To enable students identify their personal interests in a working environment and develop their own personal development.
Module content:
Pre-placement:
- Structured approaches to researching, selecting and securing a suitable work placement relevant to the student’s interests and career aspirations*.
- Writing an effective CV. Constructing a letter of application.*
- Interview skills.*
*Note: Students are required to undertake these pre-placement tasks during term 1 level 5, as part of the placement acquisition process and will be supported by the Work Based Learning team and the Careers and Employability department.
Induction Programme and Placement:
- The organisational context: research-informed analysis of the placement organisation’s aims, structure, culture.
- Self- assessment of needs: identification of the range of transferable skills, competencies and attitudes employees need and employers expect graduates to possess. (Employability Skills: e.g. verbal and written communication, analytical / problem solving capabilities; self-management; team working behaviours; negotiation skills; influencing people; positive attitude, resilience, building rapport).
- Devising a strategy for integrating into the workplace and work based teams
- Completion of online assignment tasks covering sourcing and obtaining placement; health and safety procedures in general; general workplace integrity; placement requirements.
During and post-placement: Learning effectively in and from the workplace:-
- Devising and implementing strategies to improve own approach and performance
- Critical analysis/evaluation of approach to skill development and performance in the workplace;
- Influencing the Placement Provider’s appraisal;
- Devising an action plan to develop gaps in transferable skills based on the placement experiences;
Module aims:
This module aims to enhance students’ prospects of gaining graduate level employment through engagement with a University approved work placement**, which will enable them to:
- Develop their understanding of workplace practice and lifelong learning;
- Enhance their work readiness and employability prospects through development of transferable skills;
- Take responsibility for their own learning and acquisition of workplace employability skills;
- Articulate, in writing, their employability skills.
In Year 3, you will study topics related to the research interests of academic staff in the mathematics group and which are closely linked to real-world applications. You may also have the opportunity to work on multidisciplinary projects and try to solve challenging real-world problems.
Module content:
Numerical analysis is the exploration of algorithms that rely on numerical approximation; this is invaluable for the study of many complicated problems, where an exact solution is very difficult, or even impossible to obtain. Its applications extend across mathematics, physical sciences and engineering, and, in the 21st century, have expanded into life sciences, social sciences, medicine, business, and even the arts. This module serves as an introduction to the fundamental techniques and methodologies for solving mathematical problems using numerical methods and equips students with the skills needed to analyse, design, and implement numerical algorithms effectively across a broad range of mathematical problems.
The topics include:
- Solving nonlinear equations, finding roots, Newton iteration and related methods.
- Introduction to optimisation, optimisation of functions of several variables, with and without constraints.
- Interpolation and approximations: Lagrange interpolation, Hermite interpolations,
- Numerical integration and differentiation: Trapezoidal method, Simpson method.
- Solutions of ordinary differential equations: Euler method, Runge-Kutta method, multistep methods, stability, convergence.
- Solution techniques for partial differential equations including the heat equation.
- Implementation and programming, e.g., Python, MATLAB.
- Error analysis: developing an understanding of the sources of error in numerical computations and methods for analysing and controlling numerical errors.
Module aims:
- Introduce students to theoretical numerical analysis.
- Develop skills in using computers to implement algorithms arising from theoretical numerical analysis.
- Give students an appreciation of the importance and relevance of the module content to contemporary real world applications appearing in areas such as physics, engineering, biology.
Module content:
Quality Control is an important application of statistical theory and methods. Since the industrial revolution, factories have needed to find ways to manufacture high quality products while minimising cost to maintain a competitive edge. From monitoring an automotive production line to stop out-of-control processes, to sampling techniques in the food production industries designed to minimise food waste, quality control procedures form a key part of the modern manufacturing process.
In this module you will learn the techniques companies employ to achieve the above. Topics for this module may include:
- Introduction to quality control: summary of relevant probability theory and probability distributions.
- Methods and philosophy of statistical process control.
- Control charts for variables: mean, median and range charts, special charts.
- Control charts for attributes: p-charts, np-charts, u-charts, c-charts.
- Process capability studies.
- Acceptance control charts.
- Acceptance sampling: single, double, and sequential sampling plans, rectifying inspections.
- Modified control limits.
- Cumulative sum techniques: CUSUM Charts, V-Masks, Tabular CUSUM.
Module aims:
We aim to:
- Introduce the student to the basic ideas of quality control and why it is important in current industry and business.
- Relate relevant material from Levels 4 and 5 of the programme to the methods of quality control.
- Introduce methods and techniques that are employed in quality control.
Module content:
Vector calculus and partial differential equations are indispensable tools in science. These topics are essential to our understanding of electromagnetism and quantum mechanics in physics, and are they are essential to the modelling of physical phenomenon such that fluid flow and heat conduction. This course is divided into two halves. The first half will cover topics related to three-dimensional geometry and vector calculus including: vector-valued functions, parametrised curves, line integrals and conservative vector fields, multiple integrals, surface integrals, the theorems of Green and Stokes, and the Divergence Theorem. The second half focusses on the theory of and techniques for solving partial differential equations. Topics covered will include: first order PDEs, classification and techniques for solving linear second order PDEs, Fourier series, the method of separation of variables applied to the heat, wave and Laplace equations, and Fourier transforms.
Module aims:
- Introduce students to the ideas and concepts of applied multivariate calculus, through vector and tensor-based approaches.
- Develop skills in solving problems involving curves, surfaces and volumes.
- Develop analytic techniques for solving a variety of partial differential equations.
- Introduce students to the underlying theory of some of the practical techniques developed.
Module content:
Group theory is the mathematical study of symmetry, a concept which appears throughout mathematics, science and nature. Physicists use group theory to describe the properties of fundamental particles of matter, Chemists use it to investigate crystal structure and it plays a central role in our every-day lives in cryptography. In mathematics, groups are found everywhere, in algebraic objects such as rings, field, vector spaces and matrices, in analysis, and in solutions to equations and differential equations.
This module will study groups and their actions on sets and geometric objects. Highlights include the Jordan Holder Theorem, which allows us to break down groups into their fundamental building blocks, called the simple groups; and Sylow's theorems which are of fundamental importance to understanding the structure of finite groups. Topics covered include:
- Groups
- Subgroups
- Cosets, normal subgroups, quotient groups
- Homomorphisms and the Isomorphism Theorems
- The Classification of finite abelian groups
- Group actions and the Orbit-Stabiliser Theorem
- The Jordan Holder Theorem
- Simple Groups
- Sylow Theory
- Solvable Groups
Module aims:
- Introduce students to Group Theory.
- Develop mathematical maturity, confidence and independence in solving problems arising from investigations relating to the selected content.
- Give students an appreciation of the importance and relevance of group theory methods to contemporary real world applications.
Module content:
The dissertation gives the student an opportunity to apply theory learned on the programme and to develop skills of self-discipline, project management and written communication.
Students will negotiate with tutors the precise title and objectives of the project. Students will study the art of mathematical writing and communication. Tutors will provide appropriate levels of support and advice.
Module aims:
The 2 module dissertation is designed to enable students to complete an independent research project written up in the form of a thesis that conforms with normal requirements for presentation of mathematical results.
The student will also be expected to give a 10 minute presentation on their thesis.
Mathematics at the University of Chester
Many taught sessions are lecture and classroom-based. Staff encourage an environment where you will be comfortable to seek support, practice questions and discuss your work with both staff and other students in small groups. In particular, our small class sizes mean you will get a more personal experience than at other universities – you will get to know your lecturers and interact with them regularly.
Assessment involves examinations, in-class tests, and coursework (including worksheets, presentations, projects, and investigative work). These provide the opportunity to develop a theoretical understanding of the topics, experience in using specialist software, and insight into applications of Mathematics.
Beyond the Classroom
On this course, you have the opportunity to spend five weeks working for a host organisation via our innovative Work Based Learning module. You’ll have the chance to test-drive a future career, boost your CV, and gain real work experience.
On this course, you’ll have the opportunity to undertake an Experiential Learning module, where you’ll apply what you’ve learned on the course to real-life scenarios and projects.
If you choose a degree with a Placement Year, you’ll have the opportunity to undertake a year’s paid professional placement at the end of your second year, where you’ll experience the workplace, apply your learning, and build connections for your future.
Entry Requirements
112 UCAS points
UCAS Tariff |
112 points |
GCE A Level
|
Typical offer – BCC-BBC Must include A Level Mathematics |
BTEC |
Considered alongside A Level Mathematics |
International Baccalaureate |
26 points, including 5 in an appropriate HL Mathematics course |
Irish / Scottish Highers |
Irish Highers - H3 H3 H3 H3 H4, including H3 in Mathematics Scottish Highers – BBBB, including Mathematics |
Access requirements |
Access to HE Diploma (Mathematics), to include 45 credits at level 3, of which 30 must be at Merit or above |
T Level |
T Level will be considered alongside A Level Mathematics |
OCR Cambridge Technicals |
Considered alongside A Level Mathematics |
Extra Information |
Welsh Baccalaureate Advanced and A level General Studies will be recognised in our offer. We will also consider a combination of A Levels and BTECs/OCRs. |
Students from countries outside the UK are expected to have entry qualifications roughly equivalent to UK A Level for undergraduate study and British Bachelor's degree (or equivalent) for postgraduate study. To help you to interpret these equivalents, please click on your country of residence to see the corresponding entry qualifications, along with information about your local representatives, events, information and contacts.
We accept a wide range of qualifications and consider all applications individually on merit. We may also consider appropriate work experience.
English Language Requirements
- IELTS Academic: Undergraduate: 6.0 (minimum 5.5 in each band)
- Postgraduate: 6.5 (minimum 5.5 in each band)
For more information on our English Language requirements, please visit International Entry Requirements.
72 UCAS points
UCAS Tariff |
72 points |
GCE A Level |
72 UCAS points from GCE A Levels to include grade D in Mathematics |
BTEC |
Considered alongside A Level Mathematics |
International Baccalaureate |
24 points, including 4 in an appropriate HL Mathematics course |
Irish / Scottish Highers |
Irish Highers - H4 H4 H4 H4 H4, including Mathematics Scottish Highers – CCDD, including Mathematics |
Access requirements |
Access to HE Diploma (Mathematics) – Pass overall |
T Level |
T Level will be considered alongside A Level Mathematics |
OCR Cambridge Technicals |
Considered alongside A Level Mathematics |
Extra Information |
Welsh Baccalaureate Advanced and A level General Studies will be recognised in our offer. We will also consider a combination of A Levels and BTECs/OCRs. If you are a mature student (21 or over) and have been out of education for a while or do not have experience or qualifications at Level 3 (equivalent to A Levels), then our Foundation Year courses will help you to develop the skills and knowledge you will need to succeed in your chosen degree. |
Fees and Funding
£9,250 per year (2024/25)
Our full-time undergraduate tuition fees for Home students entering University in 2024/25 are £9,250 a year, or £1,540 per 20-credit module for part-time study.
The University may increase these fees at the start of each subsequent year of your course in line with inflation at that time, as measured by the Retail Price Index. These fee levels and increases are subject to any necessary government, and other regulatory, approvals.
Students from the UK, Isle of Man, Guernsey, Jersey and the Republic of Ireland are treated as Home students for tuition fee purposes.
Students from countries in the European Economic Area and the EU starting in or after the 2021/22 academic year will pay International Tuition Fees.
Students who have been granted Settled Status may be eligible for Home Fee Status and if eligible will be able to apply for Tuition Fee Loans and Maintenance Loans.
Students who have been granted Pre-settled Status may be eligible for Home Fee Status and if eligible will be able to apply for Tuition Fee Loans.
Irish Nationals living in the UK or Republic of Ireland are treated as Home students for Tuition Fee Purposes.
£13,950 per year (2024/25)
The tuition fees for international students studying Undergraduate programmes in 2024/25 are £13,950.
This fee is set for each year of study. All undergraduate students are eligible for international and merit-based scholarships which are applicable to each year of study.
For more information, go to our International Fees, Scholarship and Finance section.
Irish Nationals living in the UK or ROI are treated as Home students for Tuition Fee Purposes.
Your course will involve additional costs not covered by your tuition fees. This may include books, printing, photocopying, educational stationery and related materials (such as a calculator), travel to placements and optional field trips. In Mathematics we do not expect our students to need to buy textbooks or software.
If you are living away from home during your time at university, you will need to cover costs such as accommodation, food, travel and bills.
The University of Chester supports fair access for students who may need additional support through a range of bursaries and scholarships.
Full details, as well as terms and conditions for all bursaries and scholarships can be found on the Fees & Finance section of our website.
Your Future Career
Job Prospects
Our graduates have excellent employment prospects. In the last five years, our maths graduates have successfully obtained roles in a variety of different sectors and industries:
- Teacher, education sector
- Maths Analyst, software development
- Operational Statistician, Central Government
- Information Analyst, NHS
- Actuary, insurance firm
- Pricing Analyst, insurance firm
- Auditor, banking sector
- Chartered Accountant, financial sector
- Credit Risk Analyst, financial sector
- Tax professional, HMRC
- Java Development Consultant, industry
- Software developer, industry
- Utility Expense Analyst, Energy sector
- Team Manager, retail sector
- Business Intelligence Developer, law firm
In addition, several of our graduates have gone on to further study for a Master's qualification or PhDs.
Progression options
Should you decide to further your journey in Higher Education, we offer a broad choice of professional, internationally recognised qualifications. This can be a popular option for students interested in developing their knowledge within a specialist area or gaining the necessary qualification to further their career.
Careers service
The University has an award-winning Careers and Employability service which provides a variety of employability-enhancing experiences; through the curriculum, through employer contact, tailored group sessions, individual information, advice and guidance.
Careers and Employability aims to deliver a service which is inclusive, impartial, welcoming, informed and tailored to your personal goals and aspirations, to enable you to develop as an individual and contribute to the business and community in which you will live and work.
We are here to help you plan your future, make the most of your time at University and to enhance your employability. We provide access to part-time jobs, extra-curricular employability-enhancing workshops and offer practical one-to-one help with career planning, including help with CVs, applications and mock interviews. We also deliver group sessions on career planning within each course and we have a wide range of extensive information covering graduate jobs and postgraduate study.