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BSc (Hons) Mathematics

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Key information

Typical offer:
Entry requirements
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UCAS code: G100
Institute code: H36
Study abroad option
Work placement option
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UCAS points	A Level	BTEC	IB requirement
120-128	BBB-ABB: A minimum of a grade B required in Mathematics.	DDM: Applied Science as well as A Level Maths grade C.	120-128 points: Must include maths at HL grade 4 or above.

Additional requirements

GCSE: Grade 4/D in English Language and 4/C Mathematics

Access Course Tariff: Diploma with 45 Level 3 credits of which 15 must be in maths at a minimum of Merit.

All students from non-majority English speaking countries require proof of English language proficiency, equivalent to an overall IELTS score of 6.0 with a minimum of 5.5 in each band.

If you do not have the required IELTS or equivalent for direct entry on to your degree programme, our Pre-sessional English and International Foundation courses can help you to achieve this level.

For more details on the University of Hertfordshire's entry requirements, please visit our Undergraduate Entry Requirements page.

Find out more about International Entry Requirements.

The University of Hertfordshire is committed to welcoming students with a wide range of qualifications and levels of experience. The entry requirements listed on the course pages provide a guide to the minimum level of qualifications needed to study each course. However, we have a flexible approach to admissions and each application will be considered on an individual basis.

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Why choose this course?

Receive excellent career support during and after the course
Lecturers are experts in their field; informed by current research

Mathematics sits within one of our smaller Departments. That means you’ll get to know your lecturers very well and vice versa. You’ll benefit from an individual approach and tailored care and support where needed. You’ll learn from research active academics, who are renowned internationally for their contributions to mathematics and mathematical physics. Three members of staff have been working on ‘Strings, Supergravity and Geometry,’ exploring string theory and differential and algebraic geometry. Other projects include researching classical and quantum integrable systems and scattering amplitudes in gauge theories. Aren’t familiar with these terms and theories? Rest assured, very few of our first-year students are. You’ll start at the basics and slowly work your way up to specialise in the areas that interest you most.

You’ll attend lectures as well as workshops and seminars. This way, you can learn from your lecturers as well as your peers. We’ve even set up a Student Proctor Scheme. This means students from higher years will be on hand to help you during and outside of your lessons. You’ll take part in practical computing classes and problem workshops.

Between your second and third year of study, you can take an optional sandwich year. Want to study abroad for a year? We’ve got you. Want to work in industry for a year? We have a dedicated placements tutor in our school, who will help you find your dream placement. Our students have worked for companies like GlaxoSmithKline (GSK), Roche, BAE Systems, and the NHS. And that’s just our UK placements. Many of our students even go on to work at their placement host company after they finish their course.

What's the course about?

You’ll study a balance of pure, applied and financial mathematics.

In your first year, you’ll learn all the foundations and basics that you need to know. We are aware that our students come from different schools and have followed different programmes. The first year is about making sure that everybody is on the same page. You’ll study linear algebra, basic statistics, and computational modelling. You’ll learn about numbers and sets, the applications of mathematics and financial maths. You’ll also take the first ‘mathematical techniques’ model to set you up with a strong foundation for your second and third year.

In your second year, you’ll take the second module on mathematical techniques. You’ll also work on differential equations, take a module in career planning and development and attend small group tutorials. You’ll be introduced to Real Analysis, one of the core topics in pure mathematics. This year there are also some optional modules for you to choose from. These include programming, algebra, number theory and numerical methods. Want to go into teaching? You can even take a module in professional teaching skills to prepare you for a career in education. There is one double-credit module – that means it’s like two modules in one: Financial markets and portfolio theory. You’ll learn how to analyse portfolios of securities and financial data. In the second half of the module you’ll learn more theories that underlie the financial markets.

Work placement/study abroad option: Between your second and final year, you’ll have the option to study abroad or do a work placement for up to a year. Not only will this give you an amazing experience to talk about but will also give your CV a boost. If you’d rather go straight to your final year, that’s absolutely fine too.

In your final year, you’ll investigate complex numbers – two dimensional numbers in an unordered set. You’ll explore the ideas of continuity and differentiability to functions. These ideas underpin many practical applications, making this a useful module for your career development. Most other modules are optional this year, so you can do what you like best. Modules include linear and non-linear optimisation, multivariate statistics, geophysical fluid dynamics and more. This year really allows you to home in on your favourite areas of mathematics. There is also a strong focus on employability and finding a fitting job for when you leave us.

For a full list of modules, see the section under ‘What will I study?’

Your main campus is College Lane  

This is where the creative arts, science and health-related subjects are based. This means you’ll share the campus with future nurses, scientists, artists and more. You can use the common rooms to relax with friends, work out in the 24-hour gym or have a drink in our on-campus pub or cafes. We also have restaurants for you to eat in or grab something on the go. Our Learning Resources Centres are open 24/7, which means you can study whenever suits you best. Want to pop over to the other campus? You can take the free shuttle bus or walk there in just 15 minutes.   

What will I study?

Degree programmes are structured into levels, 4, 5 and 6.  These correspond to your first, second and third/final year of study.  Below you can see what modules you’ll be studying in each.

Level 4

Module	Credits	Compulsory/optional
Introduction to Mathematical Reasoning	15 Credits	Compulsory
This module equips students with both the practical and conceptual tools to successfully study mathematics at university. On the practical side, students will learn key digital skills including how to use software to write technical documents and how to access, search, and reference online resources. Just as importantly, on the conceptual side, students will learn what makes university mathematics different from its school counterpart: a focus on critical thinking, accurate reasoning, and clear communication of ideas in written form. These skills are vital not only for academic mathematics, but also across the spectrum of real-world graduate-level careers. Material for discussion will be drawn from diverse sources, including e.g. YouTube videos. The focus here is less on learning specific mathematical material and more on learning how to approach new material as a mathematician.
Mathematical Methods	15 Credits	Compulsory
On entry to the degree students have a range of mathematical backgrounds and knowledge, and this module has been designed to standardise mathematical knowledge through the first semester of study. You will review core areas of A-level mathematics, which will be extended to enhance your knowledge. You will learn important and widely applicable mathematical techniques relating to hyperbolic functions, matrices, vectors, differential and integral calculus, and complex numbers. In this module you will develop your skills in mathematical problem solving, analysis and evaluation.
Probability and Statistics	15 Credits	Compulsory
This is an introductory module in statistics and probability theory. Basic ideas such as initial data analysis, the mean, standard deviation and variance, probability, statistical distributions, the use of a statistical package, the use of data for inference and decision making are covered. This involves confidence intervals for means and techniques for hypothesis testing for differences between means, differences between proportions and for the size of a correlation. Other topics covered include simple linear regression, and the analysis of category data and contingency tables. A wide variety of situations in which these techniques may be employed will be considered, with examples taken from business, engineering, science, social sciences, etc. The emphasis throughout is on conceptual understanding and the development of practical statistical skills, supported by the use of a statistical computer package.
Numbers and Sets	15 Credits	Compulsory
This module aims to present the fundamental ideas, language, and skills on which the rest of mathematics is based. The main distinction that mathematics holds over every other discipline is that, by using mathematics, we can prove our claims beyond doubt, interpretation, or debate. This is possible because mathematics, used correctly, is a precise language free from the vagueness and ambiguity of everyday discourse. In this module, you will familiarise yourself with the use of technical mathematical language and gain the skills necessary to prove simple mathematical claims. In the process, you will re-encounter many familiar concepts such as numbers, sets, or functions and learn to view them as a mathematician does.
Financial and Actuarial Mathematics	15 Credits	Compulsory
The aim of this module is to introduce students to the fundamental concepts in financial mathematics. You will learn about the range of investments available and how these are traded on the markets. You will gain an understanding of how to analyse and value these investments by applying mathematical and actuarial techniques such as compound interest, rates of return, discounting and accumulating. You will use recognised criteria to compare alternative investment opportunities, gaining an understanding of how an investor can make informed decisions when purchasing investments or can assess the performance of investments they already own. You will also gain an understanding of the risks involved in investing in securities, including the sources of risk and methods to quantify and mitigate risk. To complement the theoretical concepts explored in lectures, you will have the opportunity to download live market data and analyse it.
Linear Algebra	15 Credits	Compulsory
Linear algebra is a fundamental area of mathematics and is arguably the most powerful mathematical tool ever developed. It is a core topic of study with applications to fields as diverse as business, economics, engineering, science etc. It also has applications to our daily life: for an example of linear algebra at work, one needs to look no further than the Google search engine, which relies on linear algebra to rank the results of a search with respect to relevance. In this module you will learn basic concepts of linear algebra, including matrices, eigenvalues and eigenvectors, that provide the first step towards the understanding of how to use these tools in pure and applied mathematics.
Applications of Calculus	15 Credits	Compulsory
This module will extend the mathematical knowledge gained in the module 'Mathematical Methods'. It will explore a variety of mathematical methods that use calculus. You will learn important and widely applicable mathematical techniques relating to improper integrals, differential equations, partial differentiation, power series, and Fourier series. In this module you will develop your skills in mathematical problem solving, analysis and evaluation.
Computational Modelling	15 Credits	Compulsory
In this module you will learn how to use a programming language. You will solve exercises during practical classes and independent study time. You will see how to develop scientific and mathematical models and how they can be implemented in a computational environment. Towards the end of the module, you will carry out a mini-project on mathematical computing, and present the results. The module develops skills in problem solving, computer programming, analysis and evaluation, and interpersonal and communication skills.
Small Group Tutorial (Level 4)	0 Credits	Compulsory
The module will require students to attempt a range of problems, mostly of a mathematical nature, in the students' broad subject area. Some problems will be associated with other specific taught modules on the programme, while others will have a synoptic role sitting across several modules. The work will challenge students to develop problem solving skills that enable them to approach unfamiliar as well as familiar problems. The students will also receive pastoral care and support for any problems, either academic or personal, that they encounter as a first-year student. The Small Group Tutor will fill the role of a personal tutor and help students with their transition to university life and studying at a higher level. If necessary, their tutor will direct students towards other UH sources of support.

Level 5

Module	Credits	Compulsory/optional
Multivariable Calculus	15 Credits	Compulsory
You will learn how to integrate functions of two and three variables along plane and space curves and how to evaluate multiple integrals of such functions. You will learn about gradient, divergence and curl. You will be able to obtain the Fourier transform of a function and perform calculations involving analytic functions of a complex variable. In this module you will develop your skills in mathematical problem solving, and analysis and evaluation.
Algebra	15 Credits	Compulsory
This module introduces several core topics in abstract algebra. A recurring theme is of building from concrete examples to abstract and unifying mathematical ideas. We start with permutations on finite sets of objects; and develop techniques for working with them. We then introduce the concepts of relations on sets. We proceed to introduce one of the most important concepts in mathematics: that of a group. We discuss the group axioms in detail and show how they are motivated by means of various naturally ¬occurring examples; we stress the idea of groups as groups of transformations of some object. Key results in group theory, including Lagrange's theorem and the orbit-¬stabilizer theorem, are stated and proved, and examples are given to show their utility and power.
Real Analysis	15 Credits	Compulsory
This module introduces Real Analysis, one of the core topics in pure mathematics. We deal mainly with real-valued sequences and functions of a single real variable, and the central concepts we introduce is the precise definition of what it means for such sequences to converge and such functions to be continuous. The definitions are beautiful and yet notoriously subtle. In building up to it, we isolate the key property which distinguishes the real numbers from other number systems: that of completeness. We go on to give a similarly precise treatment of differentiability of functions. In the concluding section of the course, we look at series, which are sums of infinitely many real numbers, and when such ¬a sum converges to a limit.
Differential Equations	15 Credits	Compulsory
This module employs a variety of mathematical methods and techniques to explore, describe and predict the behaviour of scientific, industrial and engineering phenomena. The subject appeals to individuals interested in applying mathematics to real-word problems. In this module, we focus on ordinary differential equations. The emphasis is on the development of methods important in applications.¬ In this module you will develop your skills in problem solving, analysis and evaluation.
Career Planning and Development	0 Credits	Compulsory
The module aims to develop relevant the skills and understand the role of a graduate in the sphere of work. By the end of the module students should appreciate the challenges, rewards and diversity of career planning and development. In this module you will develop your skills in team and organisational working, interpersonal and communication skills, information searching, adaptation to context, personal evaluation and development.
Small Group Tutorial (Level 5)	0 Credits	Compulsory
This module is designed to give you academic support in small groups with studying the taught material from across your Level 5 modules. It also provides support and training for the Career Planning and Development module in the form of assistance with your personal skills audit, and guidance with putting together your CV. Your tutor group meets regularly during teaching periods. In meetings your tutor will facilitate discussions relating to tutorial activities, as well as in additional areas of study that you may suggest. You can also seek pastoral support from your tutor on any matters affecting your studies. The module develops skills in problem solving, interpersonal and communication skills, adaptation to context, and personal evaluation.
Programming	15 Credits	Optional
Programming is an important skill in the modern working world. This module will introduce you to programming in a modern high-level language. The module will cover control structures such as loops and logical statements. You will be shown how to build more complex programs by writing and linking separate functions and procedures. You will learn how to debug programs and produce program documentation. And you will apply your skills to a mathematical or physical problem and computationally analyse the results. The module develops skills in computer programming, interpersonal and communication skills, and conceptualisation and critical thinking.
Professional Teaching Skills	15 Credits	Optional
The module aims to develop the practical skills and understand the role of a graduate in the sphere of education. By the end of the module students should appreciate the challenges, rewards and diversity of the educational sector. In this module you will develop your skills in team and organisational working, interpersonal and communication skills, information searching, adaptation to context, personal evaluation and development.
Motion and Tensors	15 Credits	Optional
Dynamics in mathematics has a broad meaning and describes states and state ¬spaces, and the transformation or evolution of these states. This module highlights these ideas while focusing on problems of classical mechanics. The approach will emphasize the (historically accurate) way in which mathematical structures have often been devised to solve particular mechanical problems. You will learn how to work in different frames, both inertial and non-inertial. You will use tensors to simplify and solve complex problems, and to reveal their intrinsic symmetries.
Number Theory	15 Credits	Optional
Number theory is one of the oldest branches of mathematics and is concerned with the properties of integers. It has many practical applications, most importantly in areas such as cryptography. This module will look at divisibility among integers, the Euclidean algorithm and factorization into prime numbers, and it will investigate the distribution of the primes. It will also introduce modular ("clock") arithmetic that leads to the investigation of congruences, Fermat's little theorem, Chinese remainder theorem, and quadratic reciprocity. It will discuss Euler's phi function, and other topics such as Diophantine equations and continued fractions. Most of the content of the module will be placed in an historical context.
Investment Portfolios	15 Credits	Optional
This module investigates the construction and mathematical analysis of portfolios of securities. A variety of techniques from modern portfolio theory are introduced to analyse the risk and expected return of a portfolio, and applied to the construction of efficient and optimal portfolios. Live financial market data will be downloaded from the internet and used in practical computing sessions to demonstrate the concepts and theories discussed in lectures. The students have the opportunity to create their own portfolio of assets and participate in a friendly competition to achieve the highest performing portfolio.
Numerical Methods	15 Credits	Optional
Numerical techniques are important across many areas of mathematical modelling, since it is rare that real-world problems admit solutions in closed form. In this module you will discover how to use numerical methods to solve mathematical problems. We will discuss the relative performance of different methods in terms of accuracy and efficiency, and investigate the theoretical background to the methods. We will typically cover methods for numerical integration, numerical solution of systems of linear equations, computation of eigenvectors and eigenvalues, and the numerical solution of systems of ODEs.
Game Theory	15 Credits	Optional
Famous since at least the Nobel-prize winning work of John Nash, game theory analyses situations in which payoffs to players depend on their behaviour as well as behaviour of other players. Game theory has found many applications in various fields, such as economics, biology, business, law, politics, sociology, computer science and data science. The purpose of this module is to introduce the fundamentals of game theory, including the concept of Nash equilibria. It focuses on various ways of describing and solving games, and their applications in real-world situations. The students will learn how to recognize and model strategic situations, to predict when and how their action will have an influence on others, and to exploit strategic situations for the benefit of their own.
Statistical Modelling	15 Credits	Optional
Statistical modelling refers to a set of tools and techniques for modelling and understanding complex data sets and plays a key role in many areas of science, medicine, finance and industry. This module has been developed to give students a detailed understanding of the commonly used statistical modelling techniques of analysis of variance and regression analysis. The module is supported throughout by the use of a statistical computer package which facilitates the analysis of data sets, taken from a variety of application areas, using the methods taught in the lectures.
Quantum Mechanics	15 Credits	Optional
Quantum mechanics is the most fundamental and most successful theory of the physical world. It has been essential to the development of many modern technologies (lasers, solid state and tunnelling devices, entanglement and encryption). This module develops the basic formalism of quantum mechanics. The formalism is used to understand the properties of bound states, spin states, identical particles and multi-particle structures. Recent developments and conceptual problems are also discussed. The module develops skills in research enquiry and problem solving, presentation skills, conceptualisation and critical thinking.

Level 6

Module	Credits	Compulsory/optional
Complex Analysis	15 Credits	Compulsory
Complex Numbers are two dimensional, and are an unordered set. This leads to many startling and bizarre ideas. We apply the ideas of continuity and differentiability to functions of a complex variable, and reach some surprising conclusions. However, it is when applying the ideas of integration that the most beautiful and impressive results emerge, with many practical applications.
Investigations in Mathematics	15 Credits	Compulsory
Students will choose a topic from a list of typically 5-10 different mathematics topics offered by School staff (tutors), and will conduct an open-ended investigation into that topic. The students working on each topic will work independently on their investigations, under the guidance of a tutor. They will be required to produce an original, substantial and professionally presented printed report on their findings, and to prepare a presentation to summarise their findings. Students will be interviewed about their report and presentation.
Mathematical Project and investigative Skills	30 Credits	Compulsory
Students will carry out a piece of research and/or a literature review in a research topic. Mathematics research areas in the department include: algebra, representation theory, financial mathematics, and mathematical and theoretical physics. A successful project will become a feature of a student's professional profile and CV, and is often a talking point in graduate job interviews and/or postgraduate applications. The module develops skills in research enquiry and problem solving, analysis and evaluation, organisational working, interpersonal and communication skills, scientific writing and information searching, conceptualisation and critical thinking, adaptation to context, synthesis and creativity, personal evaluation and development, and ethical awareness and application.
Space Dynamics	15 Credits	Optional
Space dynamics is a coursework-only module. Students work in a computer lab supervised by the module facilitator. There are no formal lectures. Instead, students work their way through a set of computer exercises using Matlab. The exercises allow the student to tackle problems in different ways and develop their own style of problem-solving. The module covers various aspects in spacecraft dynamics including: atmospheric drag, aerobraking, transfer orbits, injection orbits, spacecraft spin, the stability of spinning motion – Euler's equations, three-dimensional spin motion, and mass models of irregular objects. The module develops skills in research enquiry and problem solving, analysis and evaluation, interpersonal and communication skills, autonomy and responsibility for actions.
Partial Differential Equations	15 Credits	Optional
Partial differential equations arise as part of the mathematical modelling of real life problems connected to many areas of science. These connections must be exploited to find a solution to these problems. PDEs provide the foundation for a robust and important area of applied mathematics. In this module we will look at the derivation of some important PDEs and their classification schemes. In this module you will develop your skills in problem solving, and analysis and evaluation.
Linear Optimisation	15 Credits	Optional
You learn to extract the relevant information from business problems and to develop linear programming models to represent them. A number of different solution methods are developed and used to solve these problems. You will develop the ability to interpret the solutions in practical terms and deal with the problem cases that sometimes arise when solving LP problems.
Further Algebra	15 Credits	Optional
This course builds on the level 5 course Algebra. We aim at deepening results on known algebraic structures by focusing on some of the following topics: polynomial rings; field extensions and introduction to Galois theory; finite fields and applications in crytography; group theory and group presentations. Also to introduce new structures such as ordered sets, lattices and universal algebra, and their applications.
Further Numerical Methods	15 Credits	Optional
This module will introduce you to advanced methods for solving mathematical and physical problems in high-level programming languages. The module will focus on numerical solution of partial differential equations because these are so common in mathematics, physics, and a range of other fields. You will study the mathematical background underpinning the numerical methods, and then apply them in practical sessions by creating programs to solve complex problems. 10. Modes of Delivery: The following represents the mode and associated learning activities. 10a. Delivery Mode: Classroom based 1 Distance 0 Flexible 0 Study Abroad 0 Work Based Learning 0 (tick the appropriate box) 10b. Activities Hours 1.Classroom based lectures 24 2.Classroom based seminars and tutorials 24 3.Classroom based practical classes, workshops, studios or demonstrations 4.Scheduled online activities (ie online versions of the above) 5.Scheduled external learning activities - fieldwork, external visits and work based learning 6.Online directed independent study 7.Other directed independent study 8.Self-directed independent study 102 9.Placement 10.Year Abroad TOTAL HOURS 150 11. Module Content: 11a. Module Content: (for publication, max 150 words) This module will introduce you to advanced methods for solving mathematical and physical problems in high-level programming languages. The module will focus on numerical solution of partial differential equations because these are so common in mathematics, physics, and a range of other fields. You will study the mathematical background underpinning the numerical methods, and then apply them in practical sessions by creating programs to solve complex problems. In this module you will develop your skills in problem solving, analysis and evaluation, computer programing, and data synthesis.
Nonlinear Optimisation	15 Credits	Optional
You will learn and explore the fundamentals of nonlinear optimisation problems, both unconstrained and constrained and how to solve them using a number of different iterative techniques. Blending theory and algorithms for solving nonlinear optimisation problems with applications to real world problems such as in finance. You will study the convergence properties of these iterative methods and learn how to use software implementations of them.
Combinatorics	15 Credits	Optional
Combinatorics is the study of finite or countable, discrete structures; as opposed to uncountable, continuous structures such as the real or complex numbers studied in Analysis and Calculus. Graphs (think of a system of islands connected by bridges) and Latin Squares (a completed Sudoku puzzle is an example of a Latin Square) are two examples of the kind of object Combinatorists are particularly interested in, but there are many more. Combinatorial problems are just as varied as Combinatorial objects and include questions such as "How many different number plates can there be?", "If you shuffle a playlist, what are the odds that at least one song is in its original position", or "Can you find six people so that no three of them are all mutual friends, but no three of them are all mutual strangers?".
Nonlinear Systems	15 Credits	Optional
You will learn how to investigate and evaluate the qualitative behaviour of the solutions of differential equations which relate to problems in a wide variety of application areas. You will recognise that the behaviour of the solution of a differential equation can be drastically altered by a small change in a parameter. These observations have important contributions in improving the applications of mathematics in industry, business and the physical sciences. The module provides the student with an understanding of differential equations by the construction, analysis and interpretation of phase portraits. In particular you will be able to identify if and when periodic solutions and other types of behaviour exist. The module develops skills in problem solving, analysis and evaluation, team and organisational working, interpersonal and communication skills, and conceptualisation.
Multivariate Statistics	15 Credits	Optional
This is a module in statistics for students who wish to study techniques widely used by statisticians working in research, commerce and industry. Multivariate statistics introduces techniques for examining relationships among a group of variables, and a number of multivariate statistical methods are introduced. Throughout the module, computer packages are used wherever relevant to analyse case studies relating to the techniques taught. The main topics studied are likely to include: - methods of viewing multivariate data; - how to describe multivariate data in a statistical manner; - how to conduct hypothesis tests using multivariate data; - how to carry out various methods of multivariate data analysis; - how to interpret the results of various methods of multivariate data analysis.
Linear Modelling	15 Credits	Optional
This is a module in statistics for students who wish to study techniques widely used by statisticians. Linear modelling brings together regression and analysis of variance into a single modelling approach based on matrix algebra and extends these methods to include category response variables. The main topics studied are likely to include: - the matrix algebra approach to linear regression; - methods of analysing non-orthogonal sums of squares; - the dummy variables approach to the analysis of experimental design models; - the analysis of contingency tables by use of log-linear models; - logistic regression; - the principles of the generalised linear model.
Geophysical Fluid Dynamics	15 Credits	Optional
This module gives a grounding in geophysical fluid dynamics, the basic principles governing the circulation of the Earth's atmosphere and ocean on large terrestrial scales. It provides a physical and mathematical description of geophysical flows and of an assortment of waves that can be supported by such flows. An emphasis is put on why the Earth's atmosphere and ocean look like they do on global scales. In-class demonstrations, laboratory experiments and computer modelling will feature. In this module you will develop your skills in problem solving research and enquiry, analysis and evaluation, team and organisational working, interpersonal communicational skills, scientific writing and information searching.
Lagrangian Dynamics	15 Credits	Optional
This module introduces the powerful mathematics used in the study of dynamical systems. We start with the calculus of variations, a topic which deals with "extremisation" questions in geometry, e.g. "What shape does a soap-film form?", or "What curve is formed by a heavy chain hanging under its own weight?". These techniques can be applied to mechanical systems, and it turns out that the laws of motion themselves arise from extremising some quantity – the "action". This Lagrangian perspective gives a powerful way to compute a system's equations of motion and to understand its symmetries. Finally the module describes how the Hamiltonian formalism reduces these second order equations to first-order, and in so doing introduces the concept of phase space while touching on the rich topic of symplectic geometry. The module develops skills in research enquiry and problem solving, analysis and evaluation, and conceptualisation and critical thinking.
Groups and Representations	15 Credits	Optional
Representation theory of groups plays an important role in abstract algebra as well as having important applications in other disciplines such as theoretical physics or crystallography. It provides a concrete way to study groups and their properties by representing them as a group of matrices, which is significantly more accessible than a generic group. This approach has been very fruitful in developing our understanding of groups over the last century and, among other applications, allowed for a proper description of elementary constituents of nature. This module will provide a rigorous introduction to the main ideas and notions of groups and their representations, including representations of finite groups and Lie groups. It will also have a strong computational strand: a large part of the module will be devoted to explicit computations of representations and character tables.

Study abroad

An opportunity for an amazing experience, which will help make you stand out from the crowd. With more and more companies working internationally, experience of living in another country can make a great impression on future employers.

This course offers you the opportunity to enhance your study and CV with a sandwich year abroad. The University has partnerships with over 150 universities around the world, including the USA, Canada, Asia, Africa, Australia, South America and closer to home in Europe.

If you study abroad between your second and third year of study, you’ll pay no tuition fee to the partner university and no tuition fee to us either. We’ll ask you to make your decision in your second year, so there is plenty of time to think about it.

Find out more about Study abroad opportunities

Please note Erasmus+ funding is only available until May 2023. For students starting their course in September 2022 and wishing to study abroad in 2023-24 or 2024-25, please refer to the Turing Scheme.
Work placement

Graduate with invaluable work experience alongside your degree and stand out from the crowd.

This course offers you the opportunity to enhance your study and CV with a work placement sandwich year. It’s a chance to explore career possibilities, make valuable contacts and gain sought after professional skills.

Our dedicated Careers and Employment team are here to help guide you through the process. Within the UK our students have worked at Glaxo-SmithKline, Roche, NHS, Warner Bros, BAE Systems.

If you take up a work placement between your second and third year of study, at the University of Hertfordshire you’ll pay no tuition fee for this year. We’ll ask you to make your decision in your second year, so there is plenty of time to think about it.

Find out more about work placements
What if I need support?

You’ll get a personal tutor to guide you through your course, all the way to graduation.
You might also want or need extra support during your time with us. Rest assured, no matter what you study, we’ve got you covered. For help with study skills, including referencing, essay writing and presentations, you’ll have access to our academic support services. You can attend workshops, 1-to-1 sessions, and online tutorials. Both our LRCs (Learning Resources Centres) run drop-in study skills sessions. And the best thing is, it’s all free.
We also offer a wide variety of support throughout your degree, from your lecturers, the School’s Maths Centre and peer support from our student proctor scheme. The Maths Support Service also provides a one to one help with your mathematical problems.

'After finishing my maths degree at University of Hertfordshire, I got a place on a graduate scheme with Kuehne and Nagel. For my first 2 years I will specialise in our oil and gas department. I’m very excited, I move to Aberdeen in March, and have to remain mobile within the UK for 2 years and then will have the opportunity to work abroad.

I am grateful to the University of Hertfordshire for many things but most notably for the discipline it has taught me. Working to deadlines, being versatile and working to my full potential even when out of my comfort zone are all skills I will never lose. The main tool I use every day is optimising fleet.

It goes without saying I would never have been considered for the job without my maths degree. The University of Hertfordshire taught me the importance of communication, and this has really contributed to the successful start to my career.'

Rachel Atherton

BSc (Hons) Mathematics

Check out our student blogs

Alumni Stories

Dr Samuel Nathan Richards

Meet Dr Samuel Nathan Richards, who has taken his degree out of this world. Samuel currently works for NASA as the Mission Director & Instrument Scientist for NASA/DLR mission: SOFIA in California.

Read more stories Find out more about this course

Current job role	Mission Director & Instrument Scientist for NASA/DLR mission: SOFIA
Year of graduation	2012
Course of study	BSc (Hons) Astrophysics with Sandwich Year

Global opportunities

Samuel currently works as the Mission Director & Instrument Scientist for the SOFIA mission, based in Palmdale, California at the Stratospheric Observatory for Infrared Astronomy. Nathan has worked toward this role since completing his degree and a PhD in Astrophysics at the University of Sydney, Australia.

He says, 'I would not be where I am without the opportunities that were available while studying at the University of Hertfordshire. From extracurricular projects, to connections with other world ranking universities. I'm thankful to the University for its guidance and support that kick-started my career.'

Samuel decided to study at the University after seeing a promo video in sixth-form that featured the Bayfordbury Observatory. He says, 'When I discovered how strong the University's Astronomy department was, I felt that this was an environment that I could thrive in.'

'The lecturers were world-class, active astronomers, so each class was dynamic to the ever-changing knowledge of their respective fields of research. Their willingness to accept keen students for extracurricular research projects gave me early first-hand experience of the career I was about to launch myself into. Their international connections opened a path for me to do a research year at the University of Sydney, where I would later return to complete a PhD!'

Just the beginning

Pursuing a career in astronomy is highly competitive but incredibly exciting. Opportunities in these industries are truly global and roles are very diverse. 'I didn't know I'd end up working at NASA, but I took all opportunities as they arose.' Samuel encourages new and current students to do the same. 'Find what you enjoy and do that, over money, status and fame. There are many routes to where I am now, my colleagues come from very different backgrounds: astronomy, electrical and mechanical engineering and computer science, and that is just within my role, let alone all the other roles under NASA's umbrella.'

'I'm still learning, developing and taking on new opportunities!'

Alumni Stories

Heather Tymms

Meet Institute of Mathematics prize-winner Heather, who loved her time at Herts and was determined not to let her sight-loss become a barrier to getting fully involved with student life and achieving a first-class degree.

Read more stories BSc (Hons) Mathematics

Current job role	Data Science and Analytics Advisor for GHD
Year of graduation	2022
Course of study	BSc (Hons) Mathematics with Placement Year

Studying at Herts with a disability

Heather hadn’t planned to go to university straight after A-Levels as she lacked the confidence. However six years ago she lost the majority of her sight and wanted to find her independence again. This was when she decided she needed a challenge and a new qualification. Her journey has led her to achieving a first-class degree in Mathematics, winning a school prize from the Institute of Mathematics and its Applications.

Heather says, ‘I can’t believe how far I have come. I have grown so much, and the future is brighter than I ever imagined it to be. When I started at Herts I would never have dreamt of being able to commute to London. Herts has given me the confidence to achieve more and provided me with the skills and ambition I needed to equip myself for a professional career in a fascinating sector!’

Heather chose to study at Herts as it was her local university and because she knew she would be able to get the support she needed.

‘Being new to having a disability, I needed some extra help and guidance along the way. The Wellbeing Team at Herts provided me with lots of support and resources. Before I started, I was taken on a tour to familiarise myself with the campus so I could learn the best routes between my lectures. This was very useful, as I can get anxious in new places. I also had help in the lectures because I couldn’t see the board! My lecturers were very accommodating and changed timetabled classrooms to improve access for me if required. I was able to claim the Disabled Students' Allowance, which enabled me to buy a specialist laptop with assistive technology and a magnifier.’

‘I stayed closely connected with my lecturers and the Wellbeing Team through my studies, and I was able to help improve the experience of other disabled students on campus. For example, working with university staff on signage and communication around building sites to enhance safety measures. The university staff were always happy to help improve the safety of all their students.’

‘I really benefited from the support I received from my school careers advisor. Through this service, I had help to secure both a placement and graduate job. I received expert practical advice to help me apply for jobs, they helped improve my confidence with job interviews, and showed how I could disclose my disability to employers in a covering letter.’

Life at Herts

Heather had a brilliant student experience and got involved with lots of extra-circular activities.

‘I really enjoyed my course, I found the lecturers extremely friendly, knowledgeable, and approachable, something which I really valued. I also enjoyed meeting and working with people from all different backgrounds. Herts is a truly diverse and inclusive place to study, and I benefited from collaborating with so many different people.

‘My favorite place on campus was the library. It has such a good atmosphere, and this was where I could concentrate on course work with friends.’

‘I also got involved with the Physics, Astronomy and Maths Society (PAMsoc) and in my final year, I was the society chair. Through PAMsoc activities I was able to learn and make friends with like-minded people, enriching my student experience. We did quizzes, pub nights, discussion groups, and invited our lecturers to speak to us about their personal career paths and the cutting-edge research they are doing.’

Heather’s future career aspirations

Heather is passionate about Maths and says, ‘You can do so many different things with a Maths degree, and not just teaching. You learn transferable skills, critical thinking, elements of computer science, and physics.’

‘I was introduced to the data sector in my placement year at Sainsbury's Digital, where I got to work on interesting projects like using data analysis to improve the experience of customers at the supermarket checkout. I now work for an Engineering Consultancy, GHD, a company who are committed to solving global challenges in the areas of water, energy and urbanisation, values which align to my own. I do a job that I love using data models and python, skills learnt on my course.’

‘I do miss academia sometimes and I may like to do further study in the future.’

Heather’s advice for other students

‘At Herts, you can learn about your chosen subject, but also learn about yourself. Make sure you take the time to reflect and understand both you and your passion throughout your studies and take every opportunity you can. Say yes to new things but know your own limit and don’t burn yourself out. At Herts, there is always support available to you, so seek out help if you need it.’

What's next for my career?

Britain has a national shortage of mathematics graduates, so once you graduate you’ll be highly valued and able to apply your skills to an exceptionally wide range of careers. A small selection of careers that our previous graduates have pursued are financial consultants, business analysts, engineering consultants, programmers, statisticians, credit analysts, meteorologists, environmental analysts, teachers, actuaries and many more. The number of people working in jobs requiring numerical ability has been steadily rising in the UK in recent years. In the world of employment, maths graduates are in high demand for their skills in problem-solving, logical thinking and their ability to understand and interpret data. Recent maths graduates from the University of Hertfordshire have gone on to exciting careers in actuarial, finance, statistics and data science, IT, business analysis, teaching and many more.

These careers are also well paid. According to data from the government’s Longitudinal Education Outcomes (LEO) Data Analysis, the University of Hertfordshire is ranked 16th (out of 64 universities) for the highest quartile earnings for maths graduates five years after graduating.
View our Alumni profiles

Dr Samuel Nathan Richards Heather Tymms

Course fact sheets
BSc (Hons) Mathematics	Download
BSc (Hons) Mathematics	Download

Programme specifications
BSc (Hons) Mathematics	Download
BSc (Hons) Mathematics	Download

Additional information
Sandwich placement or study abroad year	Optional
Applications open to international and EU students	Yes
Course length	Full Time, 3 Years Part Time, 5 Years Sandwich, 4 Years
Location	University of Hertfordshire, Hatfield

International/EU applicants without pre-settled status in the UK

Apply through our international/EU application portal

Home and EU applicants with pre-settled/settled status in the UK

Apply using the links below:

2023

Start Date	End Date	Link
28/09/2023	20/05/2024	Apply online (Full Time)
28/09/2023	20/05/2024	Apply online (Part Time)
28/09/2023	20/05/2024	Apply online (Full Time/Sandwich)
28/09/2023	20/05/2024	Apply online (Full Time/Sandwich)

2024

Start Date	End Date	Link
28/09/2024	20/05/2025	Apply online (Full Time)
28/09/2024	20/05/2025	Apply online (Part Time)
28/09/2024	20/05/2025	Apply online (Full Time/Sandwich)
28/09/2024	20/05/2025	Apply online (Full Time/Sandwich)

Fees and funding
Fees 2023
UK Students

Full time
- £9250 for the 2023/2024 academic year
Part time
- £1155 per 15 credits for the 2023/2024 academic year
EU Students

Full time
- £14750 for the 2023/2024 academic year
Part time
- £1845 per 15 credits for the 2023/2024 academic year
International Students

Full time
- £14750 for the 2023/2024 academic year
Part time
- £1845 per 15 credits for the 2023/2024 academic year
*Tuition fees are charged annually. The fees quoted above are for the specified year(s) only. Fees may be higher in future years, for both new and continuing students. Please see the University’s Fees and Finance Policy (and in particular the section headed “When tuition fees change”), for further information about when and by how much the University may increase its fees for future years.

View detailed information about tuition fees

Read more about additional fees in the course fact sheet

Other financial support

Find out more about other financial support available to UK and EU students

Living costs / accommodation

The University of Hertfordshire offers a great choice of student accommodation, on campus or nearby in the local area, to suit every student budget.

View detailed information about our accommodation

BSc (Hons) Mathematics

Key information

Typical offer:

Fees:

UCAS code: G100

Institute code: H36

Study abroad option

Work placement option

Additional requirements

Why choose this course?

What's the course about?

Your main campus is College Lane

What will I study?

Check out our student blogs

Student Blogs

My typical uni day

Student Blogs

Guide to the mathematics facilities

Student Blogs

Why I chose herts

Student Blogs

Alumni Stories

Meet Dr Samuel Nathan Richards, who has taken his degree out of this world. Samuel currently works for NASA as the Mission Director & Instrument Scientist for NASA/DLR mission: SOFIA in California.

Global opportunities

Just the beginning

Alumni Stories

Meet Institute of Mathematics prize-winner Heather, who loved her time at Herts and was determined not to let her sight-loss become a barrier to getting fully involved with student life and achieving a first-class degree.

Studying at Herts with a disability

Life at Herts

Heather’s future career aspirations

Heather’s advice for other students

International/EU applicants without pre-settled status in the UK

Home and EU applicants with pre-settled/settled status in the UK

2023

2024

Fees 2023

UK Students

Full time

Part time

EU Students

Full time

Part time

International Students

Full time

Part time

Other financial support

Living costs / accommodation

Your main campus is College Lane  