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Course overview

About statistics at the University of Nottingham

Statistics plays an essential role in data analytics, healthcare modelling and artificial intelligence. On this accredited degree, you will learn the fundamentals of statistics and data analysis. You'll study advanced techniques in probability and uncertainty modelling. You'll also explore core areas of applied statistics.

What you'll study

You can tailor your choice of optional modules to suit your interests and career plans. You can even choose subjects, such as a language, that will broaden your skills and enhance your CV further.

The Professional Skills for Mathematicians module will teach you valuable transferable skills for any career. Group project work will improve your communication skills and you'll learn to write up and report on your work in a technical and meaningful way.

How you will learn

Our lecturers are experts in data analysis and modelling. You'll learn from them through a combination of lectures, problem classes and tutorials. There's the opportunity to put the statistical and probability theory you've learnt into practice. Working in our computer labs will give you hands-on experience of using statistical software.

You can expand your skills even further with a work placement. Alternatively you may choose to spend time overseas with a semester abroad.

Why choose this course?

  • Accredited by the Institute of Mathematics & its Applications
  • Study abroad in countries such as Australia, Canada or the USA
  • Paid research internship opportunities
  • Peer-Assisted Study Support (PASS) run by like-minded maths students
  • Optional work placement year available

Entry requirements

All candidates are considered on an individual basis and we accept a broad range of qualifications. The entrance requirements below apply to 2022 entry.

UK entry requirements
A level A*AA/AAA/A*AB
Required subjects

At least A in A level mathematics. Required grades depend on whether A/AS level further mathematics is offered.

IB score IB 36; 6 in maths at Higher Level

A level

Standard offer

A*AA including A* Mathematics

or

AAA including Mathematics and Further Mathematics

or

AAA including Mathematics, plus A in AS Further Mathematics

or

A*AB including A*A in Mathematics and Further Mathematics

A level General Studies, Critical Thinking and Citizenship Studies are not accepted.

GCSEs

English 4 (C) (or equivalent)

University admissions tests

STEP/MAT/TMUA is not required but may be taken into consideration when offered.

Contextual offers

A Levels - AAB including A in Mathematics or Further Mathematics

This type of offer is given to students who meet our contextual admissions or elite athlete criteria.

Find out more about contextual offers at University of Nottingham

Alternative qualifications

In all cases we require applicants to have at least the equivalent of A level Mathematics, so we typically only accept alternative qualifications when combined with an appropriate grade in A level Mathematics.

Foundation progression options

If you don't meet our entry requirements there is the option to study the Engineering and Physical Sciences Foundation Programme. If you satisfy the progression requirements, you can progress to any of our mathematics courses.

There is a course for UK students and one for EU/international students.

Learning and assessment

How you will learn

Teaching methods

  • Computer labs
  • Lectures
  • Tutorials
  • Problem classes

How you will be assessed

You will be given a copy of our marking criteria which provides guidance on how your work is assessed. Your work will be marked in a timely manner and you will receive regular feedback. The pass mark for each module is 40%.

Your final degree classification will be based on marks gained for your second and subsequent years of study. Year two is worth 33% with year three worth 67%.

Assessment methods

  • Coursework
  • Group project
  • Poster presentation
  • Written exam

Contact time and study hours

The majority of modules are worth 10 or 20 credits.  You will study modules totalling 120 credits in each year. As a guide one credit equates to approximately 10 hours of work. During the first year, you will typically  spend approximately:

  • 12 hours a week in lectures
  • 4 hours a week in problem classes
  • 1 hour each week in tutorials with your personal tutor
  • 1 hour a week in computing workshops across the Autumn and Spring terms
  • 1 hour each fortnight in student-led academic mentoring Peer-Assisted Study Support (PASS)

You can attend optional drop-in sessions each week up to a maximum of three hours and the remaining time will be spent in independent study.

In later years, you are likely to spend approximately 12 hours per week in lectures subject to the modules chosen.

During term time in your first year you will meet with your personal tutor every week in groups of five to six students to run through core topics. Lectures in the first two years often include at least 200 students but class sizes are much more variable in the third year subject to module selection.

Core modules are typically delivered by a mixture of Professors, Associate Professors and Lecturers, supported by PhD students in problem classes and computer lab sessions.

Study abroad

You can apply to spend a period of time studying abroad (usually one semester) through the University-wide exchange programme.

Students who choose to study abroad are more likely to achieve a first-class degree and earn more on average than students who did not (Gone International:Rising Aspirations report 2016/17).

Benefits of studying abroad

  • Explore a new culture
  • A reduction in tuition fee of up to 30% for the year in which you study abroad
  • Improve your communication skills, confidence and independence

Countries you could go to:

  • Australia
  • Canada
  • China (teaching is in English)
  • France
  • Germany
  • Italy
  • New Zealand
  • Singapore (teaching is in English)
  • Spain
  • USA

To study abroad you need to achieve a 60% average mark at the time of application. A good academic reference and personal statement  should be provided as part of the application process.

The marks gained overseas will count back to your Nottingham degree programme.

Year in industry

A placement year can improve your employability.

You can apply to do a placement year between years two and three. This would add an extra year to your degree. You'll pay a reduced tuition fee for this year.

Although it is your responsibility to find a placement, you'll have help from the school and the Careers and Employability Service. It could be in the UK or abroad. While on placement, you'll be supported by a Placement Tutor.

If you are interested in spending a year in industry as part of your named degree, find out more at  BSc Mathematics with a Year in Industry

Modules

Alongside core modules, you will also have the chance to choose some modules, such as a language, from outside of mathematics. You can choose up to 20 credits.

Core modules

Analytical and Computational Foundations

The idea of proof is fundamental to all mathematics. We’ll look at mathematical reasoning using techniques from logic to deal with sets, functions, sequences and series.

This module links directly with your study in Calculus and Linear Mathematics. It provides you with the foundations for the broader area of Mathematical Analysis. This includes the rigorous study of the infinite and the infinitesimal.

You will also learn the basics of computer programming. This will give you the chance to use computational algorithms to explore many of the mathematical results you’ll encounter in your core modules.

Your study will include:

  • propositional and predicate logic; set theory, countability
  • proof: direct, indirect and induction
  • sequences and infinite series (convergence and divergence)
  • limits and continuity of functions
  • programming in Python
Applied Mathematics

How can the flight-path of a spacecraft to another planet be planned? How many fish can we catch without depleting the oceans? How long would it take a lake to recover after its pollution is stopped?

The real world is often too complicated to get exact information. Instead, mathematical models can help by providing estimates. In this module, you’ll learn how to construct and analyse differential equations which model real-life applications.

Your study will include:

  • modelling with differential equations
  • kinematics and dynamics of moving bodies
  • Newton’s laws, balance of forces
  • oscillating systems, springs, simple harmonic motion
  • work, energy and motion

You'll be able to expand on these techniques later in your degree through topics such as:

  • black holes, quantum theory
  • fluid and solid mechanics
  • mathematical medicine and biology
  • mathematical finance
Calculus

How do we define calculus? How is it used in the modern world?

The concept can be explained as the mathematics of continuous change. It allows us to analyse motion and change in time and space.

You will cover techniques for differentiating, integrating and solving differential equations. You’ll learn about the theorems which prove why calculus works. We will explore the theory and how it can be applied in the real world.

Your study will include:

  • functions: limits, continuity and differentiability, rules of differentiation
  • techniques for integration, fundamental theorem of calculus
  • solution of linear and nonlinear differential equations
  • multivariate calculus, Lagrange multipliers, stationary points
  • multiple integrals, changes of variables, Jacobians

This module gives you the mathematical tools required for later modules which involve modelling with differential equations. These include:

  • mathematical physics
  • mathematical medicine and biology
  • scientific computation
Linear Mathematics

Vectors, matrices and complex numbers are familiar topics from A level Mathematics and Further Mathematics. Their common feature is linearity. A linear mathematical operation is one which is compatible with addition and scaling.

As well as these topics you’ll study the concept of a vector space, which is fundamental to later study in abstract algebra. We will also investigate practical aspects, such as methods for solving linear systems of equations.

The module will give you the tools to analyse large systems of equations that arise in mathematical, statistical and computational models. For example, in areas such as:

  • fluid and solid mechanics
  • mathematical medicine and biology
  • mathematical finance

Your study will include:

  • complex numbers, vector algebra and geometry
  • matrix algebra, inverses, determinants
  • vector spaces, subspaces, bases
  • linear systems of simultaneous equations, Gaussian elimination
  • eigenvalues and eigenvectors, matrix diagonalisation
  • linear transformations, inner product spaces
Probability

What is the importance of probability in the modern world?

It allows us to assess risk when calculating insurance premiums. It can help when making investment decisions. It can be used to estimate the impact that government policy will have on climate change or the spread of disease.

We will look at the theory and practice of discrete and continuous probability. Your study will include:

  • sample spaces, events and counting problems
  • conditional probability, independence, Bayes’ theorem
  • random variables, expectation, variance
  • discrete and continuous probability distributions
  • multivariate random variables
  • sums of random variables, central limit theorem

These topics will help you prepare for later modules in:

  • probability methods
  • stochastic models
  • uncertainty quantification
  • mathematical finance
Statistics

Statistics is concerned with methods for collecting, organising, summarising, presenting and analysing data. It enables us to draw valid conclusions and make reasonable decisions based on the analysis. It can be used to answer a diverse range of questions such as:

  • Do the results of a clinical trial indicate that a new drug works?
  • Is the HS2 rail project likely to be cost-effective?
  • Should a company lend money to a customer with a given credit history?

In this module you’ll study statistical inference and learn how to analyse, interpret and report data. You’ll learn about the widely used statistical computer language R.

Your study will include:

  • exploratory data analysis
  • point estimators, confidence intervals
  • hypothesis testing
  • correlation, statistical inference
  • linear regression, chi-squared tests

These first-year topics give you the foundations for later related modules in:

  • statistical models and methods
  • data analysis and modelling
  • statistical machine learning

Optional modules

These modules account for the 20 credits from within mathematics that you can choose. Alternatively you can select modules from outside of the school.

Foundations of Pure Mathematics

Pure mathematics at university is typically very different to the pure mathematics you've learnt at school or college. You'll use the language of sets, functions and relations to study some very abstract mathematical ideas.

In this module, we'll develop the skills of reading and writing the language of pure mathematics. You will learn techniques to build mathematical proofs in an abstract setting.

Your study will include:

  • the language of set theory
  • relations and functions
  • rational and irrational numbers
  • modular arithmetic
  • prime factorisation

These topics will provide you with the basics you need for subsequent modules in algebra, number theory and group theory.

Mathematical Structures

Groups, rings and fields are abstract structures which underpin many areas of mathematics. For example, addition of integers fits the structure of a group. However, by analysing the general concept of a group, our proofs are relevant to many other areas of mathematics.

You will build on your understanding of Foundations of Pure Mathematics. Together we will develop a deeper knowledge of abstract algebraic structures, particularly groups. This provides the foundation for subsequent modules in abstract algebra and number theory.

Your study will include:

  • symmetries
  • groups, cyclic groups, Lagrange’s theorem
  • rings and fields
  • integer arithmetic, Euclid’s algorithm
  • polynomial arithmetic, factorisation
The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on Wednesday 24 February 2021.

Combining three compulsory modules with your choice from a range of optional modules, you will continue to study statistics, probability and applied mathematics in more depth. You will also have the option to choose some modules from outside mathematics.

Core modules

Introduction to Scientific Computation

This module introduces basic techniques in numerical methods and numerical analysis which can be used to generate approximate solutions to problems that may not be amenable to analysis. Specific topics include:

  • Implementing algorithms in Matlab
  • Discussion of errors (including rounding errors)
  • Iterative methods for nonlinear equations (simple iteration, bisection, Newton, convergence)
  • Gaussian elimination, matrix factorisation, and pivoting
  • Iterative methods for linear systems, matrix norms, convergence, Jacobi, Gauss-Siedel
  • Interpolation (Lagrange polynomials, orthogonal polynomials, splines)
  • Numerical differentiation & integration (Difference formulae, Richardson extrapolation, simple and composite quadrature rules)
  • Introduction to numerical ODEs (Euler and Runge-Kutta methods, consistency, stability) 
Probability Models and Methods

This module will give you an introduction to the theory of probability and random variables, with particular attention paid to continuous random variables. Fundamental concepts relating to probability will be discussed in detail, including well-known limit theorems and the multivariate normal distribution. You will then progress onto complex topics such as transition matrices, one-dimensional random walks and absorption probabilities.

Statistical Models and Methods

The first part of this module provides an introduction to statistical concepts and methods and the second part introduces a wide range of techniques used in a variety of quantitative subjects. The key concepts of inference including estimation and hypothesis testing will be described as well as practical data analysis and assessment of model adequacy.

Optional modules

You must take a minimum of 40 and maximum of 60 credits from the following:

Complex Functions

In this module you will learn about the theory and applications of functions of a complex variable using a method and applications approach. You will develop an understanding of the theory of complex functions and evaluate certain real integrals using your new skills.

Differential Equations and Fourier Analysis

This course is an introduction to Fourier series and integral transforms and to methods of solving some standard ordinary and partial differential equations which occur in applied mathematics and mathematical physics.

The course describes the solution of ordinary differential equations using series and introduces Fourier series and Fourier and Laplace transforms, with applications to differential equations and signal analysis. Standard examples of partial differential equations are introduced and solution using separation of variables is discussed.

Introduction to Mathematical Physics
This course develops Newtonian mechanics into the more powerful formulations due to Lagrange and Hamilton and introduces the basic structure of quantum mechanics. The course provides the foundation for a wide range of more advanced courses in mathematical physics.
Mathematical Analysis

In this module you will build on the foundation of knowledge gained from your core year one modules in Analytical and Computational Foundations and Calculus. You will learn to follow a rigorous approach needed to produce concrete proof of your workings.

Modelling with Differential Equations

This course aims to provide students with tools which enable them to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations. 

Professional Skills for Mathematicians

This module will equip you with valuable skills needed for graduate employment. You will work on two group projects based on open-ended mathematical topics agreed by your group. You will also work independently to improve your communication skills and learn how to summarise technical mathematical data for a general audience. You will be provided with some commercial and business awareness and explore how to use your mathematical sciences degree for your future career.

Vector Calculus

This course aims to give students a sound grounding in the application of both differential and integral calculus to vectors, and to apply vector calculus methods and separation of variables to the solution of partial differential equations. The module is an important pre-requisite for a wide range of other courses in Applied Mathematics.

The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on

You will choose from a range of advanced optional modules. You'll also have the option to choose modules from outside of maths if you wish.

Optional modules

Applied Statistical Modelling

In this module you will build on your theoretical knowledge of statistical inference by a practical implementation of the generalised linear model. You will move on to enhance your understanding of statistical methodology including the analysis of discrete and survival data. You will also be trained in the use of a high-level statistical computer program.

Coding and Cryptography

This course provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. It also provides an introduction to to cryptography, including classical mono- and polyalphabetic ciphers as well as modern public key cryptography and digital signatures, their uses and applications.

Data Analysis and Modelling

This module involves the application of probability and statistics to a variety of practical, open-ended problems, typical of those that statisticians encounter in industry and commerce. Specific projects are tackled through workshops and student-led group activities.

The real-life nature of the problems requires students to develop skills in model development and refinement, report writing and teamwork. Students will have an opportunity to apply a variety of statistical methods and knowledge learned in previous modules.

.

Mathematical Finance

In this module the concepts of discrete time Markov chains are explored and used to provide an introduction to probabilistic and stochastic modelling for investment strategies, and for the pricing of financial derivatives in risky markets. You will gain well-rounded knowledge of contemporary issues which are of importance in research and applications.

Multivariate Analysis

This module is concerned with the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. A theme running through the module is that of dimension reduction. Key topics to be covered include: principal components analysis, whose purpose is to identify the main modes of variation in a multivariate dataset; modelling and inference for multivariate data, including multivariate regression data, based on the multivariate normal distribution; classification of observation vectors into sub-populations using a training sample; canonical correlation analysis, whose purpose is to identify dependencies between two or more sets of random variables. Further topics to be covered include factor analysis, methods of clustering and multidimensional scaling.

Optimisation

In this module a variety of techniques and areas of mathematical optimisation will be covered including Lagrangian methods for optimisation, simplex algorithm linear programming and dynamic programming. You’ll develop techniques for application which can be used outside the mathematical arena. 

Scientific Computation and Numerical Analysis

You will learn how to use numerical techniques for determining the approximate solution of ordinary and partial differential equations where a solution cannot be found through analytical methods alone. You will also cover topics in numerical linear algebra, discovering how to solve very large systems of equations and find their eigenvalues and eigenvectors using a computer.

Statistical Inference

This course is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference. 

Topics such as sufficiency, estimating equations, likelihood ratio tests and best-unbiased estimators are explored in detail. There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

In Bayesian inference, there are three basic ingredients: a prior distribution, a likelihood and a posterior distribution, which are linked by Bayes' theorem. Inference is based on the posterior distribution, and topics including conjugacy, vague prior knowledge, marginal and predictive inference, decision theory, normal inverse gamma inference, and categorical data are pursued.

Common concepts, such as likelihood and sufficiency, are used to link and contrast the two approaches to inference. You will gain experience of the theory and concepts underlying much contemporary research in statistical inference and methodology.

Stochastic Models

In this module you will develop your knowledge of discrete-time Markov chains by applying them to a range of stochastic models. You will be introduced to Poisson and birth-and-death processes and then you will move onto more extensive studies of epidemic models and queuing models with introductions to component and system reliability.

Time Series Analysis

This module will provide a general introduction to the analysis of data that arise sequentially in time. Several commonly-occurring models will be discussed and their properties derived, along with methods for model identification for real-time series data. You will develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values. You will also gain experience of using a statistical package and interpreting its output.

The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on
  • Become a PASS leader in your second or third year. Teaching first-year students reinforces your own mathematical knowledge. It develops communication, organisational and time management skills which can help to enhance your CV when you start applying for jobs
  • The Nottingham Internship Scheme provides a range of  paid work experience opportunities and internships throughout the year
  • The Nottingham Advantage Award is our free scheme to boost your employability. There are over 200 extracurricular activities to choose from
  • Nottingham MathSoc offers students a chance to enjoy various activities with like minded individuals also studying mathematics. Examples of events are balls, river cruises, sport and other social activities.

Fees and funding

UK students

£9,250
Per year

International students

To be confirmed in 2021*
Keep checking back for more information
*For full details including fees for part-time students and reduced fees during your time studying abroad or on placement (where applicable), see our fees page.

If you are a student from the EU, EEA or Switzerland starting your course in the 2022/23 academic year, you will pay international tuition fees.

This does not apply to Irish students, who will be charged tuition fees at the same rate as UK students. UK nationals living in the EU, EEA and Switzerland will also continue to be eligible for ‘home’ fee status at UK universities until 31 December 2027.

For further guidance, check our Brexit information for future students.

Additional costs

As a student on this course, you should factor some additional costs into your budget, alongside your tuition fees and living expenses.

Books

You should be able to access most of the books you’ll need through our libraries, though you may wish to purchase your own copies.

Printing

Due to our commitment to sustainability, we don’t print lecture notes but these are available digitally. You are welcome to buy print credits if you need them. It costs 4p to print one black and white page.

Study abroad

If you study abroad, you need to consider the travel and living costs associated with your country of choice. This may include visa costs and medical insurance. 

Equipment

Personal laptops are not compulsory as we have computer labs that are open 24 hours a day but you may want to consider one if you wish to work at home.  

Scholarships and bursaries

We offer an international orientation scholarship of £2,000 to the best international (full-time, non EU) applicants on this course.

It will be paid at most once for each year of study. If you repeat a year for any reason, the scholarship will not be paid for that repeated year. The scholarship is awarded in subsequent years to students who perform well academically (at the level of a 2:1 Hons degree or better at the first attempt). 

The scholarship will be paid in December each year provided you have:

  • completed your registration
  • been recorded as a student on a relevant course in the 1 December census
  • paid the first instalment of your fee

Home students*

Over one third of our UK students receive our means-tested core bursary, worth up to £1,000 a year. Full details can be found on our financial support pages.

* A 'home' student is one who meets certain UK residence criteria. These are the same criteria as apply to eligibility for home funding from Student Finance.

Careers

Mathematics is a broad and versatile subject leading to many possible careers. Our graduates are helping to shape the future in many sectors including banking and finance, business consulting and management. Other employment sectors include education, local and central government and some graduates pursue a career in mathematical research.

They have jobs such as:

  • Actuary
  • Graduate analyst
  • IT consultant
  • Software engineer
  • Maths tutor

As this is a relatively new course, our students registered on the degree are yet to graduate.

Average starting salary and career progression

83.8% of undergraduates from the School of Mathematical Sciences secured graduate level employment or further study within 15 months of graduation. The average annual salary for these graduates was £26,985.*

* HESA Graduate Outcomes 2020. The Graduate Outcomes % is derived using The Guardian University Guide methodology. The average annual salary is based on graduates working full-time within the UK.

Studying for a degree at the University of Nottingham will provide you with the type of skills and experiences that will prove invaluable in any career, whichever direction you decide to take.

Throughout your time with us, our Careers and Employability Service can work with you to improve your employability skills even further; assisting with job or course applications, searching for appropriate work experience placements and hosting events to bring you closer to a wide range of prospective employers.

Have a look at our careers page for an overview of all the employability support and opportunities that we provide to current students.

The University of Nottingham is consistently named as one of the most targeted universities by Britain’s leading graduate employers (Ranked in the top ten in The Graduate Market in 2013-2020, High Fliers Research).

Institute of Mathematics and its Applications

This programme 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 competences to those specified by the Quality Assurance Agency (QAA) for taught masters degrees.

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Disclaimer

This online prospectus has been drafted in advance of the academic year to which it applies. Every effort has been made to ensure that the information is accurate at the time of publishing, but changes (for example to course content) are likely to occur given the interval between publishing and commencement of the course. It is therefore very important to check this website for any updates before you apply for the course where there has been an interval between you reading this website and applying.