Mathematics and Statistics (BSc) - Course full
Mathematics enhances your ability to think clearly, learn new ideas quickly, manipulate precise and intricate concepts, follow complex reasoning, construct logical arguments and expose dubious ones. The demand for mathematical statisticians has expanded so rapidly in recent years that both within and outside the academic world there is a severe shortage of well-qualified people.
This degrees enables you to specialise in both pure mathematics and statistics, offering flexibility and a wide choice of options in Computing, Operational Research and all the other topics available to Mathematics students.
The BSc and MMathStat are the same for the first two years of study, making it easy to reconsider your preference in the second year. Differences become apparent in the final years, with the MMathStat degree offering a supervised research project and the possibility to specialise in areas such as advanced statistics, biostatistics, computational statistics, actuarial and financial mathematics, and probability.
You will learn through a combination of lectures, small-group tutorials and practical sessions based in the Department's well-equipped undergraduate computing laboratory. A central part of learning in Mathematics and Statistics is problem solving. We encourage and guide students in tackling a variety of theoretical exercises and computing tasks.
Core first and second-year modules covering probability, sets, mathematical statistics, linear algebra and modelling build a solid foundation of essential mathematical and statistical knowledge and skills. You’ll also have flexibility to choose some options. In your third year, you will select half of your modules from Statistics and half from further options available in Statistics, Mathematics and other selected Departments.
The curriculum is divided up into modules consisting of lectures and assessments, which are often supplemented by smaller group teaching such as tutorials, supervisions and computer labs.
Homework assignments are often biweekly and the expectation is that students work hard trying to tackle problems covering a range of levels of difficulty.
Contact time is around 15 hours a week.
Class sizes for core modules are around 220 students, though can be higher in some core modules joint with Mathematics degree students. Size of classes for optional modules varies; it can be as large as in core modules but it can be as low as 15 in specific topics in higher years. Support classes usually consist of 15 students.
You will be assessed by a combination of closed and open-book examinations, continuous assessment and project work, depending on your options. The first year counts 10%, the second year 30% and the third year 60% towards the final BSc degree mark.
We support student mobility through study abroad programmes and all students have the opportunity to apply for an intercalated year abroad at one of our partner universities. The Study Abroad Team based in the Office for Global Engagement offers support for these activities, and the Department's dedicated Study Abroad Co-ordinator can provide more specific information and assistance.
You may additionally choose to spend an ‘intercalated’ year in an approved industry, business or university between your last two years at Warwick.
A level: A*AA to include A* in Mathematics and A in Further Mathematics or A*A*A + AS level A to include A* in Mathematics and A in AS level Further Mathematics or A*A*A* to include Mathematics or AAA to include Mathematics + 2 in STEP paper
IB: 38 overall to include 7 in Higher Level Mathematics or 38 overall to include 6 in Higher Level Mathematics and 2 in any STEP paper
Additional requirements: You will also need to meet our English Language requirements.
Contextual data and differential offers
Warwick may make differential offers to students in a number of circumstances. These include students participating in the Realising Opportunities programme, or who meet two of the contextual data criteria. Differential offers will be one or two grades below Warwick’s standard offer (to a minimum of BBB).
- Warwick International Foundation Programme (IFP)
All students who successfully complete the Warwick IFP and apply to Warwick through UCAS will receive a guaranteed conditional offer for a related undergraduate programme (selected courses only). For full details of standard offers and conditions visit the IFP website.
- We welcome applications from students with other internationally recognised qualifications. For more information please visit the international entry requirements page.
Taking a gap year
Applications for deferred entry welcomed.
We do not typically interview applicants. Offers are made based on your UCAS form which includes predicted and actual grades, your personal statement and school reference.
Linear algebra addresses simultaneous linear equations. You will learn about the properties of vector space, linear mapping and its representation by a matrix. Applications include solving simultaneous linear equations, properties of vectors and matrices, properties of determinants and ways of calculating them. You will learn to define and calculate eigenvalues and eigenvectors of a linear map or matrix. You will have an understanding of matrices and vector spaces for later modules to build on.
Analysis is the rigorous study of calculus. In this module there will be considerable emphasis throughout on the need to argue with much greater precision and care than you had to at school. With the support of your fellow students, lecturers and other helpers, you will be encouraged to move on from the situation where the teacher shows you how to solve each kind of problem, to the point where you can develop your own methods for solving problems. By the end of the year you will be able to answer interesting questions like, what do we mean by `infinity'?
Sets and Numbers
It is in its proofs that the strength and richness of mathematics is to be found. University mathematics introduces progressively more abstract ideas and structures, and demands more in the way of proof, until most of your time is occupied with understanding proofs and creating your own. Learning to deal with abstraction and with proofs takes time. This module will bridge the gap between school and university mathematics, taking you from concrete techniques where the emphasis is on calculation, and gradually moving towards abstraction and proof.
Statistical Laboratory 1
If you’re studying ST115 (Introduction to Probability) or ST111/2 (Probability), this course supports your understanding of statistical analysis. You’ll lay foundations for applying mathematical probability, and learn to calculate using probabilities and expectations. You’ll become familiar with the R software package for exploratory data analysis, and gain experience of elementary simulation techniques on real data, and, using visualisations, be able to propose probabilistic models for simple data sets. You’ll also cover sampling technique (standard discrete and continuous distributions – Bernoulli, geometric, Poisson, Gaussian and gamma) and learn generic sampling methods for univariate distributions, preparing you to move on to ST221 (Linear Statistical Modelling).
Introduction to Probability
Following modules MA137 and MA138, this builds your knowledge by introducing key notions of probability and developing your ability to calculate using probabilities and expectations. You’ll experiment with random outcomes through the notion of events and their probability, and look at examples of discrete and continuous probability spaces. You’ll learn counting methods (inclusion–exclusion formula and binomial co-efficients), and study theoretical topics including conditional probability and Bayes’ Theorem. Later, you’ll scrutinise important families of distributions and the distribution of random variables, and the light this shines on the properties of expectations. Finally, you’ll examine mean, variance and co-variance of distribution, through Chebyshev's and Cauchy-Schwartz inequalities.
Want to think like a mathematician? This practical, problem-solving module is for you. Building on your A-level knowledge, you’ll develop a deeper understanding of mathematical concepts and relations, using problem-solving techniques such as visualisation and pattern exploration. Using concrete examples from counting, combinatorics, calculus, geometry and inequalities, you will learn to express mathematical concepts clearly and precisely and enhance your mathematical and logical reasoning and communication skills. By the end of the module, you’ll be able to comprehend, construct, visualise and present a coherent mathematical argument.
Norms, Metrics and Topologies
Roughly speaking, a metric space is any set provided with a sensible notion of the “distance” between points. The ways in which distance is measured and the sets involved may be very diverse. For example, the set could be the sphere, and we could measure distance either along great circles or along straight lines through the globe; or the set could be New York and we could measure distance “as the crow flies” or by counting blocks. This module examines how the important concepts introduced in first year Mathematical Analysis, such as convergence of sequences and continuity of functions, can be extended to general metric spaces. Applying these ideas we will be able to prove some powerful and important results, used in many parts of mathematics.
Mathematical Analysis III
This module considers integration and the convergence of sequences and series of functions. The idea behind integration is to compute the area under a curve. This involves taking a limit, and the deeper properties of integration require a precise and careful analysis of this limiting process. In this module you will learn how to prove that every continuous function can be integrated, and the fundamental theorem of calculus which gives the precise relation between integration and differentiation. You will learn how integration can be applied to define some of the basic functions of analysis and to establish their fundamental properties. Furthermore, many functions can be written as limits of sequences of simpler functions (or as sums of series): thus a power series is a limit of polynomials, and a Fourier series is the sum of a trigonometric series with coefficients given by certain integrals. You will learn methods for deciding when a function defined as the limit of a sequence of other functions is continuous, differentiable, integrable, and for differentiating and integrating this limit.
The concept of a stochastic (developing randomly over time) process is a useful and surprisingly beautiful mathematical tool in economics, biology, psychology and operations research. In studying the ideas governing sequential stochastic processes, you’ll learn about Markov chains, which use conditional probability for a widely applicable family of random processes; random walks – the building blocks for constructing other processes as well as being important in their own right – and renewal theory, for processes that ‘begin all over again’. Your understanding will extend to notions of behaviour, including transience, recurrence and equilibrium, and you will apply these ideas to problems in probability theory.
Following the algebraic modules MA106 and MA137, you’ll gain expertise in the everyday techniques of probability and statistics essential to your continued study. You’ll gain a grounding in optimisation, convergence, regression and best approximation. By the end of your course, expect to apply multivariate calculus (integration, calculation of under-surface volumes, variable formulae and Fubini’s Theorem) and to use partial derivatives, critical points and extrema, and to understand constrained optimisation. You’ll work on eigenvalues and eigenvectors, diagonalisation, characteristic polynomials, constant co-efficient differential equations, and orthogonal bases and orthonormalisation. You’ll also study convergence and continuity in metric spaces to advance your mathematical thinking.
Mathematical Statistics Part A
If you have already completed ST115, on this module, you’ll have the opportunity to acquire the knowledge you need to study more advanced topics in probability. You’ll study discrete, continuous and multivariate distributions in greater depth, and also learn about Jacobian transformation formula, conditional and multivariate Gaussian distributions, and the related distributions Chi-squared, Student’s and Fisher. In the second part, you’ll move on to more advanced topics, including moment-generating functions for random variables, convergence, and the Law of Large Number and the Central Limit Theorem.
Mathematical Statistics Part B
If you’ve completed Part A, this second-term module is your next step, where you’ll study the major ideas behind statistical inference, with an emphasis on likelihood methods of estimation, repeated sampling, and testing. You’ll learn to apply important models (such as the parametrised statistical model), hypothesis tests, linear models, estimators, and the Chi-squared goodness of fit. You’ll spend time calculating sampling distributions (Fisher’s theorem), and confidence intervals, and understand the principles of data reduction, point estimation and the notion of sufficient statistics. You’ll also become familiar with asymptotic normality and contingency tables, giving you a very firm foundation for your future engagement in advanced mathematical statistics.
Linear Statistical Modelling
If you’re taking modules ST115 ST218 or ST219, you’ll benefit from the study of statistical modelling on this course. Starting with an introduction to R software, you’ll learn to use this for modelling, specifically linear models, in a variety of different scenarios. You’ll scrutinise simple linear regression and distributions of estimators and residuals, before moving to multiple and polynomial regression, and learning how the study of residuals can inform your choice of model. You’ll also become acquainted with various ANOVA models and how R software can code and interpret them. Finally, you’ll gain a basic understanding of linear models for time series and frequency data.
You will select half of your modules from Statistics and half from further options available in Statistics, Mathematics and other selected departments.
Examples of optional modules/options for current students
Differential Equations; Introduction to Quantitative Economics; Geometry and Motion; Introduction to Abstract Algebra; Games, Decisions and Behaviour; Introduction to Mathematical Finance; Professional Practice of Data Analysis; Programming for Data Science.
Recent graduates have pursued job roles such as: actuaries, economists and statisticians; software developers; chartered and certified accountants; finance and investment analysts; teachers; telecommunication designers; academics.
UK firms that have employed Warwick recent graduates from Maths and Stats include: Adder Technology; Merrill Lynch; Brainlabs; Civil Service; Conduent; Darktrace; Deloitte; Department of Health; eBay; Ford Motor Company; Fore Consulting; Goldman Sachs; Government Actuaries; Investec; Jane Street Capital; KPMG; Lloyds; MBDA; Metaswitch; Met Office; Softwire; Solid Solutions; Sword Apak; Ten10; Xafinity.
Statistics graduates develop a strong range of transferable skills including excellent numerical, problem-solving and analytical abilities. These along with your ability to communicate complex ideas effectively are highly sought after by employers.
A number of students decide to continue in academia, studying for either a Statistics related Masters or PhD. Alternative study routes have included the study of Management Science & Operational Research or the PGCE teaching qualification.
Helping you find the right career
Our department has a dedicated professionally qualified Senior Careers Consultant who works within Student Careers and Skills to help you as an individual. Additionally your Senior Careers Consultant offers impartial advice and guidance together with workshops and events, tailored to our department, throughout the year. Previous examples of workshops and events include:
- Finding experience to boost your CV in Year One and Two
- Careers in Data Science and Artificial Intelligence
- Warwick careers fairs throughout the year
- Interview skills for Statistics students
- Maths and Stats Careers Fair
- Becoming an Actuary Alumni Talk
Find out more about our Careers & Skills Services here.
Bachelor of Science (BSc)
3 years full-time
28 September 2020
Location of study
University of Warwick, Coventry
Find out more about fees and funding
Additional course costs
There may be costs associated with other items or services such as academic texts, course notes, and trips associated with your course. Students who choose to complete a work placement will pay reduced tuition fees for their third year.
This information is applicable for 2020 entry.
Given the interval between the publication of courses and enrolment, some of the information may change. It is important to check our website before you apply. Please read our terms and conditions to find out more.
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