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- Mathematics and Statistics BSc (GG13)
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## Discover more about our Mathematics and Statistics BSc at Warwick

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- GG13
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- Bachelor of Science (BSc)
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- 3 years full-time
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- 26 September 2022
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- Department of Statistics
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- University of Warwick
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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.

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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.

These degrees enable you to specialise in both pure mathematics and statistics. They offer flexibility and a wide choice of options in Computing, Operational Research and all the other topics available to Mathematics students.

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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 will 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.

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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.

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- Class sizes vary from 15 students for selected optional modules up to 350 students for some core modules. Support classes usually consist of 15 students.
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- Contact time is around 15 hours a week.
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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.

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### Study abroad

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 Student Opportunity offers support for these activities, and the Department's dedicated Study Abroad Co-ordinator can provide more specific information and assistance.

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## Placements and work experience

You may additionally choose to spend an 'intercalated' year in an approved industry, business or university between your last two years at Warwick.

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##### A level typical offer

A*A*A to include A* A* in Mathematics and Further Mathematics

**Or**A*AA to include A* A (in any order) in Mathematics and Further Mathematics and one of the following:

- STEP (grade 2)
- TMUA (score 6.5)

**Or**A*A*A*A to include A* A (in any order) in Mathematics and Further Mathematics

Where an applicant is unable to study A Level Further Mathematics, they may be considered with grades A*A*A* including Mathematics. Please see the Department of Statistics webpage for further information.

##### A level contextual offer

We welcome applications from candidates who meet the contextual eligibility criteria. The typical contextual offer is A*A*B, including A* in Mathematics and A* in Further Mathematics;

**or**A*AB including A*, A in Mathematics and Further Mathematics (any order), plus grade 2 in any STEP/6.5 in TMUA. See if you’re eligible.##### General GCSE requirements

Unless specified differently above, you will also need a minimum of GCSE grade 4 or C (or an equivalent qualification) in English Language and either Mathematics or a Science subject. Find out more about our entry requirements and the qualifications we accept. We advise that you also check the English Language requirements for your course which may specify a higher GCSE English requirement. Please find the information about this below.

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##### IB typical offer

39 overall to include 7 in Higher Level Mathematics 'Analysis and Approaches'

**Or**38 overall to include 6 in Higher Level Mathematics 'Analysis and Approaches' and one of the following:

- STEP (grade 2)
- TMUA (score 6.5)

**Or**38 overall to include 7 in Higher Level Mathematics 'Applications and Interpretations' and one of the following:

- STEP (grade 2)
- TMUA (score 6.5)

**Alternative offers and additional requirements:**Find out more about our typical conditional offers.

You will also need to meet our English Language requirements.

##### IB contextual offer

We welcome applications from candidates who meet the contextual eligibility criteria. The typical contextual offer is 37, including 7 in Higher Level Mathematics (‘Analysis and Approaches’ only)

**or**38 overall including 6 in Higher Level Mathematics (‘Analysis and Approaches’ only), plus 2 in any STEP/6 in TMUA. See if you’re eligible.##### General GCSE requirements

Unless specified differently above, you will also need a minimum of GCSE grade 4 or C (or an equivalent qualification) in English Language and either Mathematics or a Science subject. Find out more about our entry requirements and the qualifications we accept. We advise that you also check the English Language requirements for your course which may specify a higher GCSE English requirement. Please find the information about this below.

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We will consider Level 3 BTECs alongside two A Levels including A Level Maths.

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### Year One

###### Linear Algebra

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 1/2

Analysis is the rigorous study of calculus. In this module, there will be a 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. The module will allow you to deal carefully with limits and infinite summations, approximations to pi and e, and the Taylor series. The module also covers construction of the integral and the Fundamental Theorem of Calculus.

###### 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.

**Introduction to Statistical Modelling**

This module is an introduction to statistical thinking and inference. You’ll learn how the concepts you met from Probability can be used to construct a statistical model – a coherent explanation for data. You’ll be able to propose appropriate models for some simple datasets, and along the way you’ll discover how a function called the likelihood plays a key role in the foundations of statistical inference. You will also be introduced to the fundamental ideas of regression. Using the R software package you’ll become familiar with the statistical analysis pipeline: exploratory data analysis, formulating a model, assessing its fit, and visualising and communicating results. The module also prepares you for a more in-depth look at Mathematical Statistics in Year Two.**Probability 1**

Probability is a foundational module that will introduce you both to the important concepts in probability but also the key notions of mathematical formalism and problem-solving. Want to think like a mathematician? This module is for you. You will learn how to to express mathematical concepts clearly and precisely and how to construct rigorous mathematical arguments through examples from probability, enhancing your mathematical and logical reasoning skills. You will also develop your ability to calculate using probabilities and expectations by experimenting with random outcomes through the notion of events and their probability. You’ll learn counting methods (inclusion–exclusion formula and binomial co-efficients), and study theoretical topics including conditional probability and Bayes’ Theorem.**Probability 2**

This module continues from Probability 1, which prepares you to investigate probability theory in further detail here. Now you will look at examples of both discrete and continuous probability spaces. You’ll scrutinise important families of distributions and the distribution of random variables, and the light this shines on the properties of expectation. You’ll examine mean, variance and co-variance of distribution, through Chebyshev's and Cauchy-Schwarz inequalities, as well as the concept of conditional expectation. The module provides important grounding for later study in advanced probability, statistical modelling, and other areas of potential specialisation such as mathematical finance.### Year Two

###### Metric Spaces

A metric space is any set provided with a sensible notion of the `distance’ between points. In this module, you will examine how concepts such as convergence of sequences, continuity of functions and completeness can be extended to general metric spaces. This enables you to prove some powerful and important results, used in many parts of mathematics. Describing continuity in terms of open subsets takes you to the more general context of a topological space, where, instead of a distance, it is declared which subsets are open. You will be able to work with continuous functions, and recognise whether spaces are connected, compact or complete.

**Stochastic Processes**

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 stochastic processes, you’ll learn in detail about random walks – the building blocks for constructing other processes as well as being important in their own right, and a special kind of ‘memoryless’ stochastic process known as a Markov chain, which has an enormous range of application and a large and beautiful underlying theory. Your understanding will extend to notions of behaviour, including transience, recurrence and equilibrium, and you will apply these ideas to problems in probability theory.**Mathematical Methods for Statistics and Probability**

Following the mathematical modules in Year One, you’ll gain expertise in the application of mathematical techniques to probability and statistics. For example, you’ll be able to adapt the techniques of calculus to compute expectations and conditional distributions relating to a random vector, and you’ll encounter the matrix theory needed to understand covariance structure. You’ll also gain a grounding in the linear algebra underlying regression (such as inner product spaces and orthogonalization). By the end of your course, expect to apply multivariate calculus (integration, calculation of under-surface volumes, variable formulae and Fubini’s Theorem), to use partial derivatives, to derive critical points and extrema, and to understand constrained optimisation. You’ll also work on eigenvalues and eigenvectors, diagonalisation, orthogonal bases and orthonormalisation.**Probability for Mathematical Statistics**

If you have already completed Probability in Year One, on this module you’ll have the opportunity to acquire the knowledge you need to study more advanced topics in probability and to understand the bridge between probability and statistics. 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. You will also cover more advanced topics including moment-generating functions for random variables, notions of convergence, and the Law of Large Numbers and the Central Limit Theorem.**Mathematical Statistics**

If you’ve completed “Probability for Mathematical Statistics”, this second-term module is your next step, where you’ll study in detail the major ideas behind statistical inference, with an emphasis on statistical modelling and likelihoods. You’ll learn how to estimate the parameters of a statistical model through the theory of estimators, and how to choose between competing explanations of your data through model selection. This leads you on to important concepts including hypothesis testing, p-values, and confidence intervals, ideas widely used across numerous scientific disciplines. You’ll also discover the ideas underlying Bayesian statistics, a flexible and intuitive approach to inference which is especially amenable to modern computational techniques. Overall this module will provide you a very firm foundation for your future engagement in advanced statistics – in your final years and beyond.**Linear Statistical Modelling with R**

This module runs in parallel with Mathematical Statistics and gives you hands-on experience in using some of the ideas you saw there. The centrepiece of this module is the notion of a linear model, which allows you to formulate a regression model to explain the relationship between predictor variables and response variables. You will discover key ideas of regression (such as residuals, diagnostics, sampling distributions, least squares estimators, analysis of variance, t-tests and F-tests) and you will analyse estimators for a variety of regression problems. This module has a strong practical component and you will use the software package R to analyse datasets, including exploratory data analysis, fitting and assessing linear models, and communicating your results. The module will prepare you for numerous final years modules, notably the Year Three module covering the (even more flexible) generalised linear models.### Year Three

The third (final) year of the BSc has no compulsory modules, though you must take at least four statistics modules.

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- Differential Equations
- Introduction to Quantitative Economics
- Geometry
- Groups and Rings
- Games and Decisions
- Introduction to Mathematical Finance
- Professional Practice of Data Analysis
- Programming for Data Science