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BScMathematics with Statistics

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Overview

Fascinated by the power of statistics? The world increasingly needs graduates with an understanding of statistical methods, data analysis and the mathematics that underpins it all. The collection, analysis, application and representation of data are central to our globalised society. Statistics lie at the heart of our economics, accounting, banking, management and administration, communications, astronomy and the physical and social sciences.

This programme is led by renowned experts in the field and will give you a solid grounding in all the key methods and concepts of mathematics, whilst allowing you to explore the fascinating and rapidly evolving field of statistics. It helps you to link fundamental concepts of probability theory and pure mathematics to the application of a diverse array of statistical techniques. The modular structure also gives you the flexibility to tailor your studies to your own interests.

Our curriculum is broad and informed by our world-class research activities, including pioneering work in the field of statistics. We also offer an extensive array of postgraduate opportunities, and provided you make good progress in year 1 you will have the option of transferring onto our four-year Mathematics MSci programme if you decide to focus on taking your mathematics to a higher level. It might also be possible to transfer sideways into the second year of one of our other undergraduate mathematics programmes.

Join our friendly and inspiring department and you will benefit from a thoroughly supportive learning environment. We offer small group tutorials, problem solving sessions, practical workshops and IT classes, as well as generous staff office hours and a dedicated personal adviser to guide you through your studies. We also offer CV writing workshops and a competitive work placement scheme. Graduates from our department are in great demand for their numeracy, analytical skills, data handling powers, logical thinking and creative problem solving abilities.

Programme structure

Year 1

From Euclid to Mandelbrot
In this module you will develop an understanding of how mathematics has been used to describe space over the last 2,500 years. You will look at ruler and compass constructions from ancient Greece, the influence of algebra on geometry in the renaissance, and the intricate and beautiful fractal patterns developed by Benoît Mandelbrot in the 1970s. You will learn to sketch simple curves using polar coordinates, draw and classify conics, and use simple arguments to distinguish between countable and uncountable sets.

Introduction to Applied Mathematics
In this module, you will develop an understanding of how the techniques for solving differential equations can be applied to describe the real world. You will look at situations from balls flying through the air to planets orbiting the stars, including why the moon continues to orbit the Earth and not the Sun. You will consider the chatotic motion of a pendulum, and examine Einstein’s theory of special relativity to describe the propagation of matter and light at high speeds.

Principles of Statistics
In this module you will develop an understanding of the notion of probability and the basic theory and methods of statistics. You will look at random variables and their distributions, calculate probabilities of events that arise from standard distributions, estimate means and variances, and carry out t tests for means and differences of means. You will also consider the notions of types of error, power and significance levels, gaining experience in sorting a variety of data sets in a scientific way.

Calculus
In this module, you will develop an understanding of the key concepts in Calculus, including differentiation and integration. You will learn how to factorise polynomials and separate rational functions into partial fractions, differentiate commonly occurring functions, and find definite and indefinite integrals of a variety of functions using substitution or integration by parts. You will also examine how to recognise the standard forms of first-order differential equations, and reduce other equations to these forms and solve them.

Functions of Several Variables
In this module you will develop an understanding of the calculus functions of more than one variable and how it may be used in areas such as geometry and optimisation. You learn how to manipulate partial derivatives, construct and manipulate line integrals, represent curves and surfaces in higher dimensions, calculate areas under a curve and volumes between surfaces, and evaluate double integrals, including the use of change of order of integration and change of coordinates.

Number Systems
In this module you will develop an understanding of the fundamental algebraic structures, including familiar integers and polynomial rings. You will learn how to apply Euclid’s algorithm to find the greatest comon divisor of two integers, and use mathematical induction to prove simple results. You will examine the use of arithmetic operations on complex numbers, extract roots of complex numbers, prove De Morgan’s laws, and determine whether a given mapping is bijective.

Matrix Algebra
In this module you will develop an understanding of basic linear algebra, in particular the use of matrices and vectors. You will look at the basic theoretical and computational techniques of matrix theory, examining the power of vector methods and how they may be used to describe three-dimensional space. You will consider the notions of field, vector space and subspace, and learn how to calculate the determinant of an n x n matrix.

Numbers And Functions
In this module you will develop an understanding of key mathematical concepts such as the construction of real numbers, limits and convergence of sequences, and continuity of functions. You will look at the infinite processes that are essential for the development of areas such as calculus, determining whether a given sequence tends to a limit, and finding the limits of sequences defined recursively.

Year 2

Statistical Methods
In this module you will develop an understanding of statistical modelling, becoming familiar with the theory and the application of linear models. You will learn how to use the classic simple linear regression model and its generalisations for modelling dependence between variables. You will examine how to apply non-parameric methods, such as the Wilxocon and Kolmogorov-Smirnov goodness-of-fit tests, and learn to use the Minitab statistical software package.

Probability
In this module you will develop an understanding of the basic principles of the mathematical theory of probability. You will use the fundamental laws of probability to solve a range of problems, and prove simple theorems involving discrete and continuous random variables. You will learn how to forumulate an explain fundamental limit theorems, such as the weak law of large numbers and the central limit theorem.

Linear Algebra and a Group Project
In this module you will develop an understanding of vectors and matrices within the context of vector spaces, with a focus on deriving and using various decompositions of matrices, including eigenvalue decompositions and the so-called normal forms. You will learn how these abstract notions can be used to solve problems encountered in other fields of science and mathematics, such as optimisation theory. Working in small groups, you will put together different aspects of mathematics in a project on a topic of your choosing, disseminating your findings in writing and giving an oral presentation to your peers.

Complex Variable
In this module you will develop an understanding of the basic complex variable theory. You will look at the definitions of continuity and differentiability of a complex valued function at a point, and how Cauchy-Riemann equations can be applied. You will examine how to use a power series to define the complex expontential function, and how to obtain Taylor series of rational and other functions of standard type, determining zeros and poles of given functions. You will also consider how to use Cauchy’s Residue Theorem to evaulate real integrals.

Year 3

Inference
In this module you will develop an understanding of the main priciples and methods of statstics, in particular the theory of parametric estimation and hypotheses testing.You will learn how to formulate statistical problems in mathematical terms, looking at concepts such as Bayes estimators, the Neyman-Pearson framework, likelihood ratio tests, and decision theory.

Time Series Analysis
In this module you will develop an understanding of statistics by looking at the theory and methods used in time series analysis and forecasting. You will look at descriptive methods and theoretical techniques to analyse time series data from fields such as finance, economics, medicine, meteorology, and agriculture. You will learn to use the statistical computing package Minitab as a data analysis, calculation and graphical aid.

Applied Probability
In this module you will develop an understanding of the the probabilistic methods used to model systems with uncertain behaviour. You will look at the structure and concepts of discrete and continuous time Markov chains with countable stable space, and consider the methods of conditional expectation. You will learn how to generate functions, and construct a probability model for a variety of problems.

Optional modules

In addition to these mandatory course units there are a number of optional course units available during your degree studies. The following is a selection of optional course units that are likely to be available. Please note that although the College will keep changes to a minimum, new units may be offered or existing units may be withdrawn, for example, in response to a change in staff. Applicants will be informed if any significant changes need to be made.

Career opportunities

Thanks to the broad applicability of both mathematics and statistics, our graduates are in high demand. You will complete your undergraduate studies with a host of valuable and transferrable skills, including numeracy, data handling and analysis, creativity, logical thinking and problem solving.

We are part of the School of Mathematics and Information Security and we enjoy strong ties with both the information security sector and industry at large. Recent graduates from the department have gone on to enjoy successful careers in: business management, IT consultancy, computer analysis and programming, accountancy, the civil service, teaching, actuarial science, finance, risk analysis and engineering. They are working for organisations such as: KPMG, Ernst & Young, the Ministry of Defence, Barclays Bank, Lloyds Banking Group, the Department of Health, Logica, McLaren and TowersWatson. Graduates from this programme have also gone on to enjoy successful research careers, including working in advanced statistical studies with some of the leading teams in the field.

We offer a competitive work experience scheme at the end of year 2, with short-term placements available during the summer holidays. You will also attend a CV writing workshop as part of your core modules in year 2, and your personal adviser and the campus Careers team will be on hand to offer advice and guidance on your chosen career. The University of London Careers Advisory Service also offers tailored sessions for Mathematics students, on finding summer internships or holiday jobs and securing employment after graduation. Depending on your choice of courses, you could be eligible for certain membership exemptions from the Institute of Actuaries and other professional bodies.

Apply now! Fall semester 2021/22
This intake is not applicable

Application deadlines apply to citizens of: United States

Apply now! Fall semester 2021/22
This intake is not applicable

Application deadlines apply to citizens of: United States