Undergraduate BSc (Hons)
Mathematics
with a Foundation Year
Learn valuable analytical skills while exploring cutting-edge mathematical science.
Learn valuable analytical skills while exploring cutting-edge mathematical science.
We know you care about your career. So we've got a Maths course that will set you up for a well-paid one. We rapidly adapt what we teach to reflect the fast-moving graduate employment market, and our courses are built on the research expertise of our world-leading mathematicians.
Our foundation year course enables you to develop your mathematics skills and start learning some university-level material, so that you’ll be ready to succeed on your chosen mathematics programme.
Graduates have gone on to a wide range of careers from medical statistics and software development to actuarial work and chartered accountancy.
Learn industry standard software like PROPHET, R and Python.
Take a placement year to boost your professional skills and get paid to do it.
You’ll benefit from free membership of the Kent Maths Society and Invicta Actuarial Society.
You'll learn skills that are highly valued by the best employers in business, finance, computing and engineering.
CDD including a C in Mathematics. Use of Maths A level is not accepted as a required subject.
Grades Merit Merit from the BTEC National Extended Diploma plus A Level Mathematics at C (but excluding Use of Maths).
80 tariff points from your IB Diploma, including HL Maths or HL Mathematics: Analysis and Approaches at 4 or SL Maths or SL Mathematics: Analysis and Approaches at 6, typically H4, H5, H5 or equivalent.
N/A
The University will consider applicants holding T level qualifications in subjects closely aligned to the course.
A typical offer would be to obtain the Access to HE Diploma in a suitable subject with a minimum of 45 credits at Level 3, with 9 credits at Distinction and 12 credits at Merit.
We consider all applications on an individual basis during Clearing and you're encouraged to get in touch to discuss your grades. You're most likely to be offered a place in Clearing for this course if you hold the following subjects:
The following modules are offered to our current students. This listing is based on the current curriculum and may change year to year in response to new curriculum developments and innovation.
If your qualifications are not sufficient, for whatever reason, for direct entry onto a degree programme, you can apply for this programme. It covers the mathematical skills you need to enter Stage 1 of the degree.
You take the following compulsory modules.
Functions: Definition of modulus function, solving basic equations and inequalities involving modulus functions, interval notation, function notation, domain and range, one-to-one and inverse functions, composite functions, odd and even functions.
Limits: Basic introduction to limits of a function, without epsilon-delta proofs; calculation of limits in simple cases involving indeterminate forms, including factoring, simple algebraic manipulation, and limits of rational functions; continuity of a function and asymptotes.
Differential Calculus: The derivative as the gradient of the tangent to the graph, interpretation of the derivative as a rate of change, the formal definition of the derivative and the calculation of simple examples from first principles, differentiation of elementary functions, elementary properties of the derivative, including the product rule, quotient rule and the chain rule, using differentiation to find and classify stationary points, parametric and implicit differentiation of simple functions.
Applications of Differentiation: examples including finding tangents and normals to curves and optimisation problems.
This module introduces the ideas of integration and numerical methods.
a) Integration: Integration as a limit of a sum and graphical principles of integration, derivatives, anti-derivatives and the Fundamental Theorem of Calculus (without proof), definite and indefinite integrals, integration of simple functions.
b) Methods of integration: integration by parts, integration by substitution, integration using partial fractions.
c) Solving first order ordinary differential equations: separable and linear first order ordinary differential equations, construction of differential equations in context, applications of differential equations and interpretation of solutions of differential equations.
d) Numerical integration: mid-ordinate rule, trapezium rule, Simpson's rule.
Additional material may include root finding using iterative methods, parametric integration, surfaces and volumes of revolution.
Students will be introduced to key mathematical skills, necessary in studying for a mathematics degree: use of the University Library and other sources to support their learning, present an argument in oral or written form, learn about staff in the School and beyond, etc. In particular, students will study various techniques of proof (by deduction, by exhaustion, by contradiction, etc.). These techniques will be illustrated through examples chosen from various areas of mathematics (and in particular co-requisite modules).
Statistical techniques are a fundamental tool in being able to measure, analyse and communicate information about sets of data. Using illustrative data sets we show how statistics can be indispensable in applied sciences and other quantitative areas. This module covers the basic methods used in probability and statistics using Excel for larger data sets. A more detailed indication of the module content follows.
Sampling from populations. Data handling and analysis using Excel. Graphical representation for the interpretation of univariate and bivariate data; outliers. Sample summary statistics: mean, variance, standard deviation, median, quartiles, inter-quartile range, correlation. Probability: combinatorics, conditional probability, Bayes' Theorem. Random variables: discrete, continuous; expectation, variance, standard deviation. Discrete and continuous distributions: Binomial, discrete uniform, Normal, uniform. Sampling distributions for the mean and proportion. Hypothesis testing: one sample, mean of Normal with known variance and proportion, 1- and 2-tail. Confidence intervals: one sample, mean of Normal with known variance and population proportion.
This module introduces fundamental methods needed for the study of mathematical subjects at degree level.
a) Co-ordinate Geometry: co-ordinate geometry of straight lines and circles, parallel and perpendicular lines, applications to plots of experimental data.
b) Trigonometry: definitions and properties of trigonometric, inverse trigonometric, and reciprocal trigonometric functions, radians, solving basic trigonometric equations, compound angle formulae, small angle formulae, geometry in right-angled and non-right angled triangles, sine and cosine rule, opposite and alternate angle theorems.
c) Vectors: Notations for and representation of vectors in one, two, and three dimensions; addition, subtraction, and scalar multiplication of vectors; magnitude of a vector.
Through this module, students will develop the transferable linguistic and academic skills necessary to successfully complete other modules on their programme and acquire the specific language skills that they will require when entering SMSAS and SPS Stage 1 programmes. The programme of study focuses on writing and speaking skills, enhancing academic language through classroom, homework and assessed activities. Writing skills will be used to write a technical report, interpret data and describe processes. Spoken skills will be used in presentations and seminars.
Algebra: simplifying expressions and rearranging formulae, indices, surds, algebraic fractions, solution of linear and quadratic equations and simultaneous equations, quadratic equations and the discriminant, inequalities and interval notation, binomial expansions, manipulating and factorising polynomials, exponentials and logarithms, equations involving exponentials.
Functions and graphs: plotting and recognising the graphs of elementary functions (modulus, exponential, …), roots, intercepts, turning points, area (graphical methods), co-ordinate geometry of straight lines, parallel and perpendicular lines, applications to plots of experimental data, simple graph transformations.
To be confirmed.
To be confirmed.
This module serves as an introduction to algebraic methods. These methods are central in modern mathematics and have found applications in many other sciences, but also in our everyday life. In this module, students will also gain an appreciation of the concept of proof in mathematics.
This module is a sequel to Algebraic Methods. It considers the abstract theory of linear spaces together with applications to matrix algebra and other areas of Mathematics (and its applications). Since linear spaces are of fundamental importance in almost every area of mathematics, the ideas and techniques discussed in this module lie at the heart of mathematics. Topics covered will include vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalisation, orthogonality and applications including conics.
This module introduces widely-used mathematical methods for vectors and functions of two or more variables. The emphasis is on the practical use of these methods; key theorems are stated but not proved at this stage. Tutorials and Maple worksheets will be used to support taught material.
Vectors: Cartesian coordinates; vector algebra; scalar, vector and triple products (and geometric interpretation); straight lines and planes expressed as vector equations; parametrized curves; differentiation of vector-valued functions of a scalar variable; tangent vectors; vector fields (with everyday examples)
Partial differentiation: Functions of two variables; partial differentiation (including the chain rule and change of variables); maxima, minima and saddle points; Lagrange multipliers
Integration in two dimensions: Double integrals in Cartesian coordinates; plane polar coordinates; change of variables for double integrals; line integrals; Green's theorem (statement – justification on rectangular domains only).
Introduction to Probability. Concepts of events and sample space. Set theoretic description of probability, axioms of probability, interpretations of probability (objective and subjective probability).
Theory for unstructured sample spaces. Addition law for mutually exclusive events. Conditional probability. Independence. Law of total probability. Bayes' theorem. Permutations and combinations. Inclusion-Exclusion formula.
Discrete random variables. Concept of random variable (r.v.) and their distribution. Discrete r.v.: Probability function (p.f.). (Cumulative) distribution function (c.d.f.). Mean and variance of a discrete r.v. Examples: Binomial, Poisson, Geometric.
Continuous random variables. Probability density function; mean and variance; exponential, uniform and normal distributions; normal approximations: standardisation of the normal and use of tables. Transformation of a single r.v.
Joint distributions. Discrete r.v.'s; independent random variables; expectation and its application.
Generating functions. Idea of generating functions. Probability generating functions (pgfs) and moment generating functions (mgfs). Finding moments from pgfs and mgfs. Sums of independent random variables.
Laws of Large Numbers. Weak law of large numbers. Central Limit Theorem.
Real Numbers: Rational and real numbers, absolute value and metric structure on the real numbers, induction, infimum and supremum.
Limits of Sequences: Sequences, definition of convergence, epsilon terminology, uniqueness, algebra of limits, comparison principles, standard limits, subsequences and non-existence of limits, convergence to infinity.
Completeness Properties: Cantor's Intersection Theorem, limit points, Bolzano-Weierstrass theorem, Cauchy sequences.
Continuity of Functions: Functions and basic definitions, limits of functions, continuity and epsilon terminology, sequential continuity, Intermediate Value Theorem.
Differentiation: Definition of the derivative, product rule, quotient rule and chain rule, derivatives and local properties, Mean Value Theorem, L'Hospital's Rule.
Taylor Approximation: Taylor's Theorem, remainder term, Taylor series, standard examples, limits using Taylor series.”
MAST4011"
You take all compulsory modules.
This tailored module on explanatory and predictive modelling in context will help you unlock the essence of data-driven decision-making. You’ll learn about regression, the cornerstone of versatile statistical analysis, mastering diagnostics, model specification, selection, and interpretation.
Through hands-on activities and real data analysis, you’ll gain the skills to extract actionable insights and forecast future trends confidently. The module is designed to equip you with the necessary tools to navigate complex datasets across different areas of application and practice.
Having experience of genuine data science challenges will set you apart when you enter the employment market. This module is designed to simulate real-world work experiences, where you will work in groups on open-ended projects requiring a combination of diverse skills and knowledge.
You’ll collaborate with others within set time frames to tackle authentic mathematical and data science challenges using real-world data sets, honing your ability to learn new material, combine your skills, and work effectively as a team. The data sets involved will relate to current industry, societal or scientific challenges, preparing you for the complexities of working with authentic data.
You’ll present your findings in a variety of formats including presentations, posters, blog posts, and reports, allowing you to develop skills essential for your future career.
Mathematical statistics provides the theoretical framework for statistical techniques. Understanding these mathematical underpinnings allows statisticians to develop and justify various statistical methods, ensuring their validity and reliability. Mathematical statistics enables practitioners to extract valuable insights from data, make informed decisions, and drive progress in various fields of knowledge and application.
You’ll learn advanced techniques in probability and statistics, including maximum likelihood estimation, advanced hypothesis testing, moments and moment-generating functions. You’ll also discover bivariate and multivariate discrete and continuous distributions.
By the end of the module, you’ll have a solid foundation in mathematical statistics, enabling you to confidently apply and further develop advanced skills in data analysis.
Multivariable and vector calculus provide powerful tools for understanding and analysing functions and phenomena in multiple dimensions. Mastery of these concepts is essential for numerous fields and applications, providing deeper insights into complex systems and problems.
Multivariable calculus extends the concepts of calculus to functions of several variables. Vector calculus focuses on the algebraic and geometric aspects of vectors and vector-valued functions. Both are crucial for understanding and solving problems in fields such as physics, engineering, economics, and computing.
In the module, you'll learn how to differentiate and integrate functions of several variables and how to work with curves, surfaces and volumes. You’ll also examine core concepts including partial derivatives, gradients, multiple integrals, line and surface integrals, vector algebra, and vector fields.
You’ll see analogues of core theorems of calculus in the setting of multivariable functions and learn how to use vector algebra and vector calculus to analyse and solve problems in multiple dimensions. In addition, you’ll gain an understanding of how the methods and concepts of multivariable and vector calculus can be applied in other fields.
Numbers are one of the most fundamental concepts in mathematics and indeed in everyday life. Their study dates back thousands of years to Chinese, Babylonian, Greek, Indian, and Persian thinkers. In the second half of the twentieth century, amazing and far-reaching applications were found in the emerging information technology industry. Nowadays their theory provides the basis for all security on the internet and other communication channels, keeping things such as your messages and bank details safe. Surprising new applications are constantly being discovered.
In the first half of the module, you’ll learn the core results of number theory such as the Chinese Remainder Theorem and Fermat’s Little Theorem and gain technical skills in working with prime numbers, modular arithmetic, and Diophantine equations.
In the second half of the module, you’ll see how these core results and techniques are applied in cryptography, the science of protecting information. More specifically, you’ll learn about classical cryptosystems and their weak point, the ‘key distribution problem’, public key ciphers and computational security, and the challenge coming from quantum computing.
Understanding numerical methods and differential equations is essential for modelling real-world phenomena. Knowledge of these subjects equips you with the capability to forecast system behaviours, design control strategies, and contribute to technological advancements across diverse fields.
You’ll learn to use analytical and numerical tools for resolving differential equations, which is essential explicit solutions of differential equations are often not known. You’ll explore numerical approximation methods, such as Euler's method and Runge-Kutta's method, and learn about stability analysis and error estimation to gauge the reliability of these techniques.
The module also covers a spectrum of topics including methods for solving ordinary differential equations (ODE), linear ODE systems, and qualitative techniques for nonlinear ODE systems such as linearisation, examination of stationary points and their stability, as well as phase portraits. The curriculum integrates hands-on exercises aimed at developing proficient numerical programming skills, enhancing comprehension, and practical application.
Constructing suitable models for data is a key part of statistics. For example, we might want to model the yield of a chemical process in terms of the temperature and pressure of the process. Even if the temperature and pressure are fixed, there will be variation in the yield which motivates the use of a statistical model which includes a random component. In this module, students study linear regression models (including estimation from data and drawing of conclusions), the use of likelihood to estimate models and its application in simple stochastic models. Both theoretical and practical aspects are covered, including the use of R.
Probability: Joint distributions of two or more discrete or continuous random variables. Marginal and conditional distributions. Independence. Properties of expectation, variance, covariance and correlation. Poisson process and its application. Sums of random variables with a random number of terms.
Transformations of random variables: Various methods for obtaining the distribution of a function of a random variable —method of distribution functions, method of transformations, method of generating functions. Method of transformations for several variables. Convolutions. Approximate method for transformations.
Sampling distributions: Sampling distributions related to the Normal distribution — distribution of sample mean and sample variance; independence of sample mean and variance; the t distribution in one- and two-sample problems.
Statistical inference: Basic ideas of inference — point and interval estimation, hypothesis testing.
Point estimation: Methods of comparing estimators — bias, variance, mean square error, consistency, efficiency. Method of moments estimation. The likelihood and log-likelihood functions. Maximum likelihood estimation.
Hypothesis testing: Basic ideas of hypothesis testing — null and alternative hypotheses; simple and composite hypotheses; one and two-sided alternatives; critical regions; types of error; size and power. Neyman-Pearson lemma. Simple null hypothesis versus composite alternative. Power functions. Locally and uniformly most powerful tests.
Composite null hypotheses. The maximum likelihood ratio test.
Interval estimation: Confidence limits and intervals. Intervals related to sampling from the Normal distribution. The method of pivotal functions. Confidence intervals based on the large sample distribution of the maximum likelihood estimator – Fisher information, Cramer-Rao lower bound. Relationship with hypothesis tests. Likelihood-based intervals.
This module is an introduction to the methods, tools and ideas of numerical computation. In mathematics, one often encounters standard problems for which there are no easily obtainable explicit solutions, given by a closed formula. Examples might be the task of determining the value of a particular integral, finding the roots of a certain non-linear equation or approximating the solution of a given differential equation. Different methods are presented for solving such problems on a modern computer, together with their applicability and error analysis. A significant part of the module is devoted to programming these methods and running them in MATLAB.
Introduction: Importance of numerical methods; short description of flops, round-off error, conditioning
Solution of linear and non-linear equations: bisection, Newton-Raphson, fixed point iteration
Interpolation and polynomial approximation: Taylor polynomials, Lagrange interpolation, divided differences, splines
Numerical integration: Newton-Cotes rules, Gaussian rules
Numerical differentiation: finite differences
Introduction to initial value problems for ODEs: Euler methods, trapezoidal method, Runge-Kutta methods.
This module covers aspects of Statistics which are particularly relevant to insurance. Some topics (such as risk theory and credibility theory) have been developed specifically for actuarial use. Other areas (such as Bayesian Statistics) have been developed in other contexts but now find applications in actuarial fields. Indicative topics covered by the module include Bayesian Statistics; Loss Distributions; Reinsurance and Ruin; Credibility Theory; Risk Models; Ruin Theory; Generalised Linear Models; Extreme Value Theory. This module will cover a number of syllabus items set out in Subjects CS1 and CS2 – Actuarial Statistics published by the Institute and Faculty of Actuaries.
This module is designed to provide students with an introduction to the use of data analytics tools on large data sets including the analysis of text data. The module will begin by discussing the principles of text-mining and big data. The module will then discuss the techniques that can be used to explore large data sets (including pre-processing and cleaning) and the use of multivariate statistical techniques for supervised and unsupervised learning. The module will conclude by considering several data mining techniques.
Syllabus: What is "big data"? What is text mining? Exploratory data analysis for large datasets, and pre-processing and cleaning; Multivariate statistical analysis (both unsupervised, e.g. factor analysis or principle component analysis, and supervised, e.g. linear discriminant analysis); Data security; Data mining including techniques such as classification trees, neural networks, clustering, text analysis or network analysis.
In this module we study the fundamental concepts and results in game theory. We start by analysing combinatorial games, and discuss game trees, winning strategies, and the classification of positions in so called impartial combinatorial games. We then move on to discuss two-player zero-sum games and introduce security levels, pure and mixed strategies, and prove the famous von Neumann Minimax Theorem. We will see how to solve zero-sum two player games using domination and discuss a general method based on linear programming. Subsequently we analyse arbitrary sum two-player games and discuss utility, best responses, Nash equilibria, and the Nash Equilibrium Theorem. The final part of the module is devoted to multi-player games and cooperation; we analyse coalitions, the core of the game, and the Shapley value.
You take all compulsory modules and select one from a list of optional modules.
You’ll delve into the fascinating realm of mathematics through immersive experiences tailored to your interests and aspirations. Under the guidance of expert academics, embark on a journey of intellectual discovery, culminating in a dissertation that delves deep into the core of your chosen mathematical domain. You can forge connections and expand your horizons by doing a research internship, where you'll tackle a mathematical research challenge in a team led by one of our scholars.
Experience the rewarding path of mathematics education by venturing into teaching within our extensive network of local schools, and inspire the next generation of mathematical minds. You can broaden your perspective by applying your mathematical prowess to problems from industry.
As you navigate these challenges, you'll develop practical expertise and cultivate a deeper understanding of the role mathematics plays in shaping our modern world. You can embrace the power of communication by crafting engaging and informative content that brings mathematics to life. Whether through blog posts, video essays, podcasts, or magazine articles, you'll have the opportunity to share your passion for mathematics with diverse audiences, exploring current trends and topics with creativity and clarity.
Groups are the basic building blocks of modern algebra. They provide the abstract framework for analysing symmetry. Understanding the theory of groups yields insights not only in the abstract structures underpinning mathematics, but also into the fundamental laws of nature. Chemists, for example, study symmetry groups of molecules, while physicists use symmetry to develop theories to describe physical phenomena.
Field theory extends this to more complex algebraic structures that are foundational in modern mathematics and are used in a variety of modern technologies. For example, finite fields have sophisticated applications in error-correcting codes which are used to control errors in the transition of digital data over an unreliable communication channel.
You’ll develop a versatile toolkit in studying groups and fields, extending your ability to think abstractly and reason logically. You’ll cultivate a deep understanding of the abstract theory that allows you to see inside the algorithms and processes that underpin a variety of applications.
Complex analysis is a classic branch of mathematics with a long and rich history. It plays a role in many areas of modern mathematics, including geometry, number theory, and dynamical systems, but is also widely used in engineering and physics. Complex analysis extends the fundamental concepts of calculus to complex numbers.
You'll explore in detail the intricate relationships between the functions of a complex variable and the geometry and algebra of the complex plane. This provides many striking results including Cauchy's integral formula, Laurent's theorem, and the residue theorem.
You'll master new techniques to compute integrals of functions of a real variable using contour integration, see how complex analysis can be used to prove the Fundamental Theorem of Algebra and gain an appreciation of its wide-ranging applications. By the end of the module, you will have expanded your mathematical toolkit and gained a deeper appreciation of the unity of mathematics.
Embark on an exciting journey into the world of partial differential equations (PDEs) - the backbone of applied mathematics. Discover the realm of modelling fundamental processes in physics, engineering, and finance as you learn analytical techniques for solving PDEs.
From fluid motion to heat conduction, sound waves to traffic flow and models of climate change, this module will equip you with the tools to tackle a myriad of real-world problems. Explore the art of Fourier analysis and series methods, unravel the intricacies of characteristics for quasilinear PDEs, and discover the beauty of deriving similarity solutions like travelling waves.
Get ready to sharpen your expertise in specific techniques as you examine both linear and nonlinear PDEs, gaining qualitative understanding using graphical and phase space methods.
A strong grasp of statistical modelling and optimisation principles forms the bedrock of machine learning. This module covers essential and advanced topics of machine learning and deep learning, blending theory with practical computing tools, such as R and Python.
We’ll equip you with the necessary theoretical framework to navigate through complex algorithms and methodologies. You’ll explore key concepts including classification, prediction, and regression tree-based methods through engaging real-world datasets.
You’ll uncover the power of resampling techniques and support vector machines, and dive into the exciting realm of deep learning. With applications spanning biomedical statistics, finance, and insurance, this module offers a hands-on learning experience tailored to aspiring data scientists.
What are the commonly used models in actuarial science? How can we apply these models to tackle the complex problems faced by financial professionals in practical situations? Modelling is crucial for actuaries as it allows us to assess and manage risks in various circumstances. This module gives you the valuable practical and theoretical skills needed to navigate these critically relevant issues.
You’ll gain a strong foundation in financial economics modelling techniques and be able to apply them in quantitative risk management situations, including portfolio selection and the pricing and valuation of financial derivatives.
You’ll develop valuable skills to model economic decision making by forecasting potential future scenarios, and apply a range of financial risk measurement tools to evaluate suitable investment opportunities. In addition, you’ll explore a range of liability valuation modelling tools which can be used to estimate insurance claims. The modelling techniques that you learn in this module will provide you with the indispensable knowledge and skills needed for a successful career in insurance, finance and related fields.
You will also have the opportunity to gain valuable exemptions from subject CM2 of the Institute and Faculty of Actuaries (IFoA, UK).
Teaching amounts to approximately 16 hours of lectures and classes per week. Modules that involve programming or working with computer software packages usually include practical sessions.
The majority of Stage 1 modules are assessed by end-of-year examinations. Many Stage 2 and 3 modules include coursework which normally counts for 20% of the final assessment. Both Stage 2 and 3 marks count towards your final degree result.
For a student studying full time, each academic year of the programme will comprise 1200 learning hours which include both direct contact hours and private study hours. The precise breakdown of hours will be subject dependent and will vary according to modules.
Methods of assessment will vary according to subject specialism and individual modules.
Please refer to the individual module details under Course Structure.
The programme aims to:
You gain knowledge and understanding of:
You develop your intellectual skills in the following areas:
You gain subject-specific skills in the following areas:
You gain transferable skills in the following areas:
A maths degree from Kent will set you up for a wide range of careers in areas including medical statistics, pharmaceuticals, aerospace, accounting and software development.
For students continuing on this programme, fees will increase year on year by no more than RPI + 3% in each academic year of study except where regulated.*
The University will assess your fee status as part of the application process. If you are uncertain about your fee status you may wish to seek advice from UKCISA before applying.
For details of when and how to pay fees and charges, please see our Student Finance Guide.
Find out more about accommodation and living costs, plus general additional costs that you may pay when studying at Kent.
Kent offers generous financial support schemes to assist eligible undergraduate students during their studies. See our funding page for more details.
We have a range of subject-specific awards and scholarships for academic, sporting and musical achievement.
Next steps
If you are from the UK or Ireland, you must apply for this course through UCAS. If you are not from the UK or Ireland, you can apply through UCAS or directly on our website if you have never used UCAS and you do not intend to use UCAS in the future.
We welcome applications from students all around the world with a wide range of international qualifications.
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