Undergraduate BSc (Hons)
Mathematics
Learn valuable analytical skills while exploring cutting-edge mathematical science.
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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.
This degree meets the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications (IMA), when it's followed by further training and experience in employment to get the equivalent competencies to those specified by the Quality Assurance Agency (QAA) for taught master’s degrees.
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.
ABB including Maths at A but excluding Use of Maths.
If taking both A level Mathematics and A level Further Mathematics:
ABC including Maths at A and Further Maths at B but excluding Use of Maths.
The University will consider applicants holding BTEC National Diploma and Extended National Diploma Qualifications (QCF; NQF; OCR) on a case-by-case basis. Please contact us for further advice on your individual circumstances.
30 points overall or 15 points at HL including Mathematics or Mathematics: Analysis and Approaches 6 at HL
N/A
The University will consider applicants holding T level qualifications in subjects closely aligned to the course.
The University welcomes applications from Access to Higher Education Diploma candidates for consideration. A typical offer may require you to obtain a proportion of Level 3 credits in relevant subjects at merit grade or above.
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.
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"
The concept of symmetry is one of the most fruitful ideas through which mankind has tried to understand order and beauty in nature and art. This module first develops the concept of symmetry in geometry. It subsequently discusses links with the fundamental notion of a group in algebra. Outline syllabus includes: Groups from geometry; Permutations; Basic group theory; Action of groups and applications to (i) isometries of regular polyhedra; (ii) counting colouring problems; Matrix groups.
In this module we will study linear partial differential equations, we will explore their properties and discuss the physical interpretation of certain equations and their solutions. We will learn how to solve first order equations using the method of characteristics and second order equations using the method of separation of variables.
Introduction to linear PDEs: Review of partial differentiation; first-order linear PDEs, the heat equation, Laplace's equation and the wave equation, with simple models that lead to these equations; the superposition principle; initial and boundary conditions
Separation of variables and series solutions: The method of separation of variables; simple separable solutions of the heat equation and Laplace’s equation; Fourier series; orthogonality of the Fourier basis; examples and interpretation of solutions
Solution by characteristics: the method of characteristics for first-order linear PDEs; examples and interpretation of solutions; characteristics of the wave equation; d’Alembert’s solution, with examples; domains of influence and dependence; causality.
This module builds on the Stage 1 Real Analysis 1 module. We will extend our knowledge of functions of one real variable, look at series, and study functions of several real variables and their derivatives.
The outline syllabus includes: Continuity and uniform continuity of functions of one variable, series and power series, the Riemann integral, limits and continuity for functions of several variables, differentiation of functions of several variables, extrema, the Inverse and Implicit Function Theorems.
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.
The main aim of this module is to give an introduction to the basics of differential geometry, keeping in mind the recent applications in mathematical physics and the analysis of pattern recognition. Outline syllabus includes: Curves and parameterization; Curvature of curves; Surfaces in Euclidean space; The first fundamental form; Curvature of surfaces; Geodesics.
This module will present a new perspective on Newton's familiar laws of motion. First we introduce variational calculus with applications such as finding the paths of shortest distance. This will lead us to the principle of least action from which we can derive Newton's law for conservative forces. We will also learn how symmetries lead to constants of motion. We then derive Hamilton's equations and discuss their underlying structures. The formalisms we introduce in this module form the basis for all of fundamental modern physics, from electromagnetism and general relativity, to the standard model of particle physics and string theory.
Indicative syllabus:
Review of Newton mechanics: Newton's law; harmonic and anharmonic oscillators (closed and unbound orbits, turning points); Kepler problem: energy and angular momentum conservation
Lagrangian Mechanics: Introdution to variational calculus with simple applications (shortest path - geodesic, soap film, brachistochrone problem); principle of least action: Euler-Lagrange equations (Newtonian mechanics with conservative forces); constraints and generalised coordinates (particle on a hoop, double pendulum, normal modes); Noether's theorem (energy and angular momentum conservation)
Hamiltonian Dynamics: Hamilton's equations; Legendre transform; Hamiltonian phase space (harmonic oscillator, anharmonic oscillators and the mathematical pendulum); Liouville's theorem; Poisson brackets.
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 introduces the basic ideas to solve certain ordinary differential equations, like first order scalar equations, second order linear equations and systems of linear equations. It mainly considers their qualitative and analytical aspects. Outline syllabus includes: First-order scalar ODEs; Second-order scalar linear ODEs; Existence and Uniqueness of Solutions; Autonomous systems of two linear first-order ODEs.
Can we square a circle? Can we trisect an angle? These two questions were studied by the Ancient Greeks and were only solved in the 19th century using algebraic structures such as rings, fields and polynomials. In this module, we introduce these ideas and concepts and show how they generalise well-known objects such as integers, rational numbers, prime numbers, etc. The theory is then applied to solve problems in Geometry and Number Theory. This part of algebra has many applications in electronic communication, in particular in coding theory and cryptography.
The security of our phone calls, bank transfers, etc. all rely on one area of Mathematics: Number Theory. This module is an elementary introduction to this wide area and focuses on solving Diophantine equations. In particular, we discuss (without proof) Fermat's Last Theorem, arguably one of the most spectacular mathematical achievements of the twentieth century. Outline syllabus includes: Modular Arithmetic; Prime Numbers; Introduction to Cryptography; Quadratic Residues; Diophantine Equations.
Revision of complex numbers, the complex plane, de Moivre's andEuler's theorems, roots of unity, triangle inequality
Sequencesand limits: Convergence of a sequence in the complex plane. Absoluteconvergence of complex series. Criteria for convergence. Power series, radiusof convergence
Complexfunctions: Domains, continuity, complex differentiation. Differentiation ofpower series. Complex exponential and logarithm, trigonometric, hyperbolicfunctions. Cauchy-Riemann equations
ComplexIntegration: Jordan curves, winding numbers. Cauchy's Theorem. Analytic functions.Liouville's Theorem, Maximum Modulus Theorem
Singularitiesof functions: poles, classification of singularities. Residues. Laurentexpansions. Applications of Cauchy's theorem. The residue theorem. Evaluationof real integrals.
Possibleadditional topics may include Rouche’s Theorem, other proofs of the FundamentalTheorem of Algebra, conformal mappings, Mobius mappings, elementary Riemannsurfaces, and harmonic functions.
There is no specific mathematical syllabus for this module.Students will study a topic in mathematics or statistics, either individuallyor within a small group, and produce an individual or group project on thetopic as well as individual coursework assignments. Projects will be chosenfrom published lists of individual and of group projects. The coursework andproject-work are supported by a series of workshops covering various forms ofwritten and oral communication and by supervision from an academic member ofstaff.
Theworkshops may include critically evaluating the following: a research articlein mathematics or statistics; a survey or magazine article aimed at ascientifically-literate but non-specialist audience; a mathematical biography;a poster presentation of a mathematical topic; a curriculum vitae; an oralpresentation with slides or board; a video or podcast on a mathematical topic.Guidance will be given on typesetting mathematics using LaTeX.”
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. Please refer to the individual module details under Course Structure.
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.
A highlight of my placement was presenting my final piece of independent work – a deep dive into ‘what makes a globally successful TV series’.
The 2024/25 annual tuition fees for this course are:
For details of when and how to pay fees and charges, please see our Student Finance Guide.
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.
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.
At Kent we recognise, encourage and reward excellence. We have created the Kent Scholarship for Academic Excellence.
The scholarship will be awarded to any applicant who achieves a minimum of A*AA over three A levels, or the equivalent qualifications (including BTEC and IB) as specified on our scholarships pages.
We have a range of subject-specific awards and scholarships for academic, sporting and musical achievement.
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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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