Undergraduate BSc (Hons)
Mathematics
with a Foundation Year
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.
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.
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). The University will consider those not taking A Level Maths on a case by case basis.
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.
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 all compulsory modules and one of the optional modules. You take Exploring the Mathematical Sciences if you have A-level mathematics or equivalent, while all other students take Foundation Algebra and Functions.
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.
This module introduces the students to the basics of Maple and three topics in the mathematical sciences. The precise topics will vary in any particular year. Potential topics include (for example): history and/or people active in the mathematical sciences, algorithms, engaging the public in the mathematical sciences, mathematical games. Each topic is supported by a series of workshops introducing key aspects of the topic.
Maple: the Maple environment, basic commands, basic calculus, curve sketching.
There is no specific mathematical syllabus for the topics part of the module.
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 and Euler's theorems, roots of unity, triangle inequality
Sequences and limits: Convergence of a sequence in the complex plane. Absolute convergence of complex series. Criteria for convergence. Power series, radius of convergence
Complex functions: Domains, continuity, complex differentiation. Differentiation of power series. Complex exponential and logarithm, trigonometric, hyperbolic functions. Cauchy-Riemann equations
Complex Integration: Jordan curves, winding numbers. Cauchy's Theorem. Analytic functions. Liouville's Theorem, Maximum Modulus Theorem
Singularities of functions: poles, classification of singularities. Residues. Laurent expansions. Applications of Cauchy's theorem. The residue theorem. Evaluation of real integrals.
Possible additional topics may include Rouche’s Theorem, other proofs of the Fundamental Theorem of Algebra, conformal mappings, Mobius mappings, elementary Riemann surfaces, and harmonic functions.
There is no specific mathematical syllabus for this module. Students will study a topic in mathematics or statistics, either individually or within a small group, and produce an individual or group project on the topic as well as individual coursework assignments. Projects will be chosen from published lists of individual and of group projects. The coursework and project-work are supported by a series of workshops covering various forms of written and oral communication and by supervision from an academic member of staff.
The workshops may include critically evaluating the following: a research article in mathematics or statistics; a survey or magazine article aimed at a scientifically-literate but non-specialist audience; a mathematical biography; a poster presentation of a mathematical topic; a curriculum vitae; an oral presentation 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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