MMath
Mathematics and Theoretical Physics

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Key Information

Campus

Brayford Pool

Typical Offer

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Duration

4-5 years

UCAS Code

GFC3

Academic Year

Course Overview

Taking a joint honours in Mathematics and Theoretical Physics at Lincoln allows students to explore the interplay between these two important disciplines, and the ways in which they co-exist and complement each other.

The degree aims to provide a broad education in mathematics. This includes pure and applied mathematics. This is alongside fundamental and applied physics, enabling students to develop the knowledge and problem-solving skills vital to modern science and technology.

This course is designed to provide a thorough foundation in analytical and numerical methods, practical scientific skills, and research techniques. It gives students the opportunity to develop a range of transferable skills, such as communication and problem solving.

The four-year MMath course is designed for those seeking to develop advanced mathematical skills. The first three years are common with the BSc (Hons) Mathematics and Physics degree, while the fourth year offers the opportunity to study more advanced topics in greater depth. This year also includes a significant industrial or academic project.

How You Study

In the first year students can study modules including Algebra; Calculus; and Electricity, Magnetism, Thermal and Quantum Physics. In the second year, students progress to modules which include Condensed Matter Physics, Scientific Computing, and Differential Equations, alongside the opportunity to complete an group project. In the third year students can study Numerical Methods and Statistical Mechanics and have the opportunity to select from a range of optional modules.

Students who opt to enrol on this MMath programme will continue their study for a fourth year at an advanced level, examining topics in greater depth and undertaking substantial, additional project
work.

The course is taught via lectures, problem-solving classes, computer-based classes, and seminars. In addition to lectures and problem-solving classes, first year students within the School of Engineering and Physical Sciences can benefit from weekly one hour tutor sessions in small groups.

Modules

              † Some courses may offer optional modules. The availability of optional modules may vary from year to year and will be subject to minimum student numbers being achieved. This means that the availability of specific optional modules cannot be guaranteed. Optional module selection may also be affected by staff availability.

              Algebra 2025-26MTH1001MLevel 42025-26This module begins with refreshing and expanding some of the material from the A-levels Maths, such as the binomial theorem, division of polynomials, polynomial root-finding, and factorisations. Then the Euclidean algorithm is introduced with some of its many applications, both for integers and for polynomials. This naturally leads to a discussion of divisibility and congruences, for integers and for polynomials, with emphasis on similarities and as a step towards abstraction.CoreCalculus 2025-26MTH1002MLevel 42025-26This module focuses on the concepts of the derivative and the Riemann integral, which are indispensable in modern sciences. Two approaches are used: both intuitive-geometric, and mathematically rigorous, based on the definition of continuous limits. Important results are the Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration. Further calculus tools are explored, such as the general properties of the derivative and the Riemann integral, as well as the techniques of integration. In this module, students may deal with many "popular" functions used throughout mathematics.CoreComputer Algebra and Technical Computing 2025-26MTH1006MLevel 42025-26This module presents an introduction to computer packages for analytic formulas manipulation (computer algebra) and technical computing. Students will also have the opportunity to develop skills including; utilising a logbook as a factual record and as reflective self-assessment to support their learning.CoreElectricity, Magnetism, Thermal and Quantum Physics 2025-26PHY1003MLevel 42025-26This module covers basic notions of modern physics. In electricity and magnetism these include Coulomb’s law, electrostatic vector and potential fields, magnetic fields, motion of charges and currents in electromagnetic fields, and the basics of electric circuits. In thermal these include the zeroth, and first and second laws of thermodynamics applied to different model situations. The quantum physics part introduces notions such as the wave-particle duality, the concept of wavefunction, energy quantization, and simple models of the atom.CoreGeometrical Optics, Waves and Mechanics 2025-26PHY1002MLevel 42025-26This module introduces established theories describing optical, acoustic, and mechanical phenomena. The optics part includes Fermat’s principle of light propagation, Snell’s laws of reflection and refraction, thin lenses, and Huygens’s principle. The mechanics part includes the basic mathematical tools to describe the motion of objects (kinematics) and the laws of Newton (dynamics) underpinning these observed motions. The wave part of the module includes a discussion of propagating waves, the Doppler effect, phase and group velocities, and standing waves.CoreIntroduction to Modern Astronomy 2025-26PHY1006Level 42025-26This module aims to introduce fundamental concepts in modern astronomy from planets up to the universe as a whole.CoreLinear Algebra 2025-26MTH1004MLevel 42025-26This module describes vector spaces and matrices. Matrices are regarded as representations of linear mappings between vector spaces. Eigenvalues and eigenvectors are introduced, which lead to diagonalisation and reduction to other canonical forms. Special types of mappings and matrices (orthogonal, symmetric) are also introduced.CoreProbability and Statistics 2025-26MTH1005MLevel 42025-26This module begins with an introduction of a probability space, which models the possible outcomes of a random experiment. Basic concepts such as statistical independence and conditional probability are introduced, with various practical examples used as illustrations. Random variables are introduced, and certain well-known probability distributions are explored. Further study includes discrete distributions, independence of random variables, mathematical expectation, random vectors, covariance and correlation, conditional distributions and the law of total expectation. The ideas developed for discrete distributions are applied to continuous distributions. Probability theory is a basis of mathematical statistics, which has so many important applications in science, industry, government and commerce. Students will have the opportunity to gain a basic understanding of statistics and its tools. It is important that these tools are used correctly when, for example, the full picture of a problem (population) must be inferred from collected data (random sample).CoreProfessional Skills and Group Study 2025-26MTH1007MLevel 42025-26This module provides students the opportunity to learn a variety of transferable skills: to communicate scientific ideas via a variety of media, to work in groups, to manage and plan projects, to keep record of work. Students have the opportunity to develop an understanding of general and specialized databases, their uses and searches. Group study can develop Students' skills in team-working around investigating a topic from literature. Students have the opportunity to take on administrative roles within the team and work towards common aims and objectives.CoreAlgebraic Structures 2026-27MTH2001MLevel 52026-27The concepts of groups, rings and fields are introduced, as examples of arbitrary algebraic systems. The basic theory of subgroups of a given group and the construction of factor groups is introduced, and then similar constructions are introduced for rings. Examples of rings are considered, including the integers modulo n, the complex numbers and n-by-n matrices. The ring of polynomials over a given field is studied in more detail.CoreDifferential Equations 2026-27MTH2004MLevel 52026-27Calculus techniques already provide solutions of simple first-order differential equations. Solution of second-order differential equations can sometimes be achieved by certain manipulations. Students may learn about existence and geometric interpretations of solutions, even when calculus techniques do not yield solutions in a simple form. This is a part of the existence theory of ordinary differential equations and leads to fundamental techniques of the asymptotic and qualitative study of their solutions, including the important question of stability. Fourier series and Fourier transform are introduced. This module provides an introduction to the classical second-order linear partial differential equations and techniques for their solution. The basic concepts and methods are introduced for typical partial differential equations representing the three classes: parabolic, elliptic, and hyperbolic.CoreElectrodynamics 2026-27PHY2002MLevel 52026-27This modules covers the first established classical theory of fields, namely the theory of electromagnetic fields. After introducing the necessary mathematical tools such as curl, divergence, and gradient, the module discusses the macroscopic and microscopic Maxwell’s equations of electromagnetism as well as their solutions for some model problems in vacuum and in some materials. Topics covered include Gauss’s law, Maxwell’s law of induction, Faraday’s law, time-dependent electromagnetic fields, electromagnetic waves, and dielectric and magnetic materials.CoreGroup Project 2026-27MTH2005MLevel 52026-27This module aims to provide students with the experience of working as part of a team on a project. Students will have the opportunity to produce a set of deliverables relevant to their programme of study. Final deliverables will be negotiated between the group and their supervisor, the module coordinator will be responsible for ensuring that each project covers the learning outcomes of the module. Groups are expected to manage their own processes, and to hold regular meetings both with and without their supervisor. Groups will be allocated by the module coordinator and other members of staff. The process of development of the topic under study and the interaction and management of group members underpins the assessment of skills in the module.CoreIndustrial and Financial Mathematics 2026-27MTH2006MLevel 52026-27Students have the opportunity to learn how mathematics is applied to modern industrial problems, and how the mathematical apparatus finds applications in the financial sector.CoreLagrangian and Hamiltonian Mechanics 2026-27MTH2007MLevel 52026-27This module is concerned with a modern formulation of mechanics called Lagranian mechanics whereby the actually observed motion of an object is viewed as one among many potentially conceivable motions. The selection process of the actual motion satisfies the so-called Principle of Minimum Action. The corresponding formalism allows to tackle very intricate mechanical problems and has many technical advantages with regards to changes of variables. A ‘dual’ theory called Hamiltonian mechanics can also be formalized with its own advantages to address problems in mechanics. These two theories constitute the foundation on which quantum mechanics, statistical and quantum field theories are based. The module delivery includes the Minimum Action Principle, Euler-Lagrange equations, Noether’s theorem, Hamilton’s equations, and Poisson bracketsCoreScientific Computing 2026-27MTH2008MLevel 52026-27Students will have the opportunity to utilise computers for the numerical solution and simulation of models of physical and mathematical systems, including the use of computer procedural programming languages to solve computational problems. Numerical algorithms will be introduced to exemplify key concepts in computational programming, with the emphasis on understanding the nature of the algorithm and the features and limitations of its computational implementation. In creating programs, the emphasis will be on using effective programming techniques and on efficient debugging, testing and validation methods. Students may also develop skills at using a logbook as a factual record and as reflective self-assessment to support their learning.CoreStatistical and Quantum Physics I 2026-27PHY2007Level 52026-27This module introduces two pillars of modern physics: statistical mechanics and quantum physics. Both theories involve the combination of probability theory and physical concepts. The module will aim to equip students with the tools of probability theory necessary to engage with these two theories. It will then delve into a presentation of classical equilibrium statistical mechanics and the basic principles of quantum physics.CoreCosmology and General Relativity 2027-28PHY3009Level 62027-28The aim of the this module is to use appropriate cosmological models to understand the Universe from early to current and late epochs,CoreNumerical Methods 2027-28MTH3007MLevel 62027-28The module aims to equip students with knowledge of various numerical methods for solving applied mathematics problems, their algorithms and implementation in programming languages.CoreProject 2027-28PHY3003MLevel 62027-28In this module, students conduct research relating to the interface between mathematics and physics. This research can take place in a research group of the school, the university or in an external collaborating establishment.CoreQuantum Mechanics 2027-28PHY3004MLevel 62027-28This module covers the formalism of quantum mechanics underpinning a substantial part of our current understanding of the microscopic world. Topics covered include commutators, operators and observables, Shrodinger’s equation, Born rule, spin, Hydrogen atom, time-independent perturbation theory, time-dependent perturbation theory, and identical particles.CoreStatistical Mechanics 2027-28PHY3005MLevel 62027-28This module is concerned with bridging a microscopic description of the world (via classical or quantum Hamiltonian mechanics) with a macroscopic description world (via thermodynamics). This is done by considering a probability measure on the space of possible mechanical (micro)states of a system. Topics covered include the basics of probability theory, notions of statistical equilibrium, statistical ensembles (canonical and microcanonical) applied to model systems, thermodynamic potentials and partition functions, and the statistical mechanics of identical particles.CoreAdvanced Topics of Mathematics and Mathematics Seminar 2027-28MTH3001MLevel 62027-28The module will cover several advanced topics of modern mathematics. The choice of the topics will be governed by the current research interests of academic staff and/or visiting scientists. Students will also have the opportunity to participate in mathematics research seminars.OptionalAdvanced Topics of Physics and Physics Seminar 2027-28PHY3001MLevel 62027-28The module will cover several advanced topics of modern physics. The choice of the topics will be governed by the current research interests of academic staff and/or visiting scientists. Students may also participate in physics research seminars.OptionalFluid Dynamics 2027-28MTH3002MLevel 62027-28This module gives a mathematical foundation of ideal and viscous fluid dynamics and their application to describing various flows in nature and technology. Students are taught methods of analysing and solving equations of fluid dynamics using analytic and most modern computational tools.OptionalMathematics Pedagogy 2027-28MTH3004MLevel 62027-28This module is designed to provide students with an insight into the teaching of Mathematics at secondary school level and does this by combining university lectures with an experience of a placement in a secondary school Mathematics department. The module aims to provide students with an opportunity to engage with cutting-edge maths education research and will examine how this research impacts directly on classroom practice. Students will have the opportunity to gain an insight into some of the key ideas in Mathematics pedagogy and how these are implemented in the school Mathematics lessons and will develop an understanding about the barriers to learning Mathematics that many students experience.OptionalMethods of Mathematical Physics 2027-28MTH3006MLevel 62027-28The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.OptionalPhysics Pedagogy 2027-28PHY3002MLevel 62027-28This module is designed to provide students with an insight into the teaching of science at secondary school level and does this by combining university lectures with an experience of a placement in a secondary school science department. The module is particularly aimed at those considering a career in science teaching and provides students with an opportunity to engage with cutting edge science education research and will examine how this research impacts directly on classroom practice. Students will have the opportunity to gain an insight into some of the key ideas in science pedagogy and how these are implemented in the school science lessons and will develop an understanding about the barriers to learning science that many students experience.OptionalMasters Project 2028-29MTH9007MLevel 72028-29In this quadruple module a student undertakes a substantial project under supervision of a research-active member of staff. Projects will be offered to students in a wide range of subjects, which will be assigned with account for student's individual preferences and programme of their studies. The project can be undertaken at an external collaborating establishment. Students independently conduct a substantial research in modern mathematical, computational or theoretical physics working in a research group of the school, university or an external collaborating establishment.CorePhysics That Matters 2028-29PHY9052Level 72028-29The module will introduce students to a diverse range of contemporary issues in applied physics which have a high societal impact. Students will work independently on specific subjects of their choice amongst a proposed selection, and will hone their ability to synthetise contrary views from the scientific literature as well as their ability to look at multifaceted problems from multiple vantage points.CoreReading Module in Mathematics 2028-29MTH9018Level 72028-29The reading module allows students the opportunity to acquire knowledge of a particular area of mathematics, and develop the skills needed to study mathematics in a more independent manner. The module also provides an opportunity for Master's level students to study certain subjects in mathematics which may not be covered by any regular lecture modules, thus adding to the flexibility of the scheme of studies. Subject areas for proposed reading modules will be announced to students, together with an indicative syllabus. The choice offered will depend on the range of other lecture modules available to MMath students, as well as on the availability of teaching staff with particular areas of mathematical expertise, who could be able to act as moderators. The role of the reading module moderator is to provide students with support for their reading, including the setting of mathematical problems that are to be solved. The moderator also sets the written examination paper.OptionalFinancial Kinetics 2028-29MTH9001MLevel 72028-29This module brings together the main ideas and methods of the mathematical theory of financial markets. In addition, the methods of practical calculations of volatilities of traded assets from historical data are discussed. The influence of randomness of the interest rate and volatilities on price of options is studied.OptionalMolecular Modelling 2028-29PHY9002MLevel 72028-29This module introduces modern computational techniques for molecular modelling in condensed matter physics.Optional

              What You Need to Know

              We want you to have all the information you need to make an informed decision on where and what you want to study. In addition to the information provided on this course page, our What You Need to Know page offers explanations on key topics including programme validation/revalidation, additional costs, contact hours, and our return to face-to-face teaching.

              How you are assessed

              The course is assessed through a variety of means, including tests, course work, examinations, written reports and oral presentations.

              Accreditation

              Our BSc programme currently meets the educational requirements of the Chartered Mathematician designation. This is awarded by the Institute of Mathematics and its Applications (IMA), when it is followed by subsequent training and experience in employment to obtain equivalent competences to those specified by the Quality Assurance Agency for taught Master’s degrees. The MMath programme is accredited by the IMA.

              Institute of Mathematics and its Applications Logo

              Accreditation

              This programme is accredited by the Institute of Physics (IOP). Holders of accredited degrees are eligible for IOP membership and can follow a route to professional registration as a RSci, CPhys, and/or CSci.

              More Information
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              Research-informed Teaching

              Teaching on this course is conducted by academic members of staff who are active researchers in their fields. This research informs teaching at all levels of the programme. Staff conduct cutting-edge research in fundamental and applied mathematics and physics, ranging from pure mathematics to applied nano-science at the interface between biology, chemistry, physics, and mathematics. The School of Engineering and Physical Sciences collaborates with top research institutions in Germany, Japan, Norway, the Netherlands, Singapore, Spain, and the USA.

              Visiting Speakers

              The School of Engineering and Physical Sciences regularly welcomes guest speakers from around the world. Recent visitors to the University of Lincoln have included former vice president of the Royal Astronomical Society Professor Don Kurtz, mathematician and author Professor Marcus du Sautoy OBE, and operations research specialist Ruth Kaufman OBE.

              There is a wealth of materials provided by lecturers for independent study, they also show you where to find information beyond the scope of the module if you are interested and want to learn more.

              Margaret-Ann Withington

              MMath Mathematics and Physics

              Placements

              Students on this course are encouraged to obtain and undertake work placements independently in the UK or overseas during their studies, providing hands-on experience in industry. These can range from a few weeks to a full year if students choose the sandwich year option. Placements may be conducted with external research institutions (which can be overseas). The option is subject to availability and selection criteria set by the industry or external institution. A Placement Year Fee is payable to the University of Lincoln during this year for students joining in 2025/26 and beyond. Students are expected to cover their own travel, accommodation, and living costs.

              What Can I Do with a Mathematics and Theoretical Physics Degree?

              Mathematics and Physics graduates may go on to careers in science and technology, engineering, computing, medicine, education, consultancy, business and finance, and within government bodies. Some may choose to undertake further study at postgraduate level. Our courses aim to provide a thorough grounding in analytical and numerical methods, practical scientific skills, and research methods. Additionally, transferable skills such as communications, problem-solving, and decision-making, which students are expected to develop throughout their studies, are valuable in many areas of employment.

              Entry Requirements 2025-26

              United Kingdom

              112 UCAS Tariff points from a minimum of 2 A Levels or equivalent qualifications to include 48 points from Maths.

              BTEC and T Level qualifications will be considered provided a grade B is obtained in A Level Maths.

              Access to Higher Education Diploma: 45 Level 3 credits with a minimum of 112 UCAS Tariff points, including 48 points from 15 credits in Maths

              International Baccalaureate: 29 points overall to include a Higher Level 5 in Maths.

              GCSE's: Minimum of three at grade 4 or above, which must include English and Maths. Equivalent Level 2 qualifications may also be considered.


              The University accepts a wide range of qualifications as the basis for entry and do accept a combination of qualifications which may include A Levels, BTECs, EPQ etc.

              We may also consider applicants with extensive and relevant work experience and will give special individual consideration to those who do not meet the standard entry qualifications.

              International

              Non UK Qualifications:

              If you have studied outside of the UK, and are unsure whether your qualification meets the above requirements, please visit our country pages https://www.lincoln.ac.uk/studywithus/internationalstudents/entryrequirementsandyourcountry/ for information on equivalent qualifications.

              If you are an overseas student, you may require an ATAS (Academic Technology Approval Scheme) certificate in order to enrol on this course.

              https://www.gov.uk/guidance/academic-technology-approval-scheme

              EU and Overseas students will be required to demonstrate English language proficiency equivalent to IELTS 6.0 overall, with a minimum of 5.5 in each element. For information regarding other English language qualifications we accept, please visit the English Requirements page https://www.lincoln.ac.uk/studywithus/internationalstudents/englishlanguagerequirementsandsupport/englishlanguagerequirements/

              If you do not meet the above IELTS requirements, you may be able to take part in one of our Pre-sessional English and Academic Study Skills courses.

              https://www.lincoln.ac.uk/studywithus/internationalstudents/englishlanguagerequirementsandsupport/pre-sessionalenglishandacademicstudyskills/

              For applicants who do not meet our standard entry requirements, our Science Foundation Year can provide an alternative route of entry onto our full degree programmes:
              https://www.lincoln.ac.uk/course/sfysfyub/

              If you would like further information about entry requirements, or would like to discuss whether the qualifications you are currently studying are acceptable, please contact the Admissions team on 01522 886097, or email admissions@lincoln.ac.uk

              Contextual Offers

              At Lincoln, we recognise that not everybody has had the same advice and support to help them get to higher education. Contextual offers are one of the ways we remove the barriers to higher education, ensuring that we have fair access for all students regardless of background and personal experiences. For more information, including eligibility criteria, visit our Offer Guide pages. If you are applying to a course that has any subject specific requirements, these will still need to be achieved as part of the standard entry criteria.

              Fees and Scholarships

              Going to university is a life-changing step and it's important to understand the costs involved and the funding options available before you start. A full breakdown of the fees associated with this programme can be found on our course fees pages.

              Course Fees

              For eligible undergraduate students going to university for the first time, scholarships and bursaries are available to help cover costs. To help support students from outside of the UK, we are also delighted to offer a number of international scholarships which range from £1,000 up to the value of 50 per cent of tuition fees. For full details and information about eligibility, visit our scholarships and bursaries pages.

              Find out More by Visiting Us

              The best way to find out what it is really like to live and learn at Lincoln is to visit us in person. We offer a range of opportunities across the year to help you to get a real feel for what it might be like to study here.

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