Mathematics and Physics | BSc (Hons)

Dr Fabien Paillusson - Programme Leader

Dr Fabien Paillusson's interests lie in theoretical and computational modelling, the foundations of physics, physics and maths education, AI (Machine Learning and Automated Reasoning), logic, and the philosophy of science.

Academic Staff List

Welcome to BSc (Hons) Mathematics and Physics

Taking a joint honours in Mathematics and 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.

How You Study

In the first year students can study modules including Algebra; Calculus; and Electricity, Magnetism, Thermal and Quantum Physics. Second year students progress onto 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.

The course is taught through lectures, problem-solving classes, computer-based classes, and seminars. In addition to lectures and problem-solving classes, first year students in the School of Mathematics and Physics can benefit from weekly one hour tutorial sessions in small groups.

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. To help you choose the course that’s right for you, we aim to bring to your attention all the important information you may need. Our What You Need to Know page offers detailed information on key areas including contact hours, assessment, optional modules, and additional costs.

Find out More

An Introduction to Your 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 2023-24MTH1001MLevel 42023-24This 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 2023-24MTH1002MLevel 42023-24This 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 2023-24MTH1006MLevel 42023-24This 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 2023-24PHY1003MLevel 42023-24This module covers basic notions of modern physics. In electricity and magnetism these include Coulombs 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 2023-24PHY1002MLevel 42023-24This module introduces established theories describing optical, acoustic, and mechanical phenomena. The optics part includes Fermats principle of light propagation, Snells laws of reflection and refraction, thin lenses, and Huygenss 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.CoreLinear Algebra 2023-24MTH1004MLevel 42023-24This 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 2023-24MTH1005MLevel 42023-24This 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 2023-24MTH1007MLevel 42023-24This 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 2024-25MTH2001MLevel 52024-25The 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.CoreCondensed Matter Physics 2024-25PHY2001MLevel 52024-25In contemporary research condensed matter physics pertains to the physics of condensed phases of matter such as solid and liquids. Depending on the properties of interest, condensed matter physics is traditionally split in two different sub-fields: solid state physics dealing primarily with the behavior of electrons in periodic solids, and soft-matter physics dealing with the properties of assemblies of atoms in a somewhat confined space. This module introduces the basic ideas of these two worlds from Drudes model and the band theory of conductivity in solids to the physics of colloidal and polymeric systems.CoreDifferential Equations 2024-25MTH2004MLevel 52024-25Calculus 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 2024-25PHY2002MLevel 52024-25This 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 Maxwells equations of electromagnetism as well as their solutions for some model problems in vacuum and in some materials. Topics covered include Gausss law, Maxwells law of induction, Faradays law, time-dependent electromagnetic fields, electromagnetic waves, and dielectric and magnetic materials.CoreGroup Project 2024-25MTH2005MLevel 52024-25This 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 2024-25MTH2006MLevel 52024-25Students 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 2024-25MTH2007MLevel 52024-25This 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, Noethers theorem, Hamiltons equations, and Poisson bracketsCoreScientific Computing 2024-25MTH2008MLevel 52024-25Students 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.CoreNumerical Methods 2025-26MTH3007MLevel 62025-26The module aims to equip students with knowledge of various numerical methods for solving applied mathematics problems, their algorithms and implementation in programming languages.CoreProject 2025-26PHY3003MLevel 62025-26In 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 2025-26PHY3004MLevel 62025-26This 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, Shrodingers equation, Born rule, spin, Hydrogen atom, time-independent perturbation theory, time-dependent perturbation theory, and identical particles.CoreStatistical Mechanics 2025-26PHY3005MLevel 62025-26This 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 2025-26MTH3001MLevel 62025-26The 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 2025-26PHY3001MLevel 62025-26The 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 2025-26MTH3002MLevel 62025-26This 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.OptionalGroup Theory 2025-26MTH3003MLevel 62025-26Symmetry, understood in most broad sense as invariants under transformations, permeates all parts of mathematics, as well as natural sciences. Groups are measures of such symmetry and therefore are used throughout mathematics. Abstract group theory studies the intrinsic structure of groups. The course begins with definitions of subgroups, normal subgroups, and group actions in various guises. Group homomorphisms are introduced and the related isomorphism theorems are proved. Sylow p-subgroups are introduced and the three Sylow theorems are proved. Throughout, symmetry groups are used as examples.OptionalMathematics Pedagogy 2025-26MTH3004MLevel 62025-26This 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 2025-26MTH3006MLevel 62025-26The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.OptionalPhysics of the Universe 2025-26PHY3006MLevel 62025-26This module covers the physics of astronomical, astrophysical, and cosmological phenomena. Topics covered include distance measures in the universe, planetary formation, stellar physics, and some elements of cosmology.OptionalPhysics Pedagogy 2025-26PHY3002MLevel 62025-26This 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.OptionalTensor Analysis 2025-26MTH3008MLevel 62025-26This module introduces tensors, which are abstract objects describing linear relations between vectors, scalars, and other tensors. The module aims to equip students with the knowledge of tensor manipulation, and introduces their applications in modern science.Optional

Features

Research Informed

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 collaborates with top research institutions in Germany, Japan, Norway, the Netherlands, Singapore, Spain, and the USA.

Visiting Speakers

The School of Mathematics and Physics 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.

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. When undertaking optional placements, students will be required to cover their transport, accommodation, and general living costs.

Accreditations and Memberships

This 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 BSc (Hons) Mathematics and Physics programme is also accredited by the Institute of Physics (IOP).

How you are assessed

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

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. The University of Lincoln offers a variety of merit-based and subject-specific bursaries and scholarships. For full details and information about eligibility, visit our scholarships and bursaries pages.

Entry Requirements 2023-24

United Kingdom

A Level: BBB, to include a grade B from both A Level Maths and Physics (120 UCAS Tariff points from a minimum of 3 A Levels or equivalent qualifications).

Access to Higher Education Diploma: 45 Level 3 credits with a minimum of 120 UCAS Tariff points, including 40 points from 15 credits in Maths and 15 credits in Physics

International Baccalaureate: 30 points overall, with Higher Level Grade 5 in Maths and Physics.

BTEC qualifications may be considered with a grade B in A Level Maths and Physics. Please contact our Admissions team for further information (admissions@lincoln.ac.uk).

A combination of qualifications which may include A Levels, BTEC, EPQ, etc.

Applicants will also need at least three GCSEs at grade 4 (C) or above, which must include English, Maths and Science. Equivalent Level 2 qualifications may also be considered.

The University accepts a wide range of qualifications as the basis for entry. We will 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/home/studywithus/internationalstudents/entryrequirementsandyourcountry/ for information on equivalent qualifications.

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/home/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/home/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/home/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

Students inside the Isaac Newton Building

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

Margaret-Ann Withington, MPhys Mathematics and Physics student.

Career Opportunities

Graduates may choose to use their problem-solving and analytical skills to develop careers in areas such as research, IT, science, education, consultancy, finance, business, and industry in the UK and overseas. Some may go on to undertake further study at postgraduate level. Additionally, transferable skills such as communications, problem-solving, and decision-making, which students are expected to develop throughout their studies, are valuable in many spheres of employment.

Visit Us in Person

The best way to find out what it is really like to live and learn at Lincoln is to join us for one of our Open Days. Discover our Isaac Newton Building, equipped with laboratories and workshops, as well as specialist robotics facilities and advanced research equipment.

Book Your Place

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Key Information

BSc (Hons) Mathematics and Physics