Mathematics | MMath | University of Lincoln

Course Overview

Mathematical and problem-solving skills are highly valued by employers in a range of sectors, including science and technology, government, and finance.

The research-informed MMath Mathematics degree covers the core topics of mathematics. It aims to provide a thorough grounding in analytical and numerical methods, practical scientific skills, and research techniques. Additionally, students are encouraged to develop transferable communication, problem-solving, and decision making skills throughout their studies. Students can work alongside academic staff on challenging projects, which could contribute to academic research or collaboration with industry.

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 course, while the fourth year offers the opportunity to study more advanced topics in greater depth. The MMath also provides the opportunity to undertake a significant individual project.

Course Overview

Mathematical and problem-solving skills are highly valued by employers in a range of sectors, including science and technology, government, and finance.

Why Choose Lincoln

Subject ranked in the top 10 in the UK for student satisfaction*

Institute of Mathematics and its Applications (IMA) accreditation

Informed by cutting-edge research

Guest speakers from around the world

Additional problem-solving tutorials

Placement Year available

*Guardian University Guide 2023 (out of 65 ranking institutions).

How You Study

This course covers the core topics of mathematics. It aims to provide a thorough grounding in analytical and numerical methods, practical scientific skills, and research techniques. Additionally, students are encouraged to develop transferable communication, problem solving, and decision-making skills throughout their studies. Students will have the opportunity to study a broad range of mathematical topics, comprising both compulsory and optional modules.

Modules are delivered using various methods including lectures, seminars, problem-solving classes, tutorial classes, and workshops. In the first year students can benefit from an additional three hours per week of problem solving tutorials. There are also opportunities to take part in individual and group projects.

During the first year of the programme, the School of Mathematics and Physics runs a tutor system, providing one hour weekly tutor sessions in small groups.

The first three years are common with the BSc Mathematics. In the fourth year students are expected to progress to more advanced and in-depth topics, with a greater proportion of independent project work.

How You Study

During the first year of the programme, the School of Mathematics and Physics runs a tutor system, providing one hour weekly 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 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.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.CoreIdeas of Mathematical Proof 2023-24MTH1003MLevel 42023-24The purpose of this module is to introduce students to basic mathematical reasoning such as rigorous definitions and proofs, logical structure of mathematical statements. Students will have the opportunity to learn the set-theoretic notation, get acquainted with various strategies of mathematical proofs such as proof by mathematical induction or proof by contradiction. Rigorous definitions of limits of sequences and functions will form a foundation for other courses on calculus and differential equations. The importance of definitions and proofs will be illustrated by examples of "theorems" which may seem obvious but are actually false, as well as certain mathematical "paradoxes".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.CoreCoding Theory 2024-25MTH2002MLevel 52024-25Transmission of data may mean sending pictures from the Mars rover, streaming live music or videos, speaking on the phone, answering someone's question do you love me?. Problems arise if there are chances of errors creeping in, which may be catastrophic (say, receiving N instead of Y). Coding theory provides error-correcting codes, which are designed in such a way that errors that occur can be detected and corrected (within certain limits) based on the remaining symbols. The problem is balancing reliability with cost and/or slowing the transmission. Students will have the opportunity to study various types of error-correcting codes, such as linear codes, hamming codes, perfect codes, etc., some of which are algebraic and some correspond to geometrical patterns.CoreComplex Analysis 2024-25MTH2003MLevel 52024-25Ideas of calculus of derivatives and integrals are extended to complex functions of a complex variable. Students will learn that complex differentiability is a very strong condition and differentiable functions behave very well. Integration along paths in the complex plane is introduced. One of the main results of this beautiful part of mathematics is Cauchy's Theorem that states that certain integrals along closed paths are equal to zero. This gives rise to useful techniques for evaluating real integrals based on the 'calculus of residues'.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.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.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.CoreGroup 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.CoreMathematics Project 2025-26MTH3005MLevel 62025-26This is a double module in which a student undertakes a project under supervision of a research-active member of staff. The project can be undertaken at an external collaborating establishment. Projects will be offered to students in a wide range of subjects, assigned with consideration of a students' individual preferences and programme of their studies. Some projects will be more focused on a detailed study of mathematical theories or techniques in an area of current interest. Other projects may require solving specific problems that require the formulation of a mathematical model, its development and solution. Student meet regularly with their supervisor in order to receive guidance and review progress.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.CoreTensor 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.CoreFluid 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.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.OptionalFinancial Kinetics 2026-27MTH9001MLevel 72026-27This 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.CoreGalois Theory 2026-27MTH9002MLevel 72026-27Galois theory establishes a connection between the theory of polynomial equations and group theory. In fact, group theory largely originates from the work of Galois. For example, certain groups were called 'soluble' exactly because they correspond to soluble equations. Based on the previous modules Algebraic Structures and Group Theory, students will have the opportunity to learn about automorphisms of field extensions and the Galois correspondence. As an illustration, it is shown why some problems which confounded mathematicians for centuries are in fact insoluble (like the impossibility of trisecting an angle with a ruler and compass alone, or the insolubility of the general quintic equation).CoreLie Algebras 2026-27MTH9003MLevel 72026-27Lie algebras originated in the theory of continuous transformation groups as a means of introducing more linear structure and facilitate the classification of the so-called simple Lie groups. Theory of Lie algebras is now a well-established part of mathematics developing both in its own right and as a means of studying groups and even theoretical mechanics. This module deals with abstract Lie algebras. Students will have the opportunity to learn the basic properties of various classes of Lie algebras, including soluble, nilpotent, semisimple, graded, etc. Important results on automorphisms and derivations of Lie algebras and the classification of finite-dimensional simple complex Lie algebras will be discussed.CoreMathematics Masters Project 2026-27MTH9004MLevel 72026-27In this quadruple module a student may undertake 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 are expected to meet regularly with their supervisor in order to receive guidance and review progress. The project will result in a final written report/dissertation on a chosen mathematical area.CoreNilpotent Groups 2026-27MTH9005MLevel 72026-27The operation in groups is not commutative in general. It is natural to define groups that are close to commutative, such as soluble and nilpotent groups. Nilpotent groups appear throughout group theory, in particular, as important subgroups such as Sylow p-subgroups of finite groups, or unipotent matrix groups. Based on the previous module Group Theory, students will have the opportunity to learn special properties of nilpotent groups, explore powerful tools of their study, and get acquainted with several important results.OptionalReading Module in Mathematics 2026-27MTH9006MLevel 72026-27The 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.Optional

Modules

Algebra 2024-25MTH1001MLevel 42024-25This 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 2024-25MTH1002MLevel 42024-25This 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 2024-25MTH1006MLevel 42024-25This 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.CoreGeometrical Optics, Waves and Mechanics 2024-25PHY1002MLevel 42024-25This 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.CoreIdeas of Mathematical Proof 2024-25MTH1003MLevel 42024-25The purpose of this module is to introduce students to basic mathematical reasoning such as rigorous definitions and proofs, logical structure of mathematical statements. Students will have the opportunity to learn the set-theoretic notation, get acquainted with various strategies of mathematical proofs such as proof by mathematical induction or proof by contradiction. Rigorous definitions of limits of sequences and functions will form a foundation for other courses on calculus and differential equations. The importance of definitions and proofs will be illustrated by examples of "theorems" which may seem obvious but are actually false, as well as certain mathematical "paradoxes".CoreLinear Algebra 2024-25MTH1004MLevel 42024-25This 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 2024-25MTH1005MLevel 42024-25This 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 2024-25MTH1007MLevel 42024-25This 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 2025-26MTH2001MLevel 52025-26The 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.CoreCoding Theory 2025-26MTH2002MLevel 52025-26Transmission of data may mean sending pictures from the Mars rover, streaming live music or videos, speaking on the phone, answering someone's question do you love me?. Problems arise if there are chances of errors creeping in, which may be catastrophic (say, receiving N instead of Y). Coding theory provides error-correcting codes, which are designed in such a way that errors that occur can be detected and corrected (within certain limits) based on the remaining symbols. The problem is balancing reliability with cost and/or slowing the transmission. Students will have the opportunity to study various types of error-correcting codes, such as linear codes, hamming codes, perfect codes, etc., some of which are algebraic and some correspond to geometrical patterns.CoreComplex Analysis 2025-26MTH2003MLevel 52025-26Ideas of calculus of derivatives and integrals are extended to complex functions of a complex variable. Students will learn that complex differentiability is a very strong condition and differentiable functions behave very well. Integration along paths in the complex plane is introduced. One of the main results of this beautiful part of mathematics is Cauchy's Theorem that states that certain integrals along closed paths are equal to zero. This gives rise to useful techniques for evaluating real integrals based on the 'calculus of residues'.CoreDifferential Equations 2025-26MTH2004MLevel 52025-26Calculus 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.CoreGroup Project 2025-26MTH2005MLevel 52025-26This 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 2025-26MTH2006MLevel 52025-26Students 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 2025-26MTH2007MLevel 52025-26This 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 2025-26MTH2008MLevel 52025-26Students 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.CoreAdvanced Topics of Mathematics and Mathematics Seminar 2026-27MTH3001MLevel 62026-27The 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.CoreGroup Theory 2026-27MTH3003MLevel 62026-27Symmetry, 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.CoreMathematics Project 2026-27MTH3005MLevel 62026-27This is a double module in which a student undertakes a project under supervision of a research-active member of staff. The project can be undertaken at an external collaborating establishment. Projects will be offered to students in a wide range of subjects, assigned with consideration of a students' individual preferences and programme of their studies. Some projects will be more focused on a detailed study of mathematical theories or techniques in an area of current interest. Other projects may require solving specific problems that require the formulation of a mathematical model, its development and solution. Student meet regularly with their supervisor in order to receive guidance and review progress.CoreNumerical Methods 2026-27MTH3007MLevel 62026-27The module aims to equip students with knowledge of various numerical methods for solving applied mathematics problems, their algorithms and implementation in programming languages.CoreTensor Analysis 2026-27MTH3008MLevel 62026-27This 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.CoreFluid Dynamics 2026-27MTH3002MLevel 62026-27This 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 2026-27MTH3004MLevel 62026-27This 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 2026-27MTH3006MLevel 62026-27The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.OptionalFinancial Kinetics 2027-28MTH9001MLevel 72027-28This 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.CoreGalois Theory 2027-28MTH9002MLevel 72027-28Galois theory establishes a connection between the theory of polynomial equations and group theory. In fact, group theory largely originates from the work of Galois. For example, certain groups were called 'soluble' exactly because they correspond to soluble equations. Based on the previous modules Algebraic Structures and Group Theory, students will have the opportunity to learn about automorphisms of field extensions and the Galois correspondence. As an illustration, it is shown why some problems which confounded mathematicians for centuries are in fact insoluble (like the impossibility of trisecting an angle with a ruler and compass alone, or the insolubility of the general quintic equation).CoreLie Algebras 2027-28MTH9003MLevel 72027-28Lie algebras originated in the theory of continuous transformation groups as a means of introducing more linear structure and facilitate the classification of the so-called simple Lie groups. Theory of Lie algebras is now a well-established part of mathematics developing both in its own right and as a means of studying groups and even theoretical mechanics. This module deals with abstract Lie algebras. Students will have the opportunity to learn the basic properties of various classes of Lie algebras, including soluble, nilpotent, semisimple, graded, etc. Important results on automorphisms and derivations of Lie algebras and the classification of finite-dimensional simple complex Lie algebras will be discussed.CoreMathematics Masters Project 2027-28MTH9004MLevel 72027-28In this quadruple module a student may undertake 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 are expected to meet regularly with their supervisor in order to receive guidance and review progress. The project will result in a final written report/dissertation on a chosen mathematical area.CoreNilpotent Groups 2027-28MTH9005MLevel 72027-28The operation in groups is not commutative in general. It is natural to define groups that are close to commutative, such as soluble and nilpotent groups. Nilpotent groups appear throughout group theory, in particular, as important subgroups such as Sylow p-subgroups of finite groups, or unipotent matrix groups. Based on the previous module Group Theory, students will have the opportunity to learn special properties of nilpotent groups, explore powerful tools of their study, and get acquainted with several important results.OptionalReading Module in Mathematics 2027-28MTH9006MLevel 72027-28The 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.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.

What You Need to Know

How you are assessed

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

How you are assessed

The course is assessed through a variety of means, including coursework, 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.

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 Mathematics and Physics 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.

Studying Mathematics at Lincoln is a way to learn more about a subject that has many applications within the real world, whilst also learning about theoretical Mathematics. It has helped me to grow as a mathematician.

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.

What Can I Do with a Mathematics Degree?

Mathematics 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.

United Kingdom

A Level: ABB to include a grade B from A Level Maths (128 UCAS Tariff points from a minimum of 3 A Levels or equivalent qualifications).

International Baccalaureate: 32 points overall, with Higher Level Grade 5 in Maths.

Access to Higher Education Diploma: 45 Level 3 credits with a minimum of 128 UCAS Tariff points, including 40 points from 15 credits in Maths.

BTEC qualifications may be considered with a grade B in A Level Maths.
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 and Maths. 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/lifesciences/

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

Entry Requirements 2024-25

United Kingdom
International

United Kingdom

A Level: ABB to include a grade B from A Level Maths (128 UCAS Tariff points from a minimum of 3 A Levels or equivalent qualifications).

International Baccalaureate: 32 points overall, with Higher Level Grade 5 in Maths.

Access to Higher Education Diploma: 45 Level 3 credits with a minimum of 128 UCAS Tariff points, including 40 points from 15 credits in Maths.

BTEC qualifications may be considered with a grade B in A Level Maths.
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 and Maths. Equivalent Level 2 qualifications may also be considered.

International

Non UK Qualifications:

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/

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.

Fees and Scholarships

Course Fees

Find out More at an Open Day

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. Visiting us in person is important and will help you to get a real feel for what it might be like to study here.

Book Your Place

Student walking together on campus in the summer

MMath
Mathematics MMath
Mathematics

Key Information

Duration

Typical Offer

Campus

UCAS Code

Duration

Typical Offer

Campus

UCAS Code

Academic Years

United Kingdom

International

United Kingdom

International