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Full-time

4-5 years

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Campus

Brayford Pool

Validation Status

Validated

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UCAS Code

G102

Course Code

MTHMTHUM

Key Information

Full-time

4-5 years

Typical Offer

View

Campus

Brayford Pool

Validation Status

Validated

Fees

View

UCAS Code

G102

Course Code

MTHMTHUM

MMath Mathematics MMath Mathematics

Mathematics at Lincoln is ranked 4th overall in the UK in the Guardian University Guide 2021 and is ranked 2nd in the UK for learning resources in the National Student Survey 2021 (out of 69 ranking institutions).

Key Information

Full-time

4-5 years

Typical Offer

View

Campus

Brayford Pool

Validation Status

Validated

Fees

View

UCAS Code

G102

Course Code

MTHMTHUM

Key Information

Full-time

4-5 years

Typical Offer

View

Campus

Brayford Pool

Validation Status

Validated

Fees

View

UCAS Code

G102

Course Code

MTHMTHUM

Select Year of Entry

Dr Sandro Mattarei - Programme Leader

Dr Sandro Mattarei - Programme Leader

Dr Sandro Mattarei is Programme Leader for the MMath Mathematics programme. His research interests lie in finite fields, group theory, Lie algebras, and number theory.

School Staff List

Welcome to MMath Mathematics

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.

Welcome to MMath Mathematics

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.

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.

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

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.

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

Teaching and Learning During Covid-19

Information for Offer Holders Joining Us in Autumn 2021

Letter from Head of School of Mathematics and Physics

We are delighted you are interested in joining us at the University of Lincoln and I am writing to let you know about our planning for the new academic year. You currently have an offer of a place at the University and we want to keep you updated so you can start preparing for your future,   should you be successful in meeting any outstanding conditions of your offer.

We fully intend your experience with us at Lincoln will be engaging, supportive and academically challenging. We are determined to provide our students with a safe and exciting campus experience, ensuring you benefit from the best that both face-to-face and online teaching offer. We have kept our focus on friendliness and community spirit at Lincoln and we look forward to your participation in that community.

As you know, the UK Government has published its roadmap for the easing of Coronavirus lockdown restrictions in England. There are still some uncertainties for universities around possible restrictions for the next academic year, particularly in relation to social distancing in large group teaching. We are planning in line with government guidance for both face-to-face and online teaching to ensure you have a good campus experience and can complete all the requirements for your programme.  We are fully prepared to adapt and flex our plans if changes in government regulations make this necessary during the year.

Face-to-face teaching and interaction with tutors and course mates are key to students’ learning and the broader student experience. Face-to-face sessions will be prioritised where it is most valuable, particularly for seminars, tutorials, workshops, practicals and lab sessions. Students tell us that there are real benefits to some elements of online learning within a blended approach, such as revisiting recorded materials and developing new digital skills and confidence.  At Lincoln we aim to take forward the best aspects of both.

This letter sets out in detail various aspects of the planned experience at Lincoln for your chosen subject area, and we hope the information is helpful as you plan for your future.

Teaching and Learning

In the School of Mathematics and Physics your teaching will be delivered using a blended approach. You will get regular face-to-face time with your lecturers, alongside your fellow students in a setting that will comply with the public health guidelines at the time. Any on-line provision will make use of a variety of approaches and technologies to facilitate your personal engagement with staff and students. Our digital learning tools have been chosen based on what students have told us they have enjoyed the most over the past year. Your programme of study will be delivered by a combination of lectures and problem solving practicals. Your degree will also include computer laboratory classes, which will be mostly online with some sessions face-to-face. You will have access to our computer facilities and the library for your self-study in a safe environment.

Our assessment processes will likewise follow government guidelines in relation to social distancing and safety. Most of our assessments are submitted online. Where there are exams, in-class tests, or oral presentations planned, decisions as to whether they go ahead in this form or via an online alternative will depend on safety guidance nearer the assessment period.

During your study you will have a Personal Tutor – a member of academic staff who is your designated ‘go to’ person for advice and support, both pastoral and academic. The School of Mathematics and Physics is a genuine community, built on strong staff-student engagement both within the formal structures of student representation and the Personal Tutoring system, and also through staff commitment to our students. Our staff look forward to welcoming you at our induction events in October. Please get in touch using the e-mail below if you have any further enquiries about our plans for your course.

The University Campus

We are very proud of our beautiful and vibrant campuses at the University of Lincoln and we have used our extensive indoor and outdoor spaces to provide students with access to study and social areas as well as learning resources and facilities, adapting them where necessary in line with government guidance. All the mitigations and safety measures you would expect are in place on our campuses (at Lincoln, Riseholme and Holbeach), such as hand sanitisers, one-way systems, and other social distancing measures where these are required.

Student Wellbeing and Support

The University’s Student Wellbeing Centre and Student Support Centre are fully open for face-to-face and online support. Should you, as one of our applicants, have any questions about coming to Lincoln in October or any other concerns, these specialist teams are here for you. You can contact Student Wellbeing and the Student Support Centre by visiting https://studentservices.lincoln.ac.uk where service details and contact information are available, or if you are in Lincoln you can make an appointment to meet a member of the team.

To enable you to make the most out of your experience in Lincoln and to help you access course materials and other services, we recommend that you have a desktop, laptop or tablet device available during your studies. This will enable you to engage easily with our online learning platforms from your student accommodation or from home. Students can use IT equipment on campus in the Library, our learning lounges, and specialist academic areas; however, there may not always be a space free when you have a timetabled session or an assessment to complete which is why we recommend you have your own device too, if possible. If you are struggling to access IT equipment or reliable internet services, please contact ICT for technical support and Student Support who can assist you with further advice and information.

We are committed to providing you with the best possible start to university life and to helping you to prepare for your time with us. As part of this commitment, you can access our Student Life pre-arrival online support package. This collection of digital resources, advice and helpful tips created by current students is designed to help you prepare for the all-important first steps into higher education, enabling you to learn within a supportive community and to make the most of the new opportunities that the University of Lincoln provides. When you are ready, you can begin by going to studentlife.lincoln.ac.uk/starting.

Students’ Union

Your Students’ Union is here to make sure that you get the most from every aspect of your student experience. They will be providing a huge range of in-person and virtual events and opportunities - you are sure to find something perfect for you! Meet people and find a new hobby by joining one of their 150 sports teams and societies. Grab lunch between teaching or a drink with friends in The Swan, Towers or The Barge. Learn new skills and boost your CV by taking part in training courses and volunteering opportunities in your spare time. Grab a bike from the Cycle Hire and explore the city you will be calling home.

To kick-off the new academic year, your Students’ Union will be bringing you The Official Lincoln Freshers Week 2021, with a huge line-up of social events, club nights, fayres and activities for you enjoy (restrictions permitting). Keep an eye on www.facebook.com/lincolnfreshers21 for line-up and ticket updates, so you don’t miss out.

Most importantly, your Students’ Union will always be there for you when you need it most; making sure that your voice as a student is always heard. The SU Advice Centre can provide independent advice and support on housing, finance, welfare and academic issues. As well as this, your Course Representatives are always on hand to make sure that you are getting the best from your academic experience. To find out more about the Students’ Union’s events, opportunities, support and how to get in contact go to: www.lincolnsu.com.

Student Accommodation

Many applicants will choose to live in dedicated student accommodation on, or close to, campus and you may well have already booked your student residence for the upcoming year. All University-managed student accommodation will have our Residential Wardens in place. Residential Wardens are here to help you settle into your new accommodation and will be offering flatmate and residential support activities throughout the year. If you have booked University accommodation, you will have already heard from us with further details on where you will be living to help you prepare. If you have not yet booked your accommodation, we still have plenty of options available. In the meantime, lots of advice and information can be found on the accommodation pages of our website.

The information detailed in this letter will form part of your agreement with the University of Lincoln. If we do not hear from you to the contrary prior to enrolment, we will assume that you acknowledge and accept the information contained in this letter. Adaptations to how we work may have to be made in line with any future changes in government guidance, and we will communicate these with you as necessary. Please do review the University’s Admissions Terms and Conditions (in particular sections 8 and 9) and Student Complaints Procedure so you understand your rights and the agreement between the University and its students.

We very much hope this information is useful to help you plan for the next step in your academic journey, and we look forward to welcoming you here at Lincoln this Autumn. This is the start of a new phase and will be an exciting time for all of us. If you have any questions, please do email me at mathsphysics@lincoln.ac.uk.

Professor Andrei Zvelindovsky

Head of the School of Mathematics and Physics

† 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 2022-23MTH1001MLevel 42022-23This 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 2022-23MTH1002MLevel 42022-23This 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 2022-23MTH1006MLevel 42022-23This 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 2022-23PHY1002MLevel 42022-23This module will present an introduction to the fundamentals of waves, geometrical optics and mechanics, including their mathematical foundations.CoreIdeas of Mathematical Proof 2022-23MTH1003MLevel 42022-23The 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 2022-23MTH1004MLevel 42022-23This 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 2022-23MTH1005MLevel 42022-23This 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 2022-23MTH1007MLevel 42022-23This 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 2023-24MTH2001MLevel 52023-24The 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 2023-24MTH2002MLevel 52023-24Transmission 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 2023-24MTH2003MLevel 52023-24Ideas 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 2023-24MTH2004MLevel 52023-24Calculus 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 2023-24MTH2005MLevel 52023-24This 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 2023-24MTH2006MLevel 52023-24Students 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 2023-24MTH2007MLevel 52023-24The aim of this module is to introduce students to main notions of theoretical mechanics. Students will have the opportunity to learn relevant mathematical techniques and methods.CoreScientific Computing 2023-24MTH2008MLevel 52023-24Students 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 2024-25MTH3001MLevel 62024-25The 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 2024-25MTH3003MLevel 62024-25Symmetry, 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 2024-25MTH3005MLevel 62024-25This 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 2024-25MTH3007MLevel 62024-25The 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 2024-25MTH3008MLevel 62024-25This 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 2024-25MTH3002MLevel 62024-25This 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 2024-25MTH3004MLevel 62024-25This 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 2024-25MTH3006MLevel 62024-25The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.OptionalFinancial Kinetics 2025-26MTH9001MLevel 72025-26This 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 2025-26MTH9002MLevel 72025-26Galois 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 2025-26MTH9003MLevel 72025-26Lie 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 2025-26MTH9004MLevel 72025-26In 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 2025-26MTH9005MLevel 72025-26The 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 2025-26MTH9006MLevel 72025-26The 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

† 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 2021-22MTH1001MLevel 42021-22This 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 2021-22MTH1002MLevel 42021-22This 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 2021-22MTH1006MLevel 42021-22This 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 2021-22PHY1002MLevel 42021-22This module will present an introduction to the fundamentals of waves, geometrical optics and mechanics, including their mathematical foundations.CoreIdeas of Mathematical Proof 2021-22MTH1003MLevel 42021-22The 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 2021-22MTH1004MLevel 42021-22This 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 2021-22MTH1005MLevel 42021-22This 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 2021-22MTH1007MLevel 42021-22This 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 2022-23MTH2001MLevel 52022-23The 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 2022-23MTH2002MLevel 52022-23Transmission 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 2022-23MTH2003MLevel 52022-23Ideas 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 2022-23MTH2004MLevel 52022-23Calculus 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 2022-23MTH2005MLevel 52022-23This 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 2022-23MTH2006MLevel 52022-23Students 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 2022-23MTH2007MLevel 52022-23The aim of this module is to introduce students to main notions of theoretical mechanics. Students will have the opportunity to learn relevant mathematical techniques and methods.CoreScientific Computing 2022-23MTH2008MLevel 52022-23Students 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 2023-24MTH3001MLevel 62023-24The 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 2023-24MTH3003MLevel 62023-24Symmetry, 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 2023-24MTH3005MLevel 62023-24This 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 2023-24MTH3007MLevel 62023-24The 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 2023-24MTH3008MLevel 62023-24This 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 2023-24MTH3002MLevel 62023-24This 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 2023-24MTH3004MLevel 62023-24This 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 2023-24MTH3006MLevel 62023-24The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.OptionalFinancial Kinetics 2024-25MTH9001MLevel 72024-25This 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 2024-25MTH9002MLevel 72024-25Galois 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 2024-25MTH9003MLevel 72024-25Lie 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 2024-25MTH9004MLevel 72024-25In 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 2024-25MTH9005MLevel 72024-25The 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 2024-25MTH9006MLevel 72024-25The 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

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

The 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. Accreditation for both courses expires during the 2021/2022 academic year. The University intends to renew the accreditation so that it is valid for students commencing their studies in 2022/2023.

How you are assessed

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

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

Entry Requirements 2022-23

United Kingdom

GCE Advanced Levels: ABB to include a grade B from A Level Maths.

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)

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 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.

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 2021-22

United Kingdom

GCE Advanced Levels: ABB to include a grade B from A Level Maths.

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)

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 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.

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

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.

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.

"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."

William Evans, MMath Mathematics student

Career Opportunities

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. The course aims 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 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. 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

Related Courses

The University intends to provide its courses as outlined in these pages, although the University may make changes in accordance with the Student Admissions Terms and Conditions.
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