## MMath

## MMath

### Accreditations

This programme has been accredited by The Institute of Mathematics and its Applications (IMA).

**(or equivalent qualifications)**G102 4-5 years School of Mathematics and Physics Lincoln Campus [L] Validated BBB (120 UCAS Tariff points)

**(or equivalent qualifications)**G102

## Introduction

The MMath Mathematics degree aims to provide a fundamental education in mathematics, including pure and applied mathematics. There will be opportunities for students to develop high-level mathematical and problem-solving skills and to apply these in a variety of contexts. Students will also have the chance to work alongside fellow undergraduates and academic staff on projects.

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

## Accreditations

This programme is accredited by the Institute of Mathematics and its Applications.

## How You Study

The School of Mathematics and Physics is dedicated to achieving excellence in research and aims to provide a friendly, approachable culture for students to join.

The course is taught via lectures, problem solving classes, computer based classes and seminars. There is an average of 12 hours of contact study per week (additional student-managed independent study is required).

In the first year you have the chance to benefit from an additional three hours per week of problem solving tutorials. In addition, the School of Mathematics and Physics runs a tutor system for first year students, providing one hour weekly tutor sessions in small groups.

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

You study a broad range of mathematical topics, comprising both compulsory and elective modules.

### Contact Hours and Reading for a Degree

Students on this programme learn from academic staff who are often engaged in world-leading or internationally excellent research or professional practice. Contact time can be in workshops, practical sessions, seminars or lectures and may vary from module to module and from academic year to year. Tutorial sessions and project supervision can take the form of one-to-one engagement or small group sessions. Some courses offer the opportunity to take part in external visits and fieldwork.

It is still the case that students read for a degree and this means that in addition to scheduled contact hours, students are required to engage in independent study. This allows you to read around a subject and to prepare for lectures and seminars through wider reading, or to complete follow up tasks such as assignments or revision. As a general guide, the amount of independent study required by students at the University of Lincoln is that for every hour in class you are expected to spend at least two to three hours in independent study.

## How You Are Assessed

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

### Assessment Feedback

The University of Lincoln's policy on assessment feedback aims to ensure that academics will return in-course assessments to students promptly – usually within 15 working days after the submission date (unless stated differently above)..

### Methods of Assessment

The way students are assessed on this course may vary for each module. Examples of assessment methods that are used include coursework, such as written assignments, reports or dissertations; practical exams, such as presentations, performances or observations; and written exams, such as formal examinations or in-class tests. The weighting given to each assessment method may vary across each academic year. The University of Lincoln aims to ensure that staff return in-course assessments to students promptly.

## Staff

Throughout this degree, students may receive tuition from professors, senior lecturers, lecturers, researchers, practitioners, visiting experts or technicians, and they may be supported in their learning by other students.

For a comprehensive list of teaching staff, please see our School of Mathematics and Physics Staff Pages.

## Entry Requirements 2017-18

GCE Advanced Levels: BBB, including grade B from A Level Maths.

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

In addition, applicants will be required to have a minimum of three GCSEs at grade C or above (or equivalent), to include English and Maths.

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.

## Level 1

### Algebra *(Core)*

This module begins with refreshing some of the material from A-Level Maths, such as the binomial theorem and division of polynomials. The main part of the module is a systematic study of general systems of simultaneous linear equations and their solutions. Vectors and matrices are introduced in order to describe the properties of these systems and solutions, and complete answers are obtained to such questions as whether a solution exists and if so how many solutions there are.

### Calculus *(Core)*

This 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.

### Computer Algebra and Technical Computing *(Core)*

This 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.

### Geometrical Optics, Waves and Mechanics *(Core)*

This module will present an introduction to the fundamentals of waves, geometrical optics and mechanics, including their mathematical foundations.

### Ideas of Mathematical Proof *(Core)*

The 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'.

### Linear Algebra *(Core)*

This 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 diagonalization and reduction to other canonical forms. Special types of mappings and matrices (orthogonal, symmetric) are introduced. Applications of linear algebra to geometry of quadratic surfaces are explored.

### Probability and Statistics *(Core)*

This 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).

### Professional Skills and Group Study *(Core)*

This 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.

## Level 2

### Algebraic Structures *(Core)*

The 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.

### Coding Theory *(Core)*

Transmission 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.

### Complex Analysis *(Core)*

Ideas 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'.

### Differential Equations *(Core)*

Calculus 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.

### Group Project *(Core)*

This 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.

### Industrial and Financial Mathematics *(Core)*

Students have the opportunity to learn how mathematics is applied to modern industrial problems, and how the mathematical apparatus finds applications in the financial sector.

### Lagrangian and Hamiltonian Mechanics *(Core)*

The 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.

### Scientific Computing *(Core)*

Students 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.

## Level 3

### Advanced Topics of Mathematics and Mathematics Seminar *(Core)*

The 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.

### Fluid Dynamics *(Option)†*

*(Option)†*

This 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.

### Group Theory *(Core)*

Symmetry, 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.

### Mathematics Pedagogy *(Option)†*

*(Option)†*

This 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.

### Mathematics Project *(Core)*

This 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.

### Methods of Mathematical Physics *(Option)†*

*(Option)†*

The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.

### Numerical Methods *(Core)*

The module aims to equip students with knowledge of various numerical methods for solving applied mathematics problems, their algorithms and implementation in programming languages.

### Tensor Analysis *(Core)*

This 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.

## Level 4

### Financial Kinetics *(Core)*

This 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.

### Galois Theory *(Core)*

Galois 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).

### Lie Algebras *(Core)*

Lie 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.

### Mathematics Masters Project *(Core)*

In 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.

### Nilpotent Groups *(Option)†*

*(Option)†*

The 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.

### Reading Module in Mathematics *(Option)†*

*(Option)†*

The 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 MMath 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.

†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.

## Special Features

Research is a critical part of the academic environment at the University of Lincoln, and as one of our students you can expect to be taught by research academics in the field. Under our “student as producer” initiative you will be expected to contribute to new knowledge yourself. Research will form a part of your study from your first year in a variety of ways such as individual and team projects, and will culminate in the final year project.

## Placements

The degree is optionally available in a sandwich mode variant. If students choose the sandwich placement option, they take a year out in industry or external research institution (which can be oversees) between years two and three, gaining invaluable practical experience. The option is subject to availability.

### Placement Year

When students are on an optional placement in the UK or overseas or studying abroad, they will be required to cover their own transport and accommodation and meals costs. Placements can range from a few weeks to a full year if students choose to undertake an optional sandwich year in industry.

Students are encouraged to obtain placements in industry independently. Tutors may provide support and advice to students who require it during this process.

## Student as Producer

Student as Producer is a model of teaching and learning that encourages academics and undergraduate students to collaborate on research activities. It is a programme committed to learning through doing.

The Student as Producer initiative was commended by the QAA in our 2012 review and is one of the teaching and learning features that makes the Lincoln experience unique.

## Facilities

The University is developing new purpose-designed facilities for the School of Mathematics and Physics at the heart of its Brayford Pool campus.

At Lincoln, we constantly invest in our campus as we aim to provide the best learning environment for our undergraduates. Whatever the area of study, the University strives to ensure students have access to specialist equipment and resources, to develop the skills, which they may need in their future career.

View our campus pages [www.lincoln.ac.uk/home/campuslife/ourcampus/] to learn more about our teaching and learning facilities.

## Career Opportunities

MMaths Mathematics graduates are well placed to succeed in careers including science and technology, engineering, computing, medicine, education, consultancy, business and finance, and with government bodies.

The subject 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 that students are expected to develop during their studies, are valuable in many spheres of employment.

## Careers Service

The University Careers and Employability Team offer qualified advisors who can work with students to provide tailored, individual support and careers advice during their time at the University. As a member of our alumni we also offer one-to-one support in the first year after completing a course, including access to events, vacancy information and website resources; with access to online vacancies and virtual resources for the following two years.

This service can include one-to-one coaching, CV advice and interview preparation to help you maximise our graduates future opportunities.

The service works closely with local, national and international employers, acting as a gateway to the business world.

Visit our Careers Service pages for further information. [http://www.lincoln.ac.uk/home/campuslife/studentsupport/careersservice/]

## Additional Costs

For each course students may find that there are additional costs. These may be with regard to the specific clothing, materials or equipment required, depending on their subject area. Some courses provide opportunities for students to undertake field work or field trips. Where these are compulsory, the cost for the travel, accommodation and meals may be covered by the University and so is included in the fee. Where these are optional students will normally (unless stated otherwise) be required to pay their own transportation, accommodation and meal costs.

With regards to text books, the University provides students who enrol with a comprehensive reading list and our extensive library holds either material or virtual versions of the core texts that students are required to read. However, students may prefer to purchase some of these for themselves and will therefore be responsible for this cost. Where there may be exceptions to this general rule, information will be displayed in a section titled Other Costs below.

## Introduction

The research-informed MMath Mathematics degree aims to provide a fundamental education in mathematics, including pure and applied mathematics. There will be opportunities for students to develop high-level mathematical and problem-solving skills and to apply these in a variety of contexts. Students will also have the chance to work alongside fellow undergraduates and academic staff on projects.

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 gives students the opportunity to undertake a significant individual project.

## Accreditations

This programme is accredited by the Institute of Mathematics and its Applications.

## How You Study

The School of Mathematics and Physics is dedicated to achieving excellence in research and aims to provide a friendly, approachable culture for students to join. This course covers the core topics of

Mathematics and staff work alongside students to encourage them to apply imagination, creativity and rigour to the solution of various problems. There are also individual and group projects.

The subject 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.

The course is taught via lectures, problem solving classes, computer based classes and seminars. There is an average of 12 hours of contact study per week (additional student-managed independent study is required).

In the first year you have the chance to benefit from an additional three hours per week of problem solving tutorials. In addition, the School of Mathematics and Physics runs a tutor system for first year students, providing one hour weekly tutor sessions in small groups.

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

You study a broad range of mathematical topics, comprising both compulsory and elective modules.

### Contact Hours and Reading for a Degree

Students on this programme learn from academic staff who are often engaged in world-leading or internationally excellent research or professional practice. Contact time can be in workshops, practical sessions, seminars or lectures and may vary from module to module and from academic year to year. Tutorial sessions and project supervision can take the form of one-to-one engagement or small group sessions. Some courses offer the opportunity to take part in external visits and fieldwork.

It is still the case that students read for a degree and this means that in addition to scheduled contact hours, students are required to engage in independent study. This allows you to read around a subject and to prepare for lectures and seminars through wider reading, or to complete follow up tasks such as assignments or revision. As a general guide, the amount of independent study required by students at the University of Lincoln is that for every hour in class you are expected to spend at least two to three hours in independent study.

## How You Are Assessed

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

### Assessment Feedback

The University of Lincoln's policy on assessment feedback aims to ensure that academics will return in-course assessments to students promptly – usually within 15 working days after the submission date (unless stated differently above)..

### Methods of Assessment

The way students are assessed on this course may vary for each module. Examples of assessment methods that are used include coursework, such as written assignments, reports or dissertations; practical exams, such as presentations, performances or observations; and written exams, such as formal examinations or in-class tests. The weighting given to each assessment method may vary across each academic year. The University of Lincoln aims to ensure that staff return in-course assessments to students promptly.

## Staff

Throughout this degree, students may receive tuition from professors, senior lecturers, lecturers, researchers, practitioners, visiting experts or technicians, and they may be supported in their learning by other students.

For a comprehensive list of teaching staff, please see our School of Mathematics and Physics Staff Pages.

## Entry Requirements 2018-19

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

BTEC Extended Diploma: Merit, Merit, Pass plus a Grade B from A Level Maths.

International Baccalaureate: 29 points overall, with Higher Level Grade 5 in Maths.

Access to Higher Education Diploma: A minimum of 45 level 3 credits to include 30 at merit or above. To include 15 credits at Merit in Maths.

Applicants must have at least 3 GCSEs (or the equivalent) at grade C or above, to include Maths and English.

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.

## Level 1

### Algebra *(Core)*

This module begins with refreshing some of the material from A-Level Maths, such as the binomial theorem and division of polynomials. The main part of the module is a systematic study of general systems of simultaneous linear equations and their solutions. Vectors and matrices are introduced in order to describe the properties of these systems and solutions, and complete answers are obtained to such questions as whether a solution exists and if so how many solutions there are.

### Calculus *(Core)*

This 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.

### Computer Algebra and Technical Computing *(Core)*

This 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.

### Geometrical Optics, Waves and Mechanics *(Core)*

This module will present an introduction to the fundamentals of waves, geometrical optics and mechanics, including their mathematical foundations.

### Ideas of Mathematical Proof *(Core)*

The 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'.

### Linear Algebra *(Core)*

This 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 diagonalization and reduction to other canonical forms. Special types of mappings and matrices (orthogonal, symmetric) are introduced. Applications of linear algebra to geometry of quadratic surfaces are explored.

### Probability and Statistics *(Core)*

This 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).

### Professional Skills and Group Study *(Core)*

This 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.

## Level 2

### Algebraic Structures *(Core)*

The 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.

### Coding Theory *(Core)*

Transmission 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.

### Complex Analysis *(Core)*

Ideas 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'.

### Differential Equations *(Core)*

Calculus 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.

### Group Project *(Core)*

This 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.

### Industrial and Financial Mathematics *(Core)*

Students have the opportunity to learn how mathematics is applied to modern industrial problems, and how the mathematical apparatus finds applications in the financial sector.

### Lagrangian and Hamiltonian Mechanics *(Core)*

The 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.

### Scientific Computing *(Core)*

Students 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.

## Level 3

### Advanced Topics of Mathematics and Mathematics Seminar *(Core)*

The 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.

### Fluid Dynamics *(Option)†*

*(Option)†*

This 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.

### Group Theory *(Core)*

Symmetry, 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.

### Mathematics Pedagogy *(Option)†*

*(Option)†*

This 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.

### Mathematics Project *(Core)*

This 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.

### Methods of Mathematical Physics *(Option)†*

*(Option)†*

The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.

### Numerical Methods *(Core)*

The module aims to equip students with knowledge of various numerical methods for solving applied mathematics problems, their algorithms and implementation in programming languages.

### Tensor Analysis *(Core)*

This 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.

## Level 4

### Financial Kinetics *(Core)*

This 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.

### Galois Theory *(Core)*

Galois 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).

### Lie Algebras *(Core)*

Lie 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.

### Mathematics Masters Project *(Core)*

In 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.

### Nilpotent Groups *(Option)†*

*(Option)†*

The 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.

### Reading Module in Mathematics *(Option)†*

*(Option)†*

The 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 MMath 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.

†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.

## Special Features

Research is a critical part of the academic environment at the University of Lincoln, and as one of our students you can expect to be taught by research academics in the field. Under our “student as producer” initiative you will be expected to contribute to new knowledge yourself. Research will form a part of your study from your first year in a variety of ways such as individual and team projects, and will culminate in the final year project.

## Placements

The degree is optionally available in a sandwich mode variant. If students choose the sandwich placement option, they take a year out in industry or external research institution (which can be oversees) between years two and three, gaining invaluable practical experience. This option is subject to availability.

### Placement Year

When students are on an optional placement in the UK or overseas or studying abroad, they will be required to cover their own transport and accommodation and meals costs. Placements can range from a few weeks to a full year if students choose to undertake an optional sandwich year in industry.

Students are encouraged to obtain placements in industry independently. Tutors may provide support and advice to students who require it during this process.

## Student as Producer

Student as Producer is a model of teaching and learning that encourages academics and undergraduate students to collaborate on research activities. It is a programme committed to learning through doing.

The Student as Producer initiative was commended by the QAA in our 2012 review and is one of the teaching and learning features that makes the Lincoln experience unique.

## Facilities

The School of Mathematics and Physics forms part of the new Isaac Newton Building, which comprises additional spaces such as workshops and computer laboratories. The School also hosts its own supercomputer and the University’s library is open 24-hours a day, seven days a week for the majority of the academic year.

At Lincoln, we constantly invest in our campus as we aim to provide the best learning environment for our undergraduates. Whatever the area of study, the University strives to ensure students have access to specialist equipment and resources, to develop the skills, which they may need in their future career.

View our campus pages [www.lincoln.ac.uk/home/campuslife/ourcampus/] to learn more about our teaching and learning facilities.

## Career Opportunities

MMaths Mathematics graduates are well placed to succeed in careers including science and technology, engineering, computing, medicine, education, consultancy, business and finance, and with government bodies.

The subject 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 that students are expected to develop during their studies, are valuable in many spheres of employment.

## Careers Service

The University Careers and Employability Team offer qualified advisors who can work with students to provide tailored, individual support and careers advice during their time at the University. As a member of our alumni we also offer one-to-one support in the first year after completing a course, including access to events, vacancy information and website resources; with access to online vacancies and virtual resources for the following two years.

This service can include one-to-one coaching, CV advice and interview preparation to help you maximise our graduates future opportunities.

The service works closely with local, national and international employers, acting as a gateway to the business world.

Visit our Careers Service pages for further information. [http://www.lincoln.ac.uk/home/campuslife/studentsupport/careersservice/]

## Additional Costs

For each course students may find that there are additional costs. These may be with regard to the specific clothing, materials or equipment required, depending on their subject area. Some courses provide opportunities for students to undertake field work or field trips. Where these are compulsory, the cost for the travel, accommodation and meals may be covered by the University and so is included in the fee. Where these are optional students will normally (unless stated otherwise) be required to pay their own transportation, accommodation and meal costs.

With regards to text books, the University provides students who enrol with a comprehensive reading list and our extensive library holds either material or virtual versions of the core texts that students are required to read. However, students may prefer to purchase some of these for themselves and will therefore be responsible for this cost. Where there may be exceptions to this general rule, information will be displayed in a section titled Other Costs below.

## Tuition Fees

2017/18 | UK/EU | International |
---|---|---|

Full-time | £9,250 per level | £14,500 per level |

Part-time | £77.00 per credit point† | N/A |

Placement (optional) | Exempt | Exempt |

2018/19 | UK/EU | International |
---|---|---|

Full-time | £9,250 per level | £15,600 per level |

Part-time | £77.00 per credit point† | N/A |

Placement (optional) | Exempt | Exempt |

In 2018/19, fees for all new and continuing undergraduate UK and EU students will be £9,250.

†Please note that not all courses are available as a part-time option.

For more information and for details about funding your study, please see our UK/EU Fees & Funding pages or our International funding and scholarship pages. [www.lincoln.ac.uk/home/studyatlincoln/undergraduatecourses/feesandfunding/] [www.lincoln.ac.uk/home/international/feesandfunding/]