# MMath Mathematics

Apply## Key facts

**UCAS Code:**G101**Start date:**Sep 2020**Accreditation:**Institute of Mathematics and its Applications**High Flyer Programme:**qualified applicants can complete the course in 4 years**Part-time study:**available

## Study with us

- MMath is more challenging than the Honours degree

- gain the training and skills you’ll need for a career in Mathematics

- our graduates go on to work in research and development, telecommunications and consultancy

## Why this course?

Our MMath Mathematics degree shows how mathematics is applied to solve practical problems, meaning you’ll learn the skills that employers need. Statistics is the area of mathematics you’ll use to explore and try to explain the uncertain world in which we live.

Our flexible degree allows you to transfer between courses with the opportunity to study abroad.

### Accreditation

The course is accredited by the Institute of Mathematics and its Applications for the purpose of meeting in full the educational requirement for chartered status.

### What you’ll study

MMath Mathematics is a five-year programme. Each year contains compulsory classes and some years contain either optional classes, which relate to different areas of mathematics and/or elective classes from other subject areas in the University. Years 1 to 4 of the MMath and BSc (Honours) degrees follow the same curriculum. It’s possible to transfer between the MMath course and BSc Honours course at all stages, subject to satisfactory performance.

#### Years 1, 2 & 3

In addition to core mathematical methods, you’ll study applied analysis, mechanics, numerical analysis and statistics. You also choose elective classes.

In later years, you’ll choose from a range of Mathematics and Statistics classes from one or more specialist areas.

#### Years 4 & 5

You’ll undertake a project and choose from classes in topics such as financial derivatives, mathematical modelling in biology and medicine, numerical analysis, and the mathematics of networks.

### Mathematics & Statistics

If you take half of your third and fourth-year classes in Statistics you can graduate with the degree title MMath in Mathematics & Statistics.

### High Flyer Programme

Well-qualified applicants with appropriate A Levels and Advanced Highers will be admitted to the Faculty of Science prestigious 'High Flyer' Programme, which allows students to complete an Honours degree in three years and an Integrated Masters degree in four. If you are studying the relevant subjects you may receive a dual offer, specifying grades to direct entry to Year 2 as a High Flyer and also standard Year 1 entry.

### Study abroad

You have the opportunity to spend time studying abroad, normally in the third year of the course. We have links with three universities in Europe for exchanges under the European Union's SOCRATES (ERASMUS) scheme.

You can study at:

- University of Limerick, Republic of Ireland
- Johannes Kepler University, Linz, Austria
- Technical University of Denmark, Lyngby, Denmark

We also have links with several non-European universities, and our students have recently studied abroad at:

- Nanyang Technological University, Singapore
- University of Otago, New Zealand
- University of Toronto, Canada

### Facilities

You’ll have access to well-equipped, modern computing laboratories and teaching rooms, as well as 24-hour access to an advanced computer information network and a sophisticated virtual e-learning environment. We have also an undergraduate common room which gives you a modern and flexible area that's used for individual and group study work and is also a relaxing social space.

## Course content

Current students are taking the following classes, and we expect the syllabus to be similar to this in future years.

##### Introduction to Calculus

##### Applications of Calculus

The fundamental concepts of calculus (differentiation and integration) presented in Applications of Calculus will be examined in more detail, extended to a larger class of functions by means of more sophisticated methods, including an introduction to complex numbers and variables, all demonstrated in application to practical problems including solving basic first and second-order differential equations.

##### Geometry & Algebra with Applications

This class will introduce you to vectors and matrices, along with the idea of mathematical modelling through their application to real-world problems.

##### Statistics & Data Presentation

Some basic ideas and techniques of statistics will be presented while introducing some essential study skills, allowing you to develop and practice personal and technical skills eg self-study, teamwork, analysing data, writing reports and making presentations.

##### Applying Mathematics 1

To introduce students to some elementary number theory with interesting modern applications. Codes and encryption: problem description and motivation. Mathematical background: natural numbers and integers, factorisation, proof by induction, highest common factor, lowest common multiple, Euclidean Algorithm, prime numbers and the Fundamental Theorem of Arithmetic, Diophantine equations, modular arithmetic, congruence mod n, solving equations in Z_{n}, Euler's phi-function and theorem. Applications to International Standard Book Numbers, Universal Product Codes, affine and exponential ciphers, and the RSA cryptosystem.

##### Applying Mathematics 2

To introduce students to areas of mathematics (graph theory) not usually met in school or college courses. Graph theory: Problem description and motivation (e.g. Konigsberg Bridge, three utilities problem, the travelling salesman problem). Graphs, multigraphs, isomorphic graphs, sub-graphs, paths, trails, circuits and cycles, Eulerian and Hamiltonian graphs, weighted graphs, minimal spanning trees, critical path analysis, planar graphs, Euler’s formula, Colouring of Graphs, Digraphs, Network Flows, and Social Network Analysis. Brief introduction to network science.

##### Linear Algebra & Differential Equations

This class will introduce you to the basic ideas of linear algebra, such as matrices and determinants, vector spaces, bases, eigenvalues and eigenvectors. You'll study various standard methods for solving ordinary differential equations and understand their relevance.

##### Advanced Calculus

Basic ideas, techniques and results for calculus of two and three variables, along with differentiation and integration over curves, surfaces and volumes of both scalar and vector fields will be presented.

##### Applicable Analysis

This class will give a rigorous treatment of convergence of sequences and infinite series of real numbers and of continuity, differentiability and integrability of functions of a real variable, and will illustrate the importance of these concepts in the analysis of problems arising in applications.

##### Probability & Statistical Inference

Presentation of the basic concepts of probability theory and statistical inference will be covered to provide you with the tools to appropriately analyse a given data set and effectively communicate the results of such analysis.

##### Introduction to Newtonian Mechanics

This class will develop your appreciation of the basic concepts of force, momentum and energy, and of Newton’s laws of motion and will equip you to apply these concepts to model physical systems, in particular the orbital motion of bodies.

##### Mathematical & Statistical Computing

This class will introduce you to the R computing environment. It'll enable you to use R to import data and perform statistical tests, allow you to understand the concept of an algorithm and what makes a good algorithm and will equip you for implementing simple algorithms in R.

### Compulsory classes

##### Complex Variables & Integral Transforms

This class will introduce functions of a complex variable, define concepts such as continuity, differentiability, analyticity, line integration, singular points, etc. It'll examine some important properties of such functions, and consider some applications of them, eg conformal mappings, and the evaluation of real integrals using the Residue Theorem. It'll also introduce you to Fourier and Laplace transform methods for solving linear ordinary differential equations and convolution type integral equations.

##### Linear Algebra

Here we'll introduce basic algebraic structures, with particular emphasis on those pertaining to finite dimensional linear spaces and deepen your understanding of linear mappings. We'll also provide an introduction to inner product spaces and bilinear forms.

##### Differential Equations

We'll introduce you to analytical methods for solving ordinary and partial differential equations so you'll develop an understanding along with technical skills in this area.

### Optional classes

##### Applicable Analysis

We'll introduce you to the basic theory and applications of metric spaces, normed vector spaces and Banach spaces, inner product spaces and Hilbert spaces, and bounded linear operators on normed linear spaces.

##### Inference & Regression Modelling

This class will:

- review the concepts of probability distributions and how to work with these
- present approaches to parameter estimation, focusing on maximum likelihood estimation, bootstrap estimation, and properties of estimators
- present hypothesis testing procedures, including classical likelihood ratio tests and computer-based methods for testing parameter values, and goodness-of-fit tests.
- introduce and provide understanding of the least squares multiple regression model, general linear model, transformations and variable selection procedures
- present use of R functions for regression and interpretation of R output

##### Mechanics of Rigid Bodies & Fluids

This class will:

- convey the generalisation of the mechanics of single-particle systems to many-particle systems
- convey the central ideas of a continuum description of material behaviour and to understand relevant constraints
- ground students in the basic principles governing three-dimensional motions of rigid bodies
- convey how the ideas of continuum theory are applied to static and inviscid fluids.

##### Numerical Analysis

This module will motivate the need for numerical algorithms to approximate the solution of problems that can't be solved with pen and paper. It'll develop your skills in performing detailed analysis of the performance of numerical methods and will continue to develop your skills in the implementation of numerical algorithms using R.

##### Stochastics & Financial Econometrics

You'll be introduced to the basic concepts of random phenomena evolving in time, from two complementary points of view: probabilistic modelling and data-driven analysis. Presentation of underlying ideas of simple stochastic processes, time series models, and the associated probability theory and statistical techniques will be covered. In addition to applications of the methods to financial and economic systems, including modelling, data analysis, and forecasting.

##### Communicating Mathematics & Statistics

This class provides you with experience of the skills required to undertake project work, and to communicate the findings in written and oral form using a variety of sources, such as books, journals and the internet.

##### Modelling & Simulation with Applications to Financial Derivatives

Here you'll get an introduction to ideas in mathematics and statistics that can be used to model real systems, with an emphasis on the valuation of financial derivatives. This module places equal emphasis on deterministic analysis (calculus, differential equations) and stochastic analysis (Brownian motion, birth and death processes). In both cases, in addition to theoretical analysis, appropriate computational algorithms are introduced. The first half of the class introduces general modelling and simulation tools, and the second half focuses on the specific application of valuing financial derivatives, including the celebrated Black-Scholes theory.

##### Applicable Analysis 3

This class will present the main results in Functional Analysis, give an introduction to linear operators on Banach and Hilbert spaces and study applications to integral and differential equations.

##### Statistical Modelling & Analysis

This class will provide you with a range of applied statistical techniques that can be used in professional life.

##### Fluids & Waves

You'll be introduced to the theory of Newtonian fluids and its application to flow problems and the dynamics of waves on water and in other contexts.

##### Finite Element Methods for Boundary Value Problems & Approximation

You'll be presented with the basic theory and practice of finite element methods and polynomial and piecewise polynomial approximation theory.

##### Applied Statistics in Society

You'll be introduced to a range of modern statistical methods and practices used in industry, commerce and research, and will develop skills in your application and presentation.

##### Mathematical Biology & Marine Population Modelling

Here you'll learn the application of mathematical models to a variety of problems in biology, medicine, and ecology. It'll show the application of ordinary differential equations to simple biological and medical problems, the use of mathematical modelling in biochemical reactions, the application of partial differential equations in describing spatial processes such as cancer growth and pattern formation in embryonic development, and the use of delay-differential equations in physiological processes. The marine population modelling element will introduce the use of difference models to represent population processes through applications to fisheries, and the use of coupled ODE system to represent ecosystems. Practical work will include example class case studies that will explore a real-world application of an ecosystem model.

##### Mathematical Introduction to Networks

This class will demonstrate the central role network theory plays in mathematical modelling. It'll also show the intimate connection between linear algebra and graph theory and how to use this connection to develop a sound theoretical understanding of network theory. Finally, it'll apply this theory as a tool for revealing structure in networks.

##### Medical Statistics

Students will learn new statistical methodology and apply it to real data from medical research studies, with an emphasis on the interpretation of the statistical results in the context of the medical problem being investigated. This skill is necessary for the application of statistics to medical data and differs from the traditional, standard interpretation of statistical textbook problems.

##### Project

The class will provide you with experience and expertise in skills required to undertake a sustained and significant individual project in a mathematical or statistical area, using a variety of sources, such as books, journals and the internet, and to communicate the findings in written and oral form.

##### Modelling & Simulation with Applications to Financial Derivatives

##### Applicable Analysis

To present the main results in Functional Analysis, give an introduction to linear operators on Banach and Hilbert spaces and study applications to integral and differential equations.

##### Statistical Modelling & Analysis

We'll provide you with a range of applied statistical general linear modelling techniques that can be used in professional life for the analysis of univariate and multivariate data.

##### Fluids & Waves

This class will introduce the theory of Newtonian fluids and its application to flow problems and the dynamics of waves on water and in other contexts.

** **

##### Fininte Element Methods for Boundary Value Problems & Approximation

##### Applied Statistics in Society

This class will introduce students to a range of modern statistical methods and practices used in industry, commerce and research, and to develop skills in their application and presentation.

** **

##### Mathematical Biology & Marine Population Modelling

This course will teach the application of mathematical models to a variety of problems in biology, medicine, and ecology. It'll show the application of ordinary differential equations to simple biological and medical problems, the use of mathematical modelling in biochemical reactions, the application of partial differential equations in describing spatial processes such as cancer growth and pattern formation in embryonic development, and the use of delay-differential equations in physiological processes.

The marine population modelling element will introduce the use of difference models to represent population processes through applications to fisheries, and the use of coupled ODE system to represent ecosystems. Practical work will include example class case studies that'll explore a real-world application of an ecosystem model.

##### Mathematical Introduction to Networks

This class will demonstrate the central role network theory plays in mathematical modelling. It'll show the intimate connection between linear algebra and graph theory and how to use this connection to develop a sound theoretical understanding of network theory. Finally, application of the theory as a tool for revealing structure in networks.

##### Topics in Applied Analysis

This class will expose you to a number of diverse topics in modern applied analysis, explaining how key theoretical ideas underpin methods that play an important role in investigations into problems arising in the applied sciences.

##### Topics in Applied Statistics

This class will expose you to a number of diverse topics in modern applied statistics, explaining how key theoretical ideas underpin methods that play an important role in investigations into problems arising in the applied sciences.

##### Topics in Applied Mathematics

This class will expose you to a number of diverse topics in a range of applied mathematics.

##### Topics in Numerical Analysis

This class will expose you to a number of diverse topics in modern numerical analysis, explaining how key theoretical and practical ideas underpin computational methods in science, engineering and technology.

##### Topics in Biological & Ecological Modelling

This class will make you aware of modern mathematical and statistical methods used to address real life research problems in the biological and ecological problems. In particular to bring together theoretical principles, computational practices and statistical data to construct models that describe the growth of populations and the spread of infectious diseases. To show students that these models an form the basis for decision making. The class will be based on the research interests and expertise of the Department (please note not all of the syllabus topics will be taught in a particular year).

## We're a 5-star

QS-rated University

### Learning & teaching

The following teaching methods are used in Mathematics and Statistics: lectures (using a variety of media including electronic presentations and computer demonstrations), tutorials, coursework and projects.

You’ll also learn through structured group work in problem solving and presentations.

On completion of the programme, you’ll be able to:

- demonstrate knowledge in the main areas of mathematics
- show an understanding of the principal mathematical and educational theories and a critical understanding of one or more specialised areas
- demonstrate skills in calculation
- develop and evaluate logical arguments, presenting them and their conclusions clearly and accurately
- demonstrate problem-solving skills, for example, abstracting the essentials of problems, formulating them mathematically and finding appropriate solutions
- undertake a critical analysis of data and draw conclusions from the data
- demonstrate a range of general skills including IT competency

### Assessment

In Mathematics & Statistics, knowledge, understanding and subject-specific skills are assessed by coursework, assignment, reports, presentations and written examinations.

## Entry requirements

Required subjects are shown in brackets.

Highers | ## Standard entry requirements:
(Maths A, Advanced Higher Maths recommended) ## Minimum entry requirements*:ABBB (Maths A plus one of Biology, Physics, Chemistry, Computing Science or Engineering Science) or AABB (including Maths A) |
---|---|

Advanced Highers |
(Maths A) |

A Levels |
(Maths A)
(Maths A) |

International Baccalaureate | 34 (Maths HL6) |

HNC | Entry to BSc in first instance |

International students | Find out entry requirements for your country by visiting our country pages. |

Deferred entry | Accepted |

### Widening access

We want to increase opportunities for people from every background. Strathclyde selects our students based on merit, potential and the ability to benefit from the education we offer. We look for more than just your grades. We consider the circumstances of your education and will make lower offers to certain applicants as a result.

### Degree preparation course for international students

We offer international students (non-EU/UK) who do not meet the academic entry requirements for an undergraduate degree at Strathclyde the option of completing an Undergraduate Foundation year programme at the University of Strathclyde International Study Centre.

Upon successful completion, you will be able to progress to this degree course at the University of Strathclyde.

### International students

We've a thriving international community with students coming here to study from over 100 countries across the world. Find out all you need to know about studying in Glasgow at Strathclyde and hear from students about their experiences.

Visit our international students' section## Fees & funding

### 2020/21

Scotland/EU | TBC Fees for students domiciled in Scotland and the EU are subject to confirmation in early 2020 by the Scottish Funding Council. (2019/20: £1,820) |
---|---|

Rest of UK | TBC Assuming no change in RUK fees policy over the period, the total amount payable by undergraduate students will be capped. For students commencing study in 2020/21, this is capped at £27,750 (with the exception of the MPharm and integrated Masters programmes), MPharm students pay £9,250 for each of the four years. Students studying on integrated Masters degree programmes pay an additional £9,250 for the Masters year with the exception of those undertaking a full-year industrial placement where a separate placement fee will apply. (2019/20: £9,250) |

International | £15,300 |

University preparation programme fees | International students can find out more about the costs and payments of studying a university preparation programme at the University of Strathclyde International Study Centre. |

Additional costs |
Class materials (lecture notes and exercise sheets) for the majority of Mathematics & Statistics classes are available free to download. For some classes, students may need access to a textbook. Textbook costs are typically in the £20-60 price range. These prices are dependent on format (e-book, soft or hardback) and whether bought new or second hand.
Third-year Maths and Teaching students will need to pay for the full price of a PVG membership scheme.
£40 returnable deposit for PRS handsets. |

Available scholarships | Take a look at our scholarships search for funding opportunities. |

**Please note:** All fees shown are annual and may be subject to an increase each year. Find out more about fees.

## How can I fund my studies?

### Students from Scotland and the EU

If you're a Scottish or EU student, you may be able to apply to the Student Award Agency Scotland (SAAS) to have your tuition fees paid by the Scottish government. Scottish students may also be eligible for a bursary and loan to help cover living costs while at University.

For more information on funding your studies have a look at our University Funding page.

### Students from England, Wales & Northern Ireland

We have a generous package of bursaries on offer for students from England, Northern Ireland and Wales:

You don’t need to make a separate application for these. When your place is confirmed at Strathclyde, we’ll assess your eligibility. Have a look at our scholarship search for any more funding opportunities.

### International Students (Non-UK Scholarships, EEA)

We have a number of scholarships available to international students. Take a look at our scholarship search to find out more.

## Glasgow is Scotland's biggest & most cosmopolitan city

Our campus is based in the very heart of Glasgow, Scotland's largest city. National Geographic named Glasgow as one of its 'Best of the World' destinations, while Rough Guide readers have voted Glasgow the world’s friendliest city! And Time Out named Glasgow in the top ten best cities in the world - we couldn't agree more!

We're in the city centre, next to the Merchant City, both of which are great locations for sightseeing, shopping and socialising alongside your studies.

Find out what some of our students think about studying in Glasgow!

Find out all about life in Glasgow## Careers

Our graduates enter industries such as manufacturing, the actuarial, accountancy and banking professions, commerce and government, consultancy and education.

Many go on to become investment analysts, numerical analysts, statisticians, actuaries, managers and teachers.

### How much will I earn?

The average starting salary for graduates with a mathematics degree is around £24,000.

Salary potential depends on the industry you choose to work in. With experience, actuaries can earn more than £60,000, numerical analysts £60,000. Investment analysts can earn up to £100,000 with bonuses.*

*Intended only as a guide.

We don't just focus on pure Mathematics, we're shown how it's applied to solve real-life practical problems.

## Apply

### Mathematics

**Qualification: **MMath

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