This course is unavailable through clearing

This course is now full for our 2021 entry, but have a look at our clearing vacancies to see if a similar course has space.

Search all clearing vacancies

MMath Mathematics / Course details

Year of entry: 2021

Coronavirus information for applicants and offer-holders

We understand that prospective students and offer-holders may have concerns about the ongoing coronavirus outbreak. The University is following the advice from Universities UK, Public Health England and the Foreign and Commonwealth Office.

Read our latest coronavirus information

Course description

First Year BSc Mathematics with Scarlett and Hana

This flexible single-honours undergraduate Masters degree programme offers you the widest choice of options, ideal if you are mathematically gifted and wish to keep your options open. You get good all-round mathematical knowledge together with the ability to experience more specialised results, methods and ideas. You can choose courses from other disciplines and from a huge variety of mathematics options allowing you to graduate with finely-honed skills in your own chosen areas. You get an education in sufficient depth in these specialised areas to enable you to undertake postgraduate studies, conduct mathematical research or work as a specialist mathematician in industry, business or higher education.

The programme has a core of basic mathematics which provides you with the fundamental mathematical knowledge and skills, and the basis for more advanced work later on. This core material is covered in the first three semesters, up to the mid-point of your second year. You develop your capacity to learn and apply mathematical ideas, to understand the significance and power of mathematics, and to acquire a thorough knowledge and understanding of those mathematical topics that any employer would expect of a mathematics graduate. After your first three semesters, you choose your lecture courses from a widening range of options in order that you can pursue whichever areas of mathematics most interest you. You can also, from your second year onwards, choose options from other subject areas.

Special features

  • Small group teaching is a significant part of the first year.
  • A wide range of options is available in the third year.
  • All undergraduate students have affiliate membership of the Institute of Mathematics and its Applications.
  • Students have an opportunity to spend a year on a work based placement. This gives an opportunity to gain invaluable work based experience and learn more about themselves and the workplace so that they are better able to make good choices about a career post-graduation. Many students who have a year placement are taken on by the same employer once they have finished their studies. For students who take the 4 year MMath course, there is the choice of taking a placement year either between years 2 and 3, or between years 3 and 4.  Guidance will be given.  Whilst students wanting to take the work based placement are responsible for finding their own placement, they will be supported in this through a special programme set up to help them. This will be done by working closely with dedicated advisers from the Careers Service and support and mentoring within the Department. 

Teaching and learning

At Manchester you will be taught by academic staff who are leading experts in Mathematics in a diverse and inclusive learning environment. Teaching and Learning will be delivered using a variety of methods, including:

  • Live lectures and online videos
  • Small group tutorial classes
  • Computer-based sessions
  • PASS sessions and peer mentoring 

Some activities will be delivered face-to-face and others online, following a blended learning approach.  Our mathematics degrees offer both in-depth analysis of mathematical concepts and methods as well as applications to many diverse areas such as the motion of fluids, modelling of financial products or modelling epidemics, mostly using differential equations and data analysis. 

The first year of the programme consists of compulsory course units which provide the background needed for later courses. During the second year you begin to choose which aspects of mathematics you wish to pursue, and includes a group project on a choice of topics. In Year 3 you have an option of taking an individual project in an area that suits your interests in addition to choosing from a wide range of options. Each year builds on your mathematical skills and understanding, giving you the knowledge and confidence towards becoming a graduate mathematician.  

A typical week in your first year of study will comprise about 36 hours of activity, of which approximately half will be led by the lecturer, including watching tailor-made videos, and attending tutorials, lectures and review classes, and the remaining half will be independent or self-directed study, including studying the material, reading lecture notes and working through example sheets. 

As you progress through the course an increasing emphasis will be placed on independent study, and this reflects you applying your knowledge and skills in more advanced courses, and in both group and possibly individual projects. You will be supported by staff through all of your independent study, and this transition to being able to work independently is an important attribute of a Mathematics graduate.

PASS (Peer Assisted Study Sessions) and Peer Mentoring

We're proud of our innovative PASS (Peer Assisted Study Sessions) and Peer Mentoring scheme. The PASS scheme proides additional support around the current week's tutorial. It's entirely voluntary and consists of second, third and fourth-year current students helping first years to tackle problems defined by the content of the current tutorial. The emphasis is on showing students how to think about the problems, how to develop problem-solving skills and how to get the most from the educational resources available.

More about blended learning

Some of your activity will be synchronous, where you learn live with your lecturer / peers and can interact as appropriate, helping you get support and feel part of a community. At other times it will be asynchronous, where you access materials like presentations, video content, online discussion boards or collaborative documents in your own time (within a framework provided by your programme).

We believe this blended approach will help each individual study in a way that works best for them and will ensure students receive the best student-experience.

Coursework and assessment

The course is assessed by a variety of methods, each appropriate to the topic being assessed. These methods include coursework exercises, written examinations, online examinations, presentations and practical demonstrations. Some course units (such as the projects) are examined entirely by your submitted work during the semester.  You will also have many opportunities to self-assess your progress using online quizzes and tutorial exercises. The class of your degree is normally based on only your last two years' work.

Course content for year 1

Course units for year 1

The course unit details given below are subject to change, and are the latest example of the curriculum available on this course of study.

TitleCodeCredit ratingMandatory/optional
Mathematical Workshop MATH10001 10 Mandatory
Foundations of Pure Mathematics A MATH10101 20 Mandatory
Calculus and Vectors A MATH10121 20 Mandatory
Probability 1 MATH10141 10 Mandatory
Linear Algebra A MATH10202 20 Mandatory
Calculus and Applications A MATH10222 20 Mandatory
Sequences and Series MATH10242 10 Mandatory
Introduction to Statistics MATH10282 10 Mandatory

Course content for year 2

Course units for year 2

The course unit details given below are subject to change, and are the latest example of the curriculum available on this course of study.

TitleCodeCredit ratingMandatory/optional
Managing My Future MATH20041 0 Mandatory
Y2 Group Project MATH20062 10 Mandatory
Real Analysis A MATH20101 10 Mandatory
Algebraic Structures 1 MATH20201 10 Mandatory
Partial Differential Equations and Vector Calculus A MATH20401 20 Mandatory
Programming with Python MATH20621 10 Mandatory
Probability 2 MATH20701 10 Mandatory
Mathematical Communication and Group Projects MATH20062 10 Optional
Metric Spaces MATH20122 10 Optional
Calculus of Several Variables MATH20132 10 Optional
Algebraic Structures 2 MATH20212 10 Optional
Introduction to Geometry MATH20222 10 Optional
Fluid Mechanics MATH20502 10 Optional
Classical Mechanics MATH20512 10 Optional
Principles of Mathematical Modelling MATH20522 10 Optional
Numerical Analysis 1 MATH20602 10 Optional
Programming with Python MATH20621 10 Optional
Random Models MATH20712 10 Optional
Foundations of Modern Probability MATH20722 10 Optional
Statistical Methods MATH20802 10 Optional
Discrete Mathematics MATH20902 10 Optional
Introduction to Financial Mathematics MATH20912 10 Optional
Leadership of Learning - with Teaching Placement UCIL20001 10 Optional
Leadership in Action Online Unit UCIL20031 10 Optional
Creating a Sustainable World: 21st Century Challenges and the Sustainable Development Goals UCIL20311 10 Optional
From Cholera to COVID-19: A Global History of Epidemics UCIL20331 10 Optional
Leadership of Learning - with Teaching Placement UCIL21002 10 Optional
Communicating with Confidence UCIL21301 10 Optional
Communicating with Confidence UCIL21302 10 Optional
Developing an Entrepreneurial Mindset UCIL21331 10 Optional
Displaying 10 of 30 course units for year 2

Course content for year 3

Course units for year 3

The course unit details given below are subject to change, and are the latest example of the curriculum available on this course of study.

TitleCodeCredit ratingMandatory/optional
Double Project MATH30000 20 Optional
Mathematics Education MATH30002 10 Optional
Project (Semester One) MATH30011 10 Optional
Project (Semester 2) MATH30022 10 Optional
Fractal Geometry MATH31042 10 Optional
Topology MATH31052 10 Optional
Group Theory MATH32001 10 Optional
Commutative Algebra MATH32012 10 Optional
Coding Theory MATH32032 10 Optional
Hyperbolic Geometry MATH32051 10 Optional
Algebraic Geometry MATH32062 10 Optional
Number Theory MATH32072 10 Optional
Combinatorics and Graph Theory MATH32091 10 Optional
Mathematical Logic MATH33011 10 Optional
Green's Functions, Integral Equations and Applications MATH34032 10 Optional
Viscous Fluid Flow MATH35001 10 Optional
Wave Motion MATH35012 10 Optional
Elasticity MATH35021 10 Optional
Mathematical Biology MATH35032 10 Optional
Mathematics for a Finite Planet MATH35062 10 Optional
Symmetry in Geometry and Nature MATH35082 10 Optional
Matrix Analysis MATH36001 10 Optional
Numerical Analysis 2 MATH36022 10 Optional
Problem Solving by Computer MATH36031 10 Optional
Convex Optimization MATH36061 10 Optional
Martingales with Applications to Finance MATH37002 10 Optional
Markov Processes MATH37012 10 Optional
Statistical Inference MATH38001 10 Optional
Time Series Analysis MATH38032 10 Optional
Medical Statistics MATH38072 10 Optional
Regression Analysis MATH38141 10 Optional
Multivariate Statistics and Machine Learning MATH38161 10 Optional
Generalised Linear Models MATH38172 10 Optional
Mathematical Modelling in Finance MATH39032 10 Optional
Displaying 10 of 34 course units for year 3

Course content for year 4

Course units for year 4

The course unit details given below are subject to change, and are the latest example of the curriculum available on this course of study.

TitleCodeCredit ratingMandatory/optional
Double Project MATH40000 30 Mandatory
Martingales with Applications to Finance MATH37002 10 Optional
Computational Finance MATH40082 15 Optional
Differentiable Manifolds MATH41061 15 Optional
Noncommutative Algebra MATH42041 15 Optional
Representation and Characters of Groups MATH42062 15 Optional
Lie Algebras MATH42112 15 Optional
Galois Theory MATH42122 15 Optional
Algebraic Number Theory MATH42132 15 Optional
Computation and Complexity MATH43011 15 Optional
Set Theory MATH43022 15 Optional
Model Theory MATH43051 15 Optional
Dynamical Systems MATH44041 15 Optional
Introduction to Uncertainty Quantification MATH44071 15 Optional
Advanced Uncertainty Quantification MATH44082 15 Optional
Stability Theory MATH45031 15 Optional
Transport Phenomena and Conservation Laws MATH45122 15 Optional
Approximation Theory and Finite Element Analysis MATH46052 15 Optional
Numerical Linear Algebra MATH46101 15 Optional
Numerical Optimisation & Inverse Problems MATH46132 15 Optional
Stochastic Calculus MATH47101 15 Optional
Brownian Motion MATH47112 15 Optional
Martingale Theory for Finance MATH47201 15 Optional
Statistical Inference MATH48001 15 Optional
Linear Models with Nonparametric Regression MATH48011 15 Optional
Time Series Analysis and Financial Forecasting MATH48032 15 Optional
Generalised Linear Models and Survival Analysis MATH48052 15 Optional
Multivariate Statistics MATH48061 15 Optional
Design and Analysis of Experiments MATH48082 15 Optional
Statistical Computing MATH48091 15 Optional
Markov Chain Monte Carlo MATH48122 15 Optional
Longitudinal Data Analysis MATH48132 15 Optional
Extreme Values and Financial Risk MATH48181 15 Optional
Statistical Modelling in Finance MATH48191 15 Optional
Stochastic Modelling in Finance MATH49102 15 Optional
Scientific Computing MATH49111 15 Optional
Representation and Characters of Groups MATH62062 15 Optional
Displaying 10 of 37 course units for year 4

Scholarships and bursaries

The Department of Mathematics offers scholarships for academically excellent students from the UK and around the world; contact the Department for more details.


The Department of Mathematics is based in the brand new, purpose built £40 million Alan Turing Building, set at the heart of the University Campus.  Students benefit from extensive facilities for computing and study, relaxation and refreshment, in an attractive, light and comfortable environment.  Computing: The Department of Mathematics has a number of computer clusters that run the standard software as well as powerful mathematical and statistical software, such as Matlab, Minitab and Mathematica.  All our students have free access to email and the internet.  Other larger clusters are available in the University libraries and clusters are situated in most Halls of Residence; most student rooms also have Ethernet connection.  Library: You will have access to the John Rylands University Library of Manchester, one of the largest and best-equipped libraries in the UK.  A special section of this library provides a short loan facility, where you can reliably obtain textbooks that are recommended for particular courses and borrow them on an overnight basis.  The Department of Mathematics also houses a mathematical library of more advanced books and other material used mainly by research students and staff.

Disability support

Practical support and advice for current students and applicants is available from the Disability Advisory and Support Service. Email: