Undergraduate BSc (Hons)

Mathematics with Foundation Year

School of Science, Engineering and Environment



With placement


Four year

Five year

Next enrolment

September 2024


In a nutshell

Many of civilisation’s greatest achievements are built on mathematics. By choosing a mathematics degree, you will learn to make an important contribution to the world around us, be it in science, technology or engineering. The foundation year pathway is designed to help you build a strong foundation in mathematical principles, so you are ready to progress onto our BSc (Hons) Mathematics Degree.

This pathway is recommended if you don't meet the prerequisites for the full honours degree, whether you are new to higher education or seeking to develop your career in a new direction. On successful completion of the foundation year, you will progress on to the full honours degree, where you will continue to build specialised knowledge and mathematical skills. 

Our mathematics degree course is designed to take you to an advanced level. Blending applied methods with cutting-edge themes, like nanotechnology, economic stability and artificial intelligence, you’ll graduate with in-demand skills for the contemporary business environment.

Start your study journey 

Register for our next Open Day to learn more about studying maths, explore our facilities and meet the course team 

You will:

  • Identify, define and evaluate real-world problems, using applied mathematics to challenge conventional ideas
  • Be taught by a combination of experienced mathematicians and finance sector staff
  • Engage with business and industry throughout the course
  • Become familiar with modelling physical processes relevant to industries such as engineering and computing

options available

Course accreditations

Institute of Mathematics & its applications

This is for you if...


You're passionate about studying mathematics but lack the qualifications for direct entry onto the Honours degree


You want to learn how to identify, analyse and solve real-world challenges


You're a keen problem-solver who enjoyed mathematics at school/college

Course details

All about the course

Mathematics students working at computers

Foundation year

Based on the A-Level system, our Foundation Year entry route is an intensive academic programme will improve your competences in mathematics. Led by experienced staff in a small-group environment, using a range of lectures and tutorials, you’ll identify, define and evaluate real-world problems, using applied mathematics to challenge conventional ideas.   

As you gain and develop knowledge during this year, you’ll be well-placed to refine your mathematical skills. On successful completion of the Foundation Year, you will progress to our BSc Mathematics degree course.

BSc degree

Course delivery

Delivered over three years - or four with a placement year, this course will help you to explore the core fundamentals of mathematics and consolidate your A-Level knowledge before advancing your skills across a range of applied mathematics areas including statistics, computer graphics, vector calculus and more.  

Learn more about the current course modules in the section below.

Learning experience

We approach the maths subject area in a very applied way, which means that all your modules focus on the applications of the mathematical skills and knowledge that you learn. You'll be taught in small groups of typically around 20 students, which means that all the lecturers are able to give guided and focused help.

We have some unique modules. In particular the second year module 'Business and Industrial Mathematics 'helps prepare the students for the workplace. You will work in groups to solve real-life problems, which have been given to us from business and industry partners. You'll also complete a final year project on an area of mathematics of your own choosing, giving you the opportunity to focus your learning on a subject that interests you. 

Industry placement

On this course, you'll have the option to take an industry placement between years two and three. Although you’ll be responsible for securing your placement, our tutors will support you, monitor your progress and assess your final placement report.

By successfully completing a placement year, you can also add 'with professional experience' to your final degree award.

Foundation year

Foundation Mathematics A and B

These modules entail the development of mathematical and modelling skills. Subjects include algebra, transposition of formulae, coordinate systems, logarithms, introduction to calculus, problem solving in velocity and acceleration, differentiation, integration and matrices.

Foundation Physics A and B

This module provides grounding in basic physics and the development of numerical problem solving. The syllabus includes, mechanics, properties of matter and wave propagation. Electronics and electricity are introduced, along with fields (magnetic, electric, gravitation etc.) and atomic and nuclear physics.

Introduction to Probability and Statistics

This module will introduce some core mathematics equivalent to A-level, including basic probability and statistics.

Foundation IT and Study Skills

This module involves the development of IT, research, team working, presentation and scientific reporting skills. In more detail, the use of spreadsheets, graphical representation of data, report writing, scientific presentations and group-based research will be undertaken.

Year one (BSc Mathematics)


This module will build upon and extend your A-Level (or equivalent) mathematical probability knowledge and develop the subject of probability with applications.


You will be introduced to the concept of proofs and construct simple proofs. It will give you an understanding of fundamental concepts of limit, continuity, differentiability, integration and function in mathematical analysis. On completion of the module you will be able to apply the notion of limit to prove fundamental theorems and to perform integration.

Linear Algebra

Linear algebra is a fundamental topic which has applications in many branches of mathematics. You will look at the methods and theory behind the solution of simultaneous equations, and you will develop skills in solving linear problems using matrix methods and the concept of abstract vectors.

Mathematical Methods 1

You will build on your A-Level (or equivalent) mathematical techniques and knowledge in preparation for subsequent mathematics modules. Specifically, you will cover the subject of differential equations with applications.

Mathematical Modelling

This module will build upon and extend your A-Level (or equivalent) mathematical techniques providing a mathematical foundation in support of subsequent mathematics modules. You will also cover differential equations with applications and be introduced to problem solving using a symbolic computing environment.

Mechanics and Vector Calculus

You will be introduced to the principles of classical mechanics and vector calculus. You will develop skills in solving numerical problems in mechanics and vector calculus.

Year two (BSc Mathematics)

Business and Industrial Mathematics

This module will give you experience in business and industrial working practices and how to solve practical mathematical problems.

At the start of the module, a series of seminars will be given by speakers on a variety of mathematical applications in business in industry including: probability and statistics, operational research, fluids, structural and solid mechanics, (intelligent) computer algorithms, business and economic models, and how these impact on their work.

You will deliver written reports and oral presentations, which are assessed on a group basis, both during and at the end of the semester.

Mathematics Methods 2

You will extend your methods in differential and integral calculus, first and second order partial differential equations and methods in differential and integral calculus for the complex variable.


You will develop a sound knowledge in probability models and distribution theory, skills in statistics and data analysis and provide an awareness of the principles and scope of data analysis models often implemented in statistical software packages.


Dynamical Systems

An understanding of nonlinear dynamics is fundamental in modern applied mathematics, with physical applications ranging from population modelling and weather prediction to stock market datasets and anharmonic vibrations. This module will introduce some of the concepts and phenomena of dynamical systems by merging mathematical analysis and numerical computation.


Applied Mathematics 1

This module introduces you to tensors and tensor algebra. You will learn how these powerful tools can be applied to problems in fluid and structural dynamics.

Year three (BSc Mathematics)

Mathematical Methods 3

You will investigate more advanced techniques of solving differential equations using for methods such as Fourier and Laplace transforms, series methods and more.


The project will give you the opportunity to develop a mathematical model within a challenging research theme, including those areas prioritised by EPSRC and the EU Research Council and of benefit and importance to society. These are: climate, nanotechnology, renewable energy and sustainable economics. The aim is for you to demonstrate your understanding of the application of mathematics to one of these areas and give you an opportunity to demonstrate your knowledge, understanding and skills.

Mathematical Statistics

Using probability theory as well as other branches of mathematics such as linear algebra and analysis, you will revisit the foundations of statistics from a more mathematical standpoint. You will gain theoretical and practical skills in mathematical statistics, study some of the most widely used probability distributions and recognise and employ them in practical applications.


Programming and Optimisation

In this module, you will learn to apply mathematics to a variety of problems in physics, economics and life sciences.

Plus one optional module from the following:

Operational Research

You will learn the skills to construct mathematically based models to find better solutions to real-life and complex decision-making problems. These models draw upon mathematical knowledge, such as mathematical modelling, statistical analysis, mathematical optimization and artificial intelligence to find an optimal or near-optimal solution to problems from a variety of industries and government areas.


Applied Mathematics 2

In this module, you will learn to apply mathematics to problems in fluid and structural dynamics.

Please note that it may not be possible to deliver the full list of options every year as this will depend on factors such as how many students choose a particular option. Exact modules may also vary in order to keep content current. When accepting your offer of a place to study on this programme, you should be aware that not all optional modules will be running each year. Your tutor will be able to advise you as to the available options on or before the start of the programme. Whilst the University tries to ensure that you are able to undertake your preferred options, it cannot guarantee this.

What will I be doing?






You will develop your knowledge and skills through a blend of theoretical, collaborative and practical methods. These include:

  • Tutorials and seminars on specific topics
  • Talks and lectures by academics and industry guests lecturers
  • Practical workshops for computer-based problem-based learning exercises
  • Case studies and project work
  • Group assignments
  • Online learning using Blackboard


You will be assessed using a range of relevant methods. These include:

  • Presentations: individual or group presentations of the final outcome to a particular assignment or brief
  • Examinations: usually two hours in duration and aim to test material presented in lectures, workshops and seminars
  • Written assessments: class tests, reports and evaluations
  • Research project presentation:  as an individual or group presentation of the final outcome to a particular assignment or brief
  • Coursework and continuous assessment: which will include class tests, reports and evaluations

Some modules use 50% coursework/50% exam weighting, but most use 30% coursework/70% exams.

What you want to know

Frequently asked questions

What is a foundation year? 

A foundation year offers a year of studying to gain an understanding of the programme before progressing to the full three-year studies. You'll get the chance to understand the way higher education studying works and gain the relevant skills and knowledge needed to undertake the full degree. 

What is the basic definition of maths? 

Mathematics is the study of numbers, shapes, and patterns. The word comes from the Greek μάθημα (máthema), meaning ‘knowledge’ or ‘learning’. The term is often shortened to maths or math. 

What are the main types of maths? 

Mathematics is a broad field, covering a wide range of disciplines. Some of the main branches of maths include algebra, geometry, arithmetic, and trigonometry. 

School of Science, Engineering and Environment

Rising to the challenge of a changing world, our degree courses are designed to shape the next generation of urbanists, scientists, engineers, consultants and leaders.

Driven by industry, and delivered by supportive programme teams, you can develop the knowledge and skills to become unstoppable in your career.


You will experience a modern learning environment, with accessible lecture theatres and AV-equipped classrooms, computing suites and multimedia libraries, with access to industry journals, databases, and simulation software. 

Employment and stats

What about after uni?

Physics student


Studying mathematics with Salford helps you to build both a solutions-focused mindset and a work-ready skillset relevant for our increasingly data-driven society. The strong knowledge base you will develop, and your understanding of how mathematical and scientific methods are applied, will be advantageous in real-world problem-solving roles. 

Mathematics is integral to the development of society, and graduates have no shortage of exciting career options. The study and use of mathematical decision-making, and transferable analytical and problem-solving skills is highly-valued across a range of industries.  

Typical roles for mathematics graduates can include finance and investments, market research, meteorology, engineering, data analytics, and business operations.

Further study

You might find you want to learn more about how to apply mathematics. We offer a range of specialist postgraduate courses to help you take your career and interests even further. Salford graduates and alumni also receive a significant fees discount.

A taste of what you could become

A data analyst

An accountant

A financial trader

A teacher

A researcher

And more...


What you need to know

Applicant profile

We welcome applicants who have studied mathematics or physics subjects at school/college and would like to gain a deeper knowledge in these and other related subjects. 

International students

This course isn’t suitable for international students. If you are an international student and interested in studying a foundation year, please visit our International Foundation Year course page.

English language requirements

All of our courses are taught and assessed in English. If English is not your first language, you must meet our minimum English language entry requirements. An IELTS score of 6.0 (no element below 5.5) is proof of this, and we also accept a range of equivalent qualifications.  

Read more about our English language requirements, including information about pathways that can help you gain entry on to our degree courses.  

Course accreditation

This course will meet the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications, when it is followed by subsequent training and experience in employment to obtain equivalent competences to those specified by the Quality Assurance Agency (QAA) for taught masters degrees.

Standard entry requirements


English language and Mathematics at grade C/level 4 or above

You must fulfil our GCSE entry requirements as well as one of the requirements listed below.

UCAS tariff points

64 UCAS points where qualifications include both Mathematics and Physics to A-Level or equivalent standard.

72 UCAS points from any subject combination without Mathematics and Physics

A Level

64 UCAS points where qualifications include both mathematics and physics.

72 UCAS points from any subject combination without mathematics and physics

BTEC Higher National Diploma

MPP for Engineering or science subjects.

MMP for subjects without mathematics and physics modules

Access to HE

64 UCAS points from QAA-approved science or engineering courses

Scottish Highers

64 UCAS points where qualifications include both Advanced Higher level mathematics and physics.

72 UCAS points from any subject combination without Advanced Higher level mathematics and physics

Irish Leaving Certificate

64 UCAS points where qualifications include both Higher Level mathematics and physics.

72 UCAS points from any subject combination without Higher Level mathematics and physics

European Bacclaureate

Pass in Diploma of at least 60%, to include Science, Engineering or Technology

International Baccalaureate

26 points including Higher Level mathematics or physics at grade 4

Alternative entry requirements

Salford Alternative Entry Scheme (SAES)

We welcome applications from students who may not meet the stated entry criteria but who can demonstrate their ability to pursue the course successfully. Once we have received your application we will assess it and recommend it for SAES if you are an eligible candidate.  

There are two different routes through the Salford Alternative Entry Scheme and applicants will be directed to the one appropriate for their course. Assessment will either be through a review of prior learning or through a formal test.  To be considered for the scheme, you must have already achieved or be working towards GCSE Maths and English Grade C/4 (or equivalent).

Learn more about the Salford Alternative Entry Scheme.

How much?

Type of study Year Fees
Full-time home 2024/25 £8,250.00 for Foundation Year and £9,250.00 for subsequent years.
Full-time home 2025/26 £8,250.00 for Foundation Year and £9,250.00 for subsequent years.

Additional costs

You should consider further costs which may include books, stationery, printing, binding and general subsistence on trips and visits.

Apply now

All set? Let's apply

Enrolment dates

September 2024

September 2025

UCAS information

Course ID G105

Institution S03