Foundation Mathematics A and B

## 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.

Our mathematics 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.

##### 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

## 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

## All about the course

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’ll progress to our full BSc Mathematics degree course.

In year one of full undergraduate study, you'll explore core fundamentals of mathematics and consolidate and extend your knowledge. As you progress to year two, you'll continue to develop your knowledge of vector calculus and tensor algebra, statistics and numerical analysis. In your final year, you'll complete a final year project in an area of mathematics of your choice.

#### INDUSTRY PLACEMENTS

Industry placements are a great opportunity to get some hands-on experience and make those early career connections. 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.

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.

Probability

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

Analysis

You will be introduce 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.

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.

Inviscid Fluid Dynamics

This module will introduce fundamental mathematical concepts of fluid dynamics, with a focus on inviscid flow. You will learn how to apply the techniques to important physical problems such as hydrodynamics and aerodynamics.

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.

Statistics

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.

Vector Calculus and Tensor Algebra

Vector Calculus extends the one-dimensional calculus learnt in the first year. You will learn about integral methods for scalar and vector fields for multiple dimensions and be introduced to tensors and tensor algebra.

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.

Project

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.

**Optional modules**

Continuum Mechanics

You will learn how the deformation of materials can be modelled mathematically using a continuum model.

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.

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.

Viscous Fluids

You will gain the skills to derive the incompressible Navier-Stokes equations of a viscous fluid, and the ensuing Stokes, Oseen and Euler equations. You will also learn how to obtain solutions to the Stokes equation and Oseen equation in terms of the Green's integral representation by singular force solutions and how to apply to this a variety of problems, in particular flow past slender and thin bodies.

Computer Graphics

You will learn about aspects of object-programming applied to high-level real-time 3D graphics toolkits using the C++ programming language. You will study the mathematics of graphical transformations and apply this within computer laboratories in which real-world applications can be demonstrated.

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.

### School of Science, Engineering and Environment

From cyber security to biomedicine to architecture, our expanding suite of multidisciplinary courses shapes the next generation of scientists, engineers, consultants and conservationists. Through advanced research, we’re pioneering robotics and AI, smart environments and the appliance of data. With a team of over 200 dedicated academic, technical and administrative staff, you’ll experience a supportive, professional environment where you can realise your potential.

## What about after uni?

#### EMPLOYMENT

With a mathematics degree from Salford, you'll have a strong knowledge base and understanding of how mathematical and scientific methods can be applied in real-world problem-solving. You'll find graduate roles and career opportunities in a wide range of industries, including finance and investments, market research, meteorology, engineering or operations.

#### FURTHER STUDY

You might find you want to learn more about how to apply data and mathematics, so 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.

## Career Links

This course is extensively informed by collaboration between the university’s academics and industry partners from business, science, engineering and technology. The course team has a wide-range of long-standing relationships with businesses and financial service sector companies industry in the North West and beyond.

Continued collaboration with these professions also ensures a stimulating range of external guest lecturers, as well as career networking opportunities and professional memberships.

## What you need to know

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.

#### 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.

#### ENGLISH LANGUAGE REQUIREMENTS

Applicants will be required to show a proficiency in English. An IELTS score of 6.0, with no element below 5.5, is proof of this.

GCSE

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 Maths 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

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.

## How much?

Type of study | Year | Fees |
---|---|---|

Full-time home/EU | 2019/20 | £8,250 for Foundation Year and £9,250 for subsequent years. |

Full-time home/EU | 2020/21 | £8,250 for Foundation Year and £9,250 for subsequent years. |

##### Additional costs

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