Mathematics For Foundation Year Pdf

BSc Mathematics

Mathematics

Balance the study of the major areas of mathematics with the chance to specialise in the areas that interest you the most.

Key information

Award

BSc

Duration

3 years

full-time

Minimum entry

Three A-level offer: A* A* A

See full entry requirements

Applications : admissions ratio

12 : 1

Based on 2020 entry data

Apply on UCAS

Overview

Mathematics at Imperial aims to present a wide range of mathematical ideas in a way that develops your critical and intellectual abilities.

The Department is home to several Fellows of the Royal Society and international prize winners, and our degrees are built around our research expertise in four core areas:

Pure Mathematics
Applied Mathematics and Mathematical Physics
Mathematical Finance
Statistics

Mathematics students with lecturer You will cover both topics that are a direct continuation of those at A-level and those that introduce you to new ways of thinking, such as the logical structure of arguments, the proper definition of mathematical objects, the design of sophisticated mathematical models, and the legitimacy of computations.

All of our courses have a similar curriculum for the first two years, covering key areas of mathematics such as algebra, differential equations, and probability and statistics.

Elective and more specialised modules start in your second year and enable you to deepen your knowledge of some areas while maintaining a broad understanding of mathematics.

In your final year you can choose from over 50 optional modules, many of which are linked to our cutting edge research, allowing you to specialise in the areas of maths that interest you most.

Our BSc Mathematics (G100) degree gives you the broadest choice of optional modules on a three-year BSc programme, enabling you to graduate with a broad understanding of mathematical theory and application.

Transfer between courses

Successful candidates will receive the same offer for any course they apply for within the Department, so you should apply to just one. There is no advantage in applying to multiple courses within Mathematics.

The high level of shared content in the first two years means it is usually possible to transfer between any of our maths courses during this time (within stated restrictions – which would include having taken the appropriate second year options). However, transfer onto the Year Abroad course must normally be done in your first year.

If you are an international student, transferring to a different course could have an impact on yourstudent visa. Please visit our International Student Support webpage for further information.

Structure

Find out more about the limited circumstances in which we may need to make changes to or in relation to our courses, the type of changes we may make and how we will tell you about them.

Core modules

Introduction to University Mathematics
Analysis 1
Linear Algebra and Groups
Calculus and Applications
Probability and Statistics
Introduction to Computation
An Introduction to Applied Mathematics
Individual Research Project

Core modules

Linear Algebra and Numerical Analysis
Analysis 2
Multi-variable Calculus and Differential Equations
Group Research Project
I-Explore module

Optional modules

You choose four modules from below.

Groups and Rings
Lebesgue Measure and Integration
Probability for Statistics
Statistical Modelling 1
Network Science
Partial Differential Equations in Action
Principles of Programming

Optional modules may be prerequisites for modules in later years. You will be advised about such dependencies before making your choices.

Optional modules

A large selection of optional modules are available in your third year, allowing you to study areas that you are interested in.

You will choose at least seven modules from Group A. In addition, you will be able to choose a further one or two modules, depending on the number of ECTS credits awarded. This may include modules available in Year 2, and at most one offered by other departments.

Group A

Advanced Topics in Partial Differential Equations
Algebra 3
Algebraic Combinatorics
Algebraic Number Theory
Algebraic Topology
Applied Complex Analysis
Applied Probability
Asymptotic Methods
Bifurcation Theory
Communicating Mathematics
Computational Linear Algebra
Computational Partial Differential Equations
Consumer Credit Risk Modelling
Dynamical Systems
Dynamics of Games and Learning
Finite Elements: Numerical Analysis and Implementation
Fluid Dynamics 1
Fluid Dynamics 2
Function Spaces and Applications
Functional Analysis
Galois Theory
Geometric Complex Analysis
Group Representation Theory
Group Theory
High Performance Computing
Introduction to Geophysical Fluid Dynamics
Markov Processes
Mathematical Biology
Mathematical Finance: An Introduction to Option Pricing
Mathematical Logic
Mathematics of Business and Economics
Mathematics Research Project
Methods for Data Science
Number Theory
Numerical Solutions of Ordinary Differential Equations
Probability Theory
Quantum Mechanics 1
Quantum Mechanics 2
Scientific Computing
Special Relativity and Electromagnetism
Statistical Modelling
Statistical Theory
Stochastic Simulation
Survival Models
Tensor Calculus and General Relativity
Theory of Complex Systems
Time Series Analysis

The list gives you an idea of the optional modules that you may be able to choose from, not the exact modules that will be offered. You may only take the same module once, even if offered in different years and at different levels.

Imperial Horizons, Business School and modules from other departments

You may choose at most one module offered outside the Department through the Imperial Horizons programme (Imperial Horizons), the Business School (Business for Professional Engineers and Scientists), or another Department (subject to approval) for credit as part of your eight optional modules in your third year.

The Department of Mathematics approves a selection of the modules offered through these programmes, which means there are some modules you can take for credit.

Modules approved by the Department for credit are subject to change annually, but in the past have included modules such as:

Finance and Financial Management
Managing Innovation
Music Technology
Science, Politics and Human Identity

I-Explore

Through I-Explore, you'll have the chance to deepen your knowledge in a brand new subject area, chosen from a huge range of for-credit modules.

All of our undergraduate courses include one module from I-Explore's wide selection. The module you choose will be fully integrated into your course's curriculum and count as credit towards your degree.

Find out more about I-Explore

Download the programme specification‌ [PDF] – this is the most up-to-date version available for this course. It may change for your year of entry. If/when changes to this course are approved by the College, we will update this document and the information on this course page.

Teaching and assessment

Teaching

Independent learning
Group Learning
Lectures
Tutorials
Problem-solving and group learning classes
Research Projects

Teaching, independent study and placement hours

	Year 1	Year 2	Year 3
Lectures, seminars and similar	330 hours	300 hours	240 hours
Independent study	1,170 hours	1,200 hours	1,260 hours
Placement	–	–	–
Based on the typical pathway through the course

Assessment

Group assignments and projects
Individual Projects
Online tests and quizzes
Oral presentations
Poster presentations
Short, individual tests
Written examinations

Staff expertise

At Imperial, you will be taught by a range of teachers of all levels from Professors to PhD students, including some who undertake groundbreaking research and are regarded as experts in their field.

You may also experience peer teaching and be taught by specialists external to the College.

Associateship

As well as your main Imperial degree, you will also receive the award of the Associateship of the Royal College of Science (ARCS) on completion of this course.

The Royal College of Science is one of three historic Colleges that came together to form Imperial College London in 1907.

Find out more about our Associateships.

Entry requirements

We welcome students from all over the world and consider all applicants on an individual basis – see selection process below.

For advice on the requirements for the qualifications listed here please contact the Department (see Contact us).

We also accept a wide range of international qualifications. If the requirements for your qualifications are not listed here, please see our academic requirements by country page for guidance on which qualifications we accept.

Minimum entry standards

Our minimum entry standard for 2022 entry is A*A*A overall, to include:

A* in Mathematics
A* in Further Mathematics
A in another subject

General Studies and Critical Thinking are not accepted.

Typical offer range

As a guide, here are the typical offers made to at least 80% of A-level applicants for 2020 entry:

Three A-level offer: A*A*A-A*A*A*
Four A-level offer: A*A*AA

Practical endorsement (practical science assessment)

If you are made an offer you will be required to achieve a pass in the practical endorsement in all science subjects that form part of the offer.

Further Mathematics

We are able to make special cases for students who are from schools that do not offer Further Mathematics A-level, and encourage applications from them. We are often guided by performance in MAT when making these special cases. You should ask your teacher to clearly indicate this in your UCAS application form. If your school offers Further Mathematics AS but not A level, then we expect that you should be taking it.

Additional Mathematics support

Our new A-level Mathematics online course covers a range of key topic areas to help you gain a deeper understanding of the skills and techniques required to succeed in your A-level Mathematics exams.

This optional course has been built around the A-level syllabus with the aim of developing your thinking skills, fluency and confidence.

Please note: this course is not compulsory and does not form part of the entry requirements for this course. It is available free of charge via the EdX website. It is self-paced so you can start it at any time.

Minimum entry standards

Our minimum entry standard for 2022 entry is 39 points overall, to include:

7 in Mathematics at higher level
6 in another subject at higher level

Typical offer range

As a guide, the typical offer made to at least 80% of IB applicants for 2020 entry was39-40 points overall.

Mathematics Higher Level for award in 2022

For entry in 2022, the Mathematics Analysis and Approaches or the Applications and Interpretation syllabi will be accepted at higher level, but Analysis and Approaches is preferred.

Additional Mathematics support

We have recently launched an A-level Mathematics online course, which is available free of charge via the EdX website.

Although this optional course has been built around the A-level syllabus, it is relevant to your curriculum too.

Please note: this course is not compulsory and does not form part of the entry requirements for this course. It is self-paced so you can start it at any time.

The grades detailed below are the minimum requirements for students offering only Advanced Placements as their exams for entry to Imperial.

If you are studying a High School Diploma that is accepted by Imperial alongside Advanced Placements, requirements may apply to both your Diploma and Advanced Placements.

Please consult our country index to check whether we accept your High School Diploma programme for admission.

Our minimum requirement for this course is grades 5, 5, 5 to include:

5 in Calculus BC
5 in Chemistry, Physics C (Electricity and Magnetism, or Mechanics), Statistics or Computer Science
5 in another subject

Additional Mathematics support

We have recently launched an A-level Mathematics online course, which is available free of charge via the EdX website.

Although this optional course has been built around the A-level syllabus, it is relevant to your curriculum too.

Please note: this course is not compulsory and does not form part of the entry requirements for this course. It is self-paced so you can start it at any time.

Places will also be available to those with other equivalent qualifications, e.g. Abitur, Diploma Di Esame Di Stato, European Baccalaureate, Scottish Highers, Titullo de Bachiller, and to applicants with appropriate educational experience or other competencies. See admission of students with other competencies.

Mathematics Admissions Test (MAT)

All candidates who apply prior to 15 October are required to sit the Mathematics Admissions Test (MAT) . The MAT allows us to have a common measure with which to benchmark all our applicants, regardless of which qualifications they are taking as well or those they already have.

The MAT is a paper-based, subject-specific admissions test which lasts 2.5 hours and takes place in early November. For more information about the test, visit the Admission Testing Service's website. You must register for the test before taking it. Find out how to register for the test.

Applicants may request their MAT result from April onwards the year after their test sitting. A request must be made in writing to ugmaths.admissions@imperial.ac.uk and confirm your full name, UCAS ID and MAT registration number.

Sixth Term Examination Paper (STEP)

Conditional offers to post-15 applicants who were unable to take MAT will include a STEP requirement. This may also be applied to conditional offers to applicants taking other qualification types.

Our minimum STEP offer is a Grade 2 in either the STEP II or STEP III papers. Both the grade and the number of papers may be increased in some cases.

In addition, some MAT candidates who have a borderline mark may be considered for a STEP offer and that offer may also be increased. Find out more about STEP (Sixth Term Examination Paper), which is also administered by ATS.

Assessing your application

Admissions Tutors consider all the evidence available during our rigorous selection process and the College flags key information providing assessors with a more complete picture of the educational and social circumstances relevant to the applicant. Some applicants may be set lower offers and some more challenging ones.

Interviews

We don't currently use interviews as part of our regular admissions process.

We may consider students for interview where there are mitigating circumstances that need investigating, or where the background of the student means that their application requires further consideration.In these cases, our conditional offer may change as a result of the interview, and as with all candidates, each application is considered on its individual merits.

A foundation course is a one-year preparation course, designed for international students, which leads to undergraduate programmes in the UK. Foundation programmes are normally for school-leavers who have studied a non-British curriculum but wish to pursue a degree at a UK university.

Foundation programmes are offered by many UK universities, butonly two would be considered for entry to Imperial:

UCL's Undergraduate Preparatory Certificate for Science and Engineering (UPCSE), and
Warwick's International Foundation Programme (IFP) in Science & Engineering

UCL UPCSE

A year-long programme for international students whose school leaving qualifications do not allow them direct entry to UK universities. Students must complete four modules across the year – two compulsory and two elective modules:

Summary of the table's contents
Module	Status
Research and Academic Skills: Science and Society	Compulsory
Academic English	Compulsory
Biology	Elective
Chemistry	Elective
Mathematics	Elective
Physics	Elective
Information correct at time of publishing, but subject to change

To be considered for admission to Mathematics, international students studying UCL UPCSE must achieve:

70% overall
80% Mathematics
80% Chemistry or Physics

Grade 2 in Step 2 or Step 3 may also be required

Warwick IFP Science and Engineering

A year-long programme for international students whose school leaving qualifications do not allow them direct entry to UK universities.

To be considered for admission to the Department of Computing, international students studying Warwick IFP Science and Engineering must achieve:

80% overall
80% Mathematics, Physics and Computer Scienceor 80% Mathematics, Statistics and Further Mathematics, and Computer Scienceor80% Mathematics, Statistics and Further Mathematics, and Mathematical Modelling and Interdisciplinary Mathematics

To meet these requirements, students should choose from the following IFP pathways:

Computer Science
Mathematics & Statistics
Engineering

All candidates must demonstrate a minimum level of English language proficiency for admission to the College.

For admission to this course, you must achieve the higher College requirement in the appropriate English language qualification. For details of the minimum grades required to achieve this requirement, please see the English language requirements for undergraduate applicants.

Our competence standards highlight the core skills students should be able to demonstrate by the end of this course.

View the Department of Mathematics' competence standards [PDF]

We believe in providing the widest practicable access to all of our degree programmes and will make reasonable adjustments wherever possible to support your study. For more information, please contact the Department using the contact details below.

Department of Mathematics

T: +44 (0)20 7594 8484
E: ugmaths.admissions@imperial.ac.uk

Tuition fees and funding

We charge tuition fees for every year that your course lasts. The fee you will be charged is based on your fee status, which is determined by government regulations.

2022 entry

The fee for Home students has not been confirmed for the 2022-23 academic year. The feeis controlled by the UK government and we will update this page when it is announced.

As a guide, the Home fee for 2021-22 was £9,250.

For each subsequent year, you should expect and budget for your tuition fee to increase by an amount in line with inflation. The measure of inflation used will be the Retail Price Index (RPIX) value, taken from April in the calendar year in which the academic session starts.

For example, the RPIX value in April 2022 will apply to fees for the academic year 2022–2023.

Fee status

Whether you pay the Home fee depends on your fee status.

Your fee status is assessed based on UK Government legislation and includes things like where you live and your nationality or residency status.

Find out more about how we assess your fee status.

EU/EEA/Swiss students

The Government has confirmed that EU/EEA/Swiss students who begin a course before the 31 July 2021 will be eligible to pay the same fee as Home students and have access to student finance for the duration of their course, as long as they meet certain requirements which are unchanged from previous years. This includes students who begin the course remotely.

EU/EEA/Swiss students starting a course on or after 1 August 2021 will no longer be eligible for the Home fee rate and so will be charged the Overseas fee. Please note we do not expect this to apply to Irish students or students benefitting from Citizens' rights under the EU Withdrawal Agreement, EEA EFTA Separation Agreement or Swiss Citizens' Rights Agreement respectively. However, we are currently awaiting the formal publication of the amended Fees and Awards regulations.

The UK Council for International Student Affairs (UKCISA) website has useful information onthe conditions you currently need to meet to be entitled to pay tuition fees at the Home rate for study on a higher education course in England and reflect the regulations as they currently stand (not the amended regulations which are subject to publication).

UKCISA has also provided some information in response to Questions for students starting their course from the 1 August 2021.

Government funding

If you're a Home student, you can apply for aTuition Fee Loan from the UK government to cover the entire cost of tuition for every year of your course.

You can also apply for a means-tested Maintenance Loan to help towards your living costs.

2022 entry

£34,000 per year.

Fee status

Whether you pay the Overseas fee depends on your fee status.

Your fee status is assessed based on UK Government legislation and includes things like where you live and your nationality or residency status.

Find out more about how we assess your fee status.

EU/EEA/Swiss students

UKCISA has also provided some information in response to Questions for students starting their course from the 1 August 2021.

Bursaries and scholarships

Careers

The logical and analytical skills developed through a degree in mathematics are highly valued by a wide range of employers. Our graduates go on to a wide range of careers in industry, government and education, as well as international banking, computing, business, law and accountancy.

The MSci programmes in particular prepare you for research careers and are recognised throughout the European Union, where four-year undergraduate degrees tend to be the norm.

Recent graduates of the Department have become:

Quantitative Analyst, Multinational financial services company
Accountant, KPMG
Software Developer, Healthcare technology company
Technology Analyst, Goldman Sachs
E-Commerce Manager, UK-based financial services group

How to apply

UCAS key information

UCAS course code: G100
UCAS institution code: I50

Apply on UCAS

You can start and track your application on UCAS Hub. There you can add this course as one of your choices.

Application deadlines

26 January 2022 at 18.00 (UK time).

If your application includes a medicine course, the deadline is 15 October 2021 at 18.00 (UK time).

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