Study  ›   Undergraduate courses

Applied Mathematics

We've set the country or region your qualifications are from as United Kingdom. Change it here

Apply for this course

Ready to apply? You can apply for this course online now using the UCAS website. The deadline for UK students to apply for this course is 29 January 2025.

The deadline for international students is 30 June 2025.

Add choice to your UCAS application

Use these details to apply for this course through UCAS:

  • University name: University of Liverpool
  • Course: Applied Mathematics G121
  • Location: Main site
  • Start date: 22 September 2025

Related courses

There are twenty-four courses related to Applied Mathematics that you might be interested in.

Change country or region

We’re showing entry requirements and other information for applicants with qualifications from: United Kingdom.

Commonly selected...

Change to the United Kingdom


Not on the list?

If your country or region isn’t listed here, please contact us with any questions about studying with us.

Get a prospectus or course leaflet

Bachelor of Science

Bachelor of Science (BSc) is a bachelor’s degree awarded for an undergraduate programme in the sciences.

Return to top

Course overview

Applied Mathematics at the University of Liverpool will teach you how to think differently about the world around us. You will engage with powerful mathematical concepts that will enhance your problem-solving and critical thinking skills, enabling you to understand complex phenomena across all aspects of the modern world, from physics to engineering, computer science, epidemiology, AI, and machine learning.

Introduction

Not only is Mathematics a fascinating, beautiful and diverse subject to study, but it also forms the foundation of all modern science. The concepts, methods, and philosophy of Mathematics is critical to understanding the world around us – whether that be climate change, epidemics, financial markets, or unravelling the mysteries of the universe.

Applied Mathematics degree from the University of Liverpool offers a powerful blend of theory and real-world problem solving, preparing you for a wide range of exciting careers. Whether you’re interested in biology, engineering, finance, data science, environmental modelling, computer science, healthcare, or physics, this degree equips you with the mathematical tools and computational skills to tackle complex challenges. You’ll learn how to analyse data, optimize systems, and build models to predict outcomes in a diverse range of fields.

With a strong emphasis on practical applications, an Applied Mathematics degree opens doors to jobs that are in high demand and gives you the flexibility to innovate and make an impact in nearly every industry. Plus, the problem-solving abilities you develop will be invaluable no matter where your career takes you!

You will be taught in a friendly, supportive environment by exceptionally qualified staff, who have first-class reputations in teaching and research, covering a wide range of applications across all areas of science.

This programme also has the options of undertaking a year abroad and a year in industry.

What you'll learn

• The fundamental concepts in the core areas of mathematics including analysis, linear algebra, differential equations and statistics.
• How to think differently, reason clearly and critically, and to construct mathematical arguments.
• How to analyse a mathematical problem and select appropriate tools to solve it.
• How to construct and assess mathematical models for real-world problems and use these models to offer unique insights.
• How to communicate and present mathematical information and ideas clearly, both to specialists and non-specialist audiences – an essential skill in any future career.

Teaching Excellence Framework 2023

We’re proud to announce we’ve been awarded a Gold rating for educational excellence.

Course content

Discover what you'll learn, what you'll study, and how you'll be taught and assessed.

Year one

In year one you will study eight compulsory modules, to learn the fundamentals of a range of mathematical topics

Compulsory modules

Calculus I (MATH101)

Credits: 15 / Semester: semester 1

​At its heart, calculus is the study of limits. Many quantities can be expressed as the limiting value of a sequence of approximations, for example the slope of a tangent to a curve, the rate of change of a function, the area under a curve, and so on. Calculus provides us with tools for studying all of these, and more. Many of the ideas can be traced back to the ancient Greeks, but calculus as we now understand it was first developed in the 17th Century, independently by Newton and Leibniz. The modern form presented in this module was fully worked out in the late 19th Century. MATH101 lays the foundation for the use of calculus in more advanced modules on differential equations, differential geometry, theoretical physics, stochastic analysis, and many other topics. It begins from the very basics – the notions of real number, sequence, limit, real function, and continuity – and uses these to give a rigorous treatment of derivatives and integrals for real functions of one real variable.​ ​

Introduction to Linear Algebra (MATH103)

Credits: 15 / Semester: semester 1

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It is the study of lines, planes, and subspaces and their intersections using algebra.

Linear algebra first emerged from the study of determinants, which were used to solve systems of linear equations. Determinants were used by Leibniz in 1693, and subsequently, Cramer’s Rule for solving linear systems was devised in 1750. Later, Gauss further developed the theory of solving linear systems by using Gaussian elimination. All these classical themes, in their modern interpretation, are included in the module, which culminates in a detailed study of eigenproblems. A part of the module is devoted to complex numbers which are basically just planar vectors. Linear algebra is central to both pure and applied mathematics. This module is an essential pre-requisite for nearly all modules taught in the Department of Mathematical Sciences.

Introduction to Study and Research in Mathematics (MATH107)

Credits: 15 / Semester: semester 1

This module looks at what it means to be a mathematician as an undergraduate and beyond. The module covers the discussion of mathematics at university, research mathematics and careers for mathematicians as well as core elements of mathematical language and writing such as logic, proofs, numbers, sets and functions. The activities include sessions delivered by staff on their research areas, sessions by alumni and other mathematicians working outside academia on careers for mathematicians and sessions by careers services. The module also provides key tools needed for studying mathematics at university level. You will explore the core mathematical concepts in more detail in groups and individually and practice communicating mathematics in speech and writing.

Mathematical IT skills (MATH111)

Credits: 15 / Semester: semester 1

This module introduces students to powerful mathematical software packages such as Maple and Matlab which can be used to carry out numerical computations or to produce a more complicated sequence of computations using their programming features. We can also do symbolic or algebraic computations in Maple. These software packages have built-in functions for solving many kinds of equations, for working with matrices and vectors, for differentiation and integration. They also contain functions which allow us to create visual representations of curves and surfaces from their mathematical descriptions, to work interactively, generate graphics and create mathematical documents. This module will teach students many of the above-mentioned features of mathematical software packages. This knowledge will be helpful in Years 2, 3 and 4 when working on different projects, for example in the modules MATH266 and MATH371.

CALCULUS II (MATH102)

Credits: 15 / Semester: semester 2

This module, the last one of the core modules in Year 1, is built upon the knowledge you gain from MATH101 (Calculus I) in the first semester. The syllabus is conceptually divided into three parts: Part I, relying on your knowledge of infinite series, presents a thorough study of power series (Taylor expansions, binomial theorem); part II begins with a discussion of functions of several variables and then establishes the idea of partial differentiation together with its various applications, including chain rule, total differential, directional derivative, tangent planes, extrema of functions and Taylor expansions; finally, part III is on double integrals and their applications, such as finding centres of mass of thin bodies. Undoubtedly, this module, together with the other two core modules from Semester 1 (MATH101 Calculus I and MATH103 Introduction to linear algebra), forms an integral part of your ability to better understand modules you will be taking in further years of your studies.

Introduction to Statistics using R (MATH163)

Credits: 15 / Semester: semester 2

Students will learn fundamental concepts from statistics and probability using the R programming language and will learn how to use R to some degree of proficiency in certain contexts. Students will become aware of possible career paths using statistics.

NEWTONIAN MECHANICS (MATH122)

Credits: 15 / Semester: semester 2

This module is an introduction to classical (Newtonian) mechanics. It introduces the basic principles like conservation of momentum and energy, and leads to the quantitative description of motions of bodies under simple force systems. It includes angular momentum, rigid body dynamics and moments of inertia.

Numbers, Groups and Codes (MATH142)

Credits: 15 / Semester: semester 2

A group is a formal mathematical structure that, on a conceptual level, encapsulates the symmetries present in many structures. Group homomorphisms allow us to recognise and manipulate complicated objects by identifying their core properties with a simpler object that is easier to work with. The abstract study of groups helps us to understand fundamental problems arising in many areas of mathematics. It is moreover an extremely elegant and interesting part of pure mathematics. Motivated by examples in number theory, combinatorics and geometry, as well as applications in data encryption and data retrieval, this module is an introduction to group theory. We also develop the idea of mathematical rigour, formulating our theorems and proofs precisely using formal logic.

Any optional modules listed above are illustrative only and may vary from year to year. Modules may be subject to minimum student numbers being achieved and staff availability. This means that the availability of specific optional modules cannot be guaranteed.

Our curriculum

The Liverpool Curriculum framework sets out our distinctive approach to education. Our teaching staff support our students to develop academic knowledge, skills, and understanding alongside our graduate attributes:

  • Digital fluency
  • Confidence
  • Global citizenship

Our curriculum is characterised by the three Liverpool Hallmarks:

  • Research-connected teaching
  • Active learning
  • Authentic assessment

All this is underpinned by our core value of inclusivity and commitment to providing a curriculum that is accessible to all students.

Course options

Studying with us means you can tailor your degree to suit you. Here's what is available on this course.

Global Opportunities

University of Liverpool students can choose from an exciting range of study placements at partner universities worldwide. Choose to spend a year at XJTLU in China or a year or semester at an institution of your choice.

What's available on this course?

Year in China

Immerse yourself in Chinese culture on an optional additional year at Xi'an Jiaotong Liverpool University in stunning Suzhou.

  • Learn Chinese
  • Study in a bustling world heritage city
  • Improve employment prospects
  • Study Chinese culture
  • 30 minutes from Shanghai
  • Learn new skills

Read more about Year at XJTLU, China

Year in industry

Year in industry placements give you an in-depth workplace experience where you can develop your skills and apply your learning.

  • Develop key employability skills that graduate employers are looking for
  • Experience and understand workplace culture and disciple
  • Understand the relationship between academic theory and real world application
  • Begin your professional network
  • Gain industry insight and insight into potential career options.

You don't need to decide now - you can choose to add a year in industry after you've begun your degree.

To spend a year in industry, you'll need to secure a placement with an organisation. If you're unable to find a placement, you'll continue with the standard version of the course without a year in industry.

Study as part of XJTLU 2+2

Students studying Applied Mathematics BSc at XJTLU can study this course at the University of Liverpool. Read more about Applied Mathematics BSc (Hons) as part of the 2+2 programme.

The natural next step for ambitious XJTLU students who want to build a brilliant career.

  • Spend two years at the University of Liverpool campus
  • Improve your prospects of progressing to postgraduate study at a top 100 university
  • Receive two degrees: one from XJTLU, one from the University of Liverpool
  • Get support with visas, accommodation and your career.

Read more about the 2+2 programme.

Your experience

Studying a Mathematics degree at the University of Liverpool is an excellent investment in your future. We have a large department with highly qualified staff, a first-class reputation in teaching and research, and a great city in which to live and work.

Your course will be delivered by the Department of Mathematical Sciences.

Virtual tour

Supporting your learning

From arrival to alumni, we’re with you all the way:

Careers and employability

A degree in applied mathematics provides access to an almost limitless range of rewarding career paths. As a graduate with an applied mathematics degree from the University of Liverpool, you’ll have an extremely valuable set of analytical and critical thinking skills that employers value, enabling you to pursue careers in almost any field.

Graduates with an applied mathematics degree are in high demand across a broad spectrum of industries, thanks to their expertise in quantitative analysis, problem-solving, and mathematical modelling. Some of the key career paths include:

• Data Science and Analytics: Applied mathematics graduates are well-equipped to work as data scientists, data analysts, or business analysts. Their skills in statistical modelling, machine learning, and data interpretation are highly sought after in sectors like finance, healthcare, and tech.
• Engineering and Technology: Applied mathematics graduates can work in engineering roles, including systems engineering, computational modelling, and simulation. They may also contribute to software development, particularly in fields that require complex algorithms, like AI and cybersecurity.
• Operations Research and Logistics: Companies in manufacturing, transportation, and supply chain management often hire applied mathematics graduates to optimize processes, improve efficiency, and reduce costs. Roles include operations research analyst, supply chain planner, and logistics coordinator.
• Healthcare and Biostatistics: Applied mathematics is increasingly used in medical research, epidemiology, and healthcare analytics. Careers may include biostatistician, health data analyst, or mathematical modeler in disease forecasting.

The versatility of an applied mathematics degree allows graduates to enter nearly any sector that requires mathematical modelling, statistical analysis, and algorithmic problem-solving. The growing demand for data-driven decision making in today’s world ensures that career prospects remain strong, with opportunities for advancement and specialization across fields.

95% of Mathematics BSc graduates at the University of Liverpool go on to work and/or study within 15 months of graduation

Graduate outcomes survey, Discover Uni (Students graduating 2021-22)

Meet our alumni

Hear what graduates say about their career progression and life after university.

Fees and funding

Your tuition fees, funding your studies, and other costs to consider.

Tuition fees

UK fees (applies to Channel Islands, Isle of Man and Republic of Ireland)
Full-time place, per year £9,535
Year in industry fee £1,850
Year abroad fee £1,385
International fees
Full-time place, per year £26,600
Year in industry fee £1,850
Year abroad fee £13,300
The UK full-time tuition fee, international course fee and fee for the year abroad for international students shown are correct for 2025/26 entry. We are currently awaiting confirmation of whether the year abroad fee for UK students, as well as the year in industry fee will change, so the fees shown are for 2024/25. Please note that the year abroad fee also applies to the year in China.

Tuition fees cover the cost of your teaching and assessment, operating facilities such as libraries, IT equipment, and access to academic and personal support. Learn more about fees and funding.

Additional costs

Your tuition fee covers almost everything but you may have additional study costs to consider, such as books.

Find out more about the additional study costs that may apply to this course.

Additional study costs

Your tuition fee covers almost everything but you may have additional study costs to consider, such as books.

Find out more about additional study costs.

Scholarships and bursaries

We offer a range of scholarships and bursaries that could help pay your tuition and living expenses.

We've set the country or region your qualifications are from as United Kingdom. Change it here


Undergraduate Global Advancement Scholarship

  • International students

If you’re a high-achieving international student starting an undergraduate degree with us from September 2024, you could be eligible to receive a fee discount of up to £5,000. You’ll need to achieve grades equivalent to AAA in A levels and be joining a non-clinical degree.

The Liverpool Bursary

  • Home students

If you’re a UK student joining an undergraduate degree and have a household income below £35,000, you could be eligible for a Liverpool Bursary worth up to £2,000 for each year of undergraduate study.

Asylum Seekers Scholarship

  • Home students

Apply for an Asylum Seekers Scholarship and you could have your tuition fees paid in full and receive help with study costs. You’ll need to have applied for asylum in the UK, or be the dependant of an asylum seeker, and be joining an eligible undergraduate degree.

Care Leavers’ Opportunity Bursary

  • Home students

If you’ve spent 13 or more weeks in Local Authority care since age 14, you could be eligible for a bursary of £3,000 per year of study. You’ll need to be a UK student joining an eligible undergraduate degree and be aged 28 or above on 1 September in the year you start.

Cowrie Foundation Scholarship

  • Home students

Are you a UK student with a Black African or Caribbean heritage and a household income of £25,000 or less? You could be eligible to apply for a Cowrie Foundation Scholarship worth up to £8,000 for each year of undergraduate study.

Estranged Students Bursary

  • Home students

If you’re a UK student identified as estranged by Student Finance England (or the equivalent UK funding body), you could be eligible for a bursary of £1,000 for each year of undergraduate study.

Genesys Life Sciences Scholarship

  • Home students

Joining a School of Biosciences degree in a non-clinical subject and have a household income of less than £25,000? If you’re a UK student, you could apply to receive £4,500 per year for three years of your undergraduate course.

Graduate Association Hong Kong & Tung Undergraduate Scholarships

  • International students
  • Hong Kong

If you’re an undergraduate student from Hong Kong who can demonstrate academic excellence, you may be eligible to apply for a scholarship worth £10,000 in partnership with the Tung Foundation.

Kaplan Digital Pathways Excellence Scholarship

  • International students

Completed a Kaplan Digital Pathways Foundation Certificate? We’re offering a £5,000 fee discount off the first year of undergraduate study for a maximum of two high achieving students joining one of our non-clinical degrees from an online Kaplan Foundation Certificate.

Nolan Scholarships

  • Home students

Do you live in the Liverpool City Region with a household income of £25,000 or less? Did neither of your parents attend University? You could be eligible to apply for a Nolan Scholarship worth £5,000 per year for three years of undergraduate study.

Rigby Enterprise Award

  • Home students

Are you a UK student with a household income of £25,000 or less? If you’ve participated in an eligible outreach programme, you could be eligible to apply for a Rigby Enterprise Award worth £5,000 per year for three years of your undergraduate degree.

ROLABOTIC Scholarship

  • Home students

Are you a UK student with a household income of £25,000 or less? Did neither of your parents attend University? You could be eligible to apply for a ROLABOTIC Scholarship worth £4,500 for each year of your undergraduate degree.

Sport Liverpool Performance Programme

  • Home and international students

Apply to receive tailored training support to enhance your sporting performance. Our athlete support package includes a range of benefits, from bespoke strength and conditioning training to physiotherapy sessions and one-to-one nutritional advice.

Technetix Broadhurst Engineering Scholarship

  • Home students

Joining a degree in the School of Electrical Engineering, Electronics and Computer Science? If you’re a UK student with household income below £25,000, you could be eligible to apply for £5,000 a year for three years of study. Two awards will be available per academic year.

University of Liverpool International College Excellence Scholarship

  • International students

Completed a Foundation Certificate at University of Liverpool International College (UoLIC)? We’re offering a £5,000 fee discount off the first year of undergraduate study to some of the highest achieving students joining one of our non-clinical degrees from UoLIC.

University of Liverpool International College First Class Scholarship

  • International students

We’re offering a £1,000 fee discount for years 2 and 3 of undergraduate study to eligible students progressing from University of Liverpool International College. You’ll need to be studying a non-clinical subject and get an average of 70% or above in year 1 of your degree.

University of Liverpool International College Impact Progression Scholarships

  • International students

If you’re a University of Liverpool International College student awarded a Kaplan Impact Scholarship, we’ll also consider you for an Impact Progression Scholarship. If selected, you’ll receive a £3,000 fee discount off the first year of your undergraduate degree.

Young Adult Carer’s (YAC) Bursary

  • Home students

If you’re a young adult and a registered carer in the UK, you might be eligible for a £1,000 bursary for each year of study. You’ll need to be aged 18-25 on 1 September in the year you start your undergraduate degree.

Entry requirements

The qualifications and exam results you'll need to apply for this course.

We've set the country or region your qualifications are from as United Kingdom. Change it here

Your qualification Requirements

About our typical entry requirements

A levels

ABB including Mathematics A level grade A.

Applicants with the Extended Project Qualification (EPQ) are eligible for a reduction in grade requirements. For this course, the offer is ABC with A in the EPQ.

If you don't meet the entry requirements, you may be able to complete a foundation year which would allow you to progress to this course.

Available foundation years:

T levels

T levels are not currently accepted.

GCSE 4/C in English and 4/C in Mathematics
Subject requirements

Applicants must have studied Mathematics at Level 3 within 2 years of the start date of their course.

For applicants from England: For science A levels that include the separately graded practical endorsement, a "Pass" is required.

International qualifications

Many countries have a different education system to that of the UK, meaning your qualifications may not meet our entry requirements. Completing your Foundation Certificate, such as that offered by the University of Liverpool International College, means you're guaranteed a place on your chosen course.

English language requirements

You'll need to demonstrate competence in the use of English language, unless you’re from a majority English speaking country.

We accept a variety of international language tests and country-specific qualifications.

International applicants who do not meet the minimum required standard of English language can complete one of our Pre-Sessional English courses to achieve the required level.

English language qualification Requirements
IELTS 6.0 overall, with no component below 5.5
TOEFL iBT 78 overall, with minimum scores of listening 17, writing 17, reading 17 and speaking 19. TOEFL Home Edition not accepted.
Duolingo English Test 105 overall, with no component below 95
Pearson PTE Academic 59 overall, with no component below 59
LanguageCert Academic 65 overall, with no skill below 60
Cambridge IGCSE First Language English 0500 Grade C overall, with a minimum of grade 2 in speaking and listening. Speaking and listening must be separately endorsed on the certificate.
Cambridge IGCSE First Language English 0990 Grade 4 overall, with Merit in speaking and listening
Cambridge IGCSE Second Language English 0510/0511 0510: Grade C overall, with a minimum of grade 2 in speaking. Speaking must be separately endorsed on the certificate. 0511: Grade C overall.
Cambridge IGCSE Second Language English 0993/0991 0993: Grade 5 overall, with a minimum of grade 2 in speaking. Speaking must be separately endorsed on the certificate. 0991: Grade 5 overall.
Cambridge ESOL Level 2/3 Advanced 169 overall, with no paper below 162

PRE-SESSIONAL ENGLISH

Do you need to complete a Pre-Sessional English course to meet the English language requirements for this course?

The length of Pre-Sessional English course you’ll need to take depends on your current level of English language ability.

Find out the length of Pre-Sessional English course you may require for this degree.

Pre-sessional English

If you don’t meet our English language requirements, we can use your most recent IELTS score, or the equivalent score in selected other English language tests, to determine the length of Pre-Sessional English course you require.

Use the table below to check the course length you're likely to require for your current English language ability and see whether the course is available on campus or online.

Your most recent IELTS score Pre-Sessional English course length On campus or online
5.5 overall, with no component below 5.5 6 weeks On campus
5.5 overall, with no component below 5.0 10 weeks On campus and online options available
5.0 overall, with no component below 5.0 12 weeks On campus and online options available
5.0 overall, with no component below 4.5 20 weeks On campus
4.5 overall, with no component below 4.5 30 weeks On campus
4.0 overall, with no component below 4.0 40 weeks On campus

If you’ve completed an alternative English language test to IELTS, we may be able to use this to assess your English language ability and determine the Pre-Sessional English course length you require.

Please see our guide to Pre-Sessional English entry requirements for IELTS 6.0, with no component below 5.5, for further details.

About our entry requirements

Our entry requirements may change from time to time both according to national application trends and the availability of places at Liverpool for particular courses. We review our requirements before the start of the new UCAS cycle each year and publish any changes on our website so that applicants are aware of our typical entry requirements before they submit their application.

Recent changes to government policy which determine the number of students individual institutions may admit under the student number control also have a bearing on our entry requirements and acceptance levels, as this policy may result in us having fewer places than in previous years.

We believe in treating applicants as individuals, and in making offers that are appropriate to their personal circumstances and background. For this reason, we consider a range of factors in addition to predicted grades, widening participation factors amongst other evidence provided. Therefore the offer any individual applicant receives may differ slightly from the typical offer quoted in the prospectus and on the website.

Alternative entry requirements

Changes to Applied Mathematics BSc (Hons)

See what updates we've made to this course since it was published. We document changes to information such as course content, entry requirements and how you'll be taught.

10 December 2024: Applied Mathematics BSc (Hons) – modules

MATH368 removed from year three.