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Mathematical Physics

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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 25 January 2023.

The deadline for international students is 30 June 2023.

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Use these details to apply for this course through UCAS:

  • University name: University of Liverpool
  • Course: Mathematical Physics FGH1
  • Location: Main site
  • Start date: 25 September 2023

Related courses

There are sixteen courses related to Mathematical Physics that you might be interested in.

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Master of Mathematics

Master of Mathematics (MMath) is a master’s degree awarded for a postgraduate taught programme in mathematics.

Course overview

Combining the study of Physics and Mathematics in your degree programme will give you a strong foundation for your future career. You will learn mathematical techniques to help you deal with new ideas and will understand new concepts such as quantum mechanics and relativity. This four year courses means you will graduate with a Master's qualification.


Mathematics is a fascinating, beautiful and diverse subject to study. It underpins a wide range of disciplines; from physical sciences to social science, from biology to business and finance.

Physics is the most fundamental of the sciences. New concepts, such as quantum mechanics and relativity, are introduced at degree level in order to understand nature at the deepest level. These theories have profound philosophical implications because they challenge our view of the everyday world. At the same time they have a huge impact on society since they underpin the technological revolution.

Combining the study of Physics and Mathematics in your degree programme will give you a strong mathematical training. You will learn mathematical techniques to help you to deal with new ideas that often seem counterintuitive, such as string theory, black holes, superconductors and chaos theory.

Physics and Mathematics degrees are highly prized and our graduates have excellent career opportunities.

With this degree programme you also have the option to spend your third year abroad, an incredible opportunity to spend one academic year at one our partner universities expanding your academic and cultural horizons.

What you'll learn

  • Numeracy
  • Problem solving skills
  • Ability to reason and communicate clearly
  • Teamwork
  • Presentation skills

Course content

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

Year one

n Year One you will take three core mathematics modules, a module in Newtonian Mechanics, and four physics modules. After passing the first year, you have the flexibility of transferring to Mathematics or Physics if you wish, subject to approval.

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.​ ​


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.

Foundations of Quantum Physics (PHYS104)

Credits: 15 / Semester: semester 2

This module illustrates how a series of fascinating experiments, some of which physics students will carry out in their laboratory courses, led to the realisation that Newtonian mechanics does not provide an accurate description of physical reality. As is described in the module, this failure was first seen in interactions at the atomic scale and was first seen in experiments involving atoms and electrons. The module shows how Newton’s ideas were replaced by Quantum mechanics, which has been critical to explaining phenomena ranging from the photo-electric effect to the fluctuations in the energy of the Cosmic Microwave Background. The module also explains how this revolution in physicist’s thinking paved the way for developments such as the laser.


Credits: 7.5 / Semester: semester 1

​ The "Introduction to computational physics" (Phys105) module is designed to introduce physics students to the use of computational techniques appropriate to the solution of physical problems. No previous computing experience is assumed. During the course of the module, students are guided through a series of structured exercises which introduce them to the Python programming language and help them acquire a range of skills including: plotting data in a variety of ways; simple Monte Carlo techniques; algorithm development; and basic symbolic manipulations. The exercises are based around the content of the first year physics modules, both encouraging students to recognise the relevance of computing to their physics studies and enabling them to develop a deeper understanding of aspects of their first year course.  

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.


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. MATH122 provides the foundations for more advanced modules like MATH228, 322, 325, 326, 423, 425 and 431.


Credits: 7.5 / Semester: second semester,whole session

This is a practical-based module exclusively for students taking joint maths and physics degree programmes. In the sessions you will work through progressively more challenging experiments with increasingly complex equipment. You may work alone or in a pair, but you will be supported by a demonstrator who will give you a lot of feedback on your work.  In the classes you will be expected to contribute to class discussions and put your results on a whiteboard. There is an assessment associated with each laboratory practical.  Again, there will be a variety of activities that will allow you to demonstrate different parts of your learning. You will also have to write at least two full reports for which you will receive written and verbal feedback.​

Thermal Physics and Properties of Matter (PHYS102)

Credits: 15 / Semester: semester 1

Einstein said in 1949 that "Thermodynamics is the only physical theory of universal content which I am convinced, within the areas of applicability of its basic concepts, will never be overthrown." In this module, different aspects of thermal physics are addressed: (i) classical thermodynamics which deals with macroscopic properties, such as pressure, volume and temperature – the underlying microscopic physics is not included; (ii) kinetic theory of gases describes the properties of gases in terms of probability distributions associated with the motions of individual molecules; and (iii) statistical mechanics which starts from a microscopic description and then employs statistical methods to derive macroscopic properties. The laws of thermodynamics are introduced and applied.


Credits: 15 / Semester: semester 2

Waves lie at the heart of physics, being phenomena associated with quantum wave mechanics, electromagnetic fields, communication, lasers and, spectacularly, gravitational waves. The course is divided into several major sections. The first, can be viewed as a pre-wave study of oscillations. This teaches the basics of oscillatory systems which form the backbone of an understanding of waves. The second, deals with waves in abstract; solution of the wave equation and the principles of superposition. Finally, we look at examples of wave phenomena. These are the first introduction to what will be covered in the remainder of your degree.

Programme details and modules listed are illustrative only and subject to change.

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.

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

Language study

Every student at The University of Liverpool can study a language as part of, or alongside their degree. You can choose:

  • A dedicated languages degree
  • A language as a joint or major/ minor degree
  • Language modules (selected degrees)
  • Language classes alongside your studies

Read more about studying a language

Your experience

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

What students say...

The academic staff in the Department are fantastic and their doors are all open if you want to go and talk to them

Kate Johnson, MMath Mathematics

Careers and employability

Physics and Mathematics degrees are highly prized and our graduates have excellent career opportunities in industrial research and development, computing, business, finance and teaching.

87.5% of mathematical sciences graduates go on to work or further study within 15 months of graduation.

Discover Uni, 2018-19

Typical types of work our graduates have gone onto include:

  • An actuarial trainee analyst
  • A graduate management trainee risk analyst
  • A trainee chartered accountant

Recent employers of our graduates are:

  • Barclays Bank plc
  • Deloitte
  • Forrest Recruitment
  • Marks and Spencer
  • Mercer Human Resource Consulting Ltd

Preparing you for future success

At Liverpool, our goal is to support you to build your intellectual, social, and cultural capital so that you graduate as a socially-conscious global citizen who is prepared for future success. We achieve this by:

  • Embedding employability within your , through the modules you take and the opportunities to gain real-world experience offered by many of our courses.
  • Providing you with opportunities to gain experience and develop connections with people and organisations, including student and graduate employers as well as our global alumni.
  • Providing you with the latest tools and skills to thrive in a competitive world, including access to Handshake, a platform which allows you to create your personalised job shortlist and apply with ease.
  • Supporting you through our peer-to-peer led Careers Studio, where our career coaches provide you with tailored advice and support.

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

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 tuition fees, funding and student finance.

UK fees
Full-time place, per year £9,250
Year in industry fee £1,850
Year abroad fee £1,385
International fees
Full-time place, per year £23,750
Fees stated are for the 2022-23 academic year and may rise for 2023-24.

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 to help cover tuition fees and help with living expenses while at university.

Scholarships and bursaries you can apply for from the United Kingdom

Entry requirements

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

My qualifications are from: United Kingdom.

Your qualification Requirements

About our typical entry requirements

A levels


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

You may automatically qualify for reduced entry requirements through our contextual offers scheme.

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

Mathematics A level at grade A and Physics A level at grade B.

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.

BTEC Level 3 National Extended Diploma

Applications considered. Relevant when combined with A level Mathematics grade A

International Baccalaureate

35 including 6 at higher level in Physics and Mathematics

Irish Leaving Certificate H1, H1, H2, H2, H2, H3 including Mathematics at H1 and Physics at H2.
Scottish Higher/Advanced Higher

Advanced Highers accepted at grades AAB including grade A in Mathematics and grade B in Physics.

Welsh Baccalaureate Advanced Acceptable at grade B alongside AB at A level including grade A in Mathematics and grade B in Physics.
Access Considered
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.

Contextual offers: reduced grade requirements

Based on your personal circumstances, you may automatically qualify for up to a two-grade reduction in the entry requirements needed for this course. When you apply, we consider a range of factors – such as where you live – to assess if you’re eligible for a grade reduction. You don’t have to make an application for a grade reduction – we’ll do all the work.

Find out more about how we make reduced grade offers.

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.

Contextual offers: reduced grade requirements


Alternative entry requirements

Changes to Mathematical Physics MMath

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.

7 June 2022: New course pages

New course pages launched.