| Program start date | Application deadline |
| 2023-09-25 | - |
Program Overview
Course overview
Studying Mathematics at Liverpool is an excellent foundation for a wide range of careers. At Liverpool you will be part of a department which is first-class in teaching and research.
Introduction
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. At Liverpool, our programmes are designed with the needs of employers in mind, to give you a solid foundation from which you may take your career in any number of directions.
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. You will see a broad range of degree programmes at Liverpool – Mathematics can be combined with many other subjects to widen your options even further.
In the first two years of this programme, you will study a range of topics covering important areas of both pure and applied mathematics, no assumptions are made about whether or not you have previously studied mechanics or statistics, or have previous experience of the use of computers. The modules studied in year one help to get all students at the same level, studying fundamental ideas and reinforcing A level work.
This programme also has a year abroad option, an incredible opportunity to spend an academic year at one of our partner universities.
What you'll learn
Program Outline
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.
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 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 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.
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.
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.
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. MATH122 provides the foundations for more advanced modules like MATH228, 322, 325, 326, 423, 425 and 431.
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.
Careers and employability
A mathematically-based degree opens up a wide range of career opportunities, including some of the most lucrative professions.
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:
Recent employers of our graduates are:
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:
Meet our alumni
Hear what graduates say about their career progression and life after university.
Read more about Lydia Dutton
Lydia Dutton, MMath Mathematics 2016
Read about the path Lydia took at Liverpool and the skills she highlights as being important to employers.
Read this story
University of Liverpool
Entry requirements
The qualifications and exam results you'll need to apply for this course.
My qualifications are from:
United States
.
Entry requirements for applicants from the United States
Entry requirements: which qualifications do you need?
Undergraduate
The UK and US Higher Education systems are very similar, with only two main differences:
Specialisation
Undergraduate students take nearly all of their courses in their major right from the start of their course. At graduate level, programmes continue to be more specialised than in the US. For example, whereas US students might follow a Masters degree in English Literature, Liverpool programmes focus on a particular area such as Victorian Literature.
Shorter duration
Completing a UK Bachelor degree usually takes only three years. A Masters degree typically lasts for one full year. PhD programmes are usually three years in length.
Entry requirements
Undergraduate
| A Level | SAT II Subject Tests/AP Exams (accompanied by High School Graduation Diploma and SAT I Reasoning Tests/ACT Tests |
|---|---|
|
AAA |
3 AP exams (5, 5, 5) * PLUS High School Diploma GPA 3.0 or above PLUS either SAT I Reasoning Test at 1290+ (minimum Math Section 620+, Evidence-Based Reading and Writing 660+) or ACT Composite Score at 27 or above |
|
AAB |
3 AP exams (5, 5, 4) * PLUS High School Diploma GPA 3.0 or above PLUS either SAT I Reasoning Test at 1290+ (minimum Math Section 620+, Evidence-Based Reading and Writing 660+) or ACT Composite Score at 27 or above |
|
ABB |
3 AP exams (5, 4, 4) * PLUS High School Diploma GPA 3.0 or above PLUS either SAT I Reasoning Test at 1290+ (minimum Math Section 620+, Evidence-Based Reading and Writing 660+) or ACT Composite Score at 27 or above |
|
BBB |
3 AP exams (4, 4, 4) * PLUS High School Diploma GPA 3.0 or above PLUS either SAT I Reasoning Test at 1290+ (minimum Math Section 620+, Evidence-Based Reading and Writing 660+) or ACT Composite Score at 27 or above |
* We will also consider a combination of AP Level and Honours Level/College Level courses taken in High School on a case by case basis - grade B+ or higher).
English language requirements
Applicants from your country are assumed to meet all minimum English language requirements. You won’t need any language qualifications to study here or apply for a visa.
More information for visitors from the United States
| 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 withA in the EPQ.You may automatically qualify for reduced entry requirements through our contextual offers scheme .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:
|
| 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. |
| BTEC Level 3 National Extended Diploma |
D*DD in relevant diploma, when combined with A Level Mathematics grade A |
| International Baccalaureate |
33 including 6 in Higher Mathematics. |
| Irish Leaving Certificate | H1, H2, H2, H2, H3, H3 including Mathematics at H1. |
| Scottish Higher/Advanced Higher |
Advanced Highers accepted at grades ABB including grade A in Mathematics. |
| Welsh Baccalaureate Advanced | Acceptable at grade B or above alongside AB at A level including grade A in Mathematics. |
| Access | Access - 45 Level 3 credits in graded units in a relevant Diploma, including 39 at Distinction and a further 6 with at least Merit. 15 Distinctions are required in Mathematics. |
| International qualifications |
Entry requirements for applicants from United States. 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.
Alternative entry requirements
