# Mathematics MMath

School of Mathematics and Statistics

You are viewing this course for 2021-22 entry. 2022-23 entry is also available.

## Course description

The MMath is our flagship course for those thinking of a career as a professional mathematician.

A major component of the final year of the MMath course is spent on a research project, providing an opportunity for independent study, guided by a member of academic staff in their area of expertise.

Your study will include core mathematics, pure mathematics, applied mathematics, and probability and statistics. You can specialise later in your course, and may have the option to switch between our degrees. You'll have the chance to study scientific programming and simulation, and practical and applied statistics.

For applied mathematics and probability and statistics, you don't need to have prior knowledge of the subject. You'll have plenty of opportunities to focus on your career and skills development too.

## Modules

The modules listed below are examples from the last academic year. There may be some changes before you start your course. For the very latest module information, check with the department directly.

Choose a year to see modules for a level of study:

Title: Mathematics MMath course structure
UCAS code: G103
Years: 2021

Core modules:

Introduction to Probability and Statistics

The module provides an introduction to the fields of probability and statistics, which form the basis of much of applicable mathematics and operations research. The theory behind probability and statistics will be introduced, along with examples occurring in diverse areas. Some of the computational statistical work may make use of the statistics package R.

20 credits
Mathematics Core 1

The module explores topics in mathematics which will be used throughout many degree programmes. The module will consider techniques for solving equations, special functions, calculus (differentiation and integration), differential equations, Taylor series, complex numbers and finite and infinite series.

20 credits
Mathematics Core II

The module continues the study of core mathematical topics begun in MS4F1015, which will be used throughout many degree programmes. The module will discuss 2-dimensional co-ordinate geometry, discussing the theory of matrices geometrically and algebraically, and will define and evaluate derivatives and integrals for functions which depend on more than one variable, with an emphasis on functions of two variables.

20 credits
Numbers and Groups

The module provides an introduction to more specialised Pure Mathematics. The first half of the module will consider techniques of proof, and these will be demonstrated within the study of properties of integers and real numbers. The second semester will study symmetries of objects, and develop a theory of symmetries which leads to the more abstract study of groups.

20 credits
Vectors and Mechanics

The module begins with the algebra of vectors, essential for the study of many branches of applied mathematics. The theory is illustrated by many examples, with emphasis on geometry including lines and planes. Vectors are then used to define the velocity and acceleration of a moving particle, thus leading to an introduction to Newtonian particle mechanics. Newton's laws are applied to particle models in areas such as sport, rides at theme parks and oscillation theory.

20 credits

Optional modules:

Mathematical Investigation Skills

This module introduces topics which will be useful throughout students time as undergraduates and beyond. These skills fall into two categories: computer literacy and presentation skills. Various computer packages are introduced in other modules; these share some programming capabilities, and one aim of this module is to develop programming techniques to perform mathematical investigations within the context of these mathematical packages. In addition, spreadsheets have substantial scientific capabilities, and Excel is the program of choice within industry. Finally, students will meet the typesetting package LaTeX, preparing reports and presentations into mathematical topics.

20 credits
Principles of Ecology and Conservation

This course is an introduction to the principles of ecology and conservation. It covers ecological concepts about the abundance and distribution of species and key ideas about conserving populations, communities and habitats.

20 credits
Climate Change and Sustainability

This course introduces the core scientific issues required to understand climate change and sustainability. Students will learn the causes of climate change, its impacts in natural and agricultural ecosystems, the influence of biogeochemical cycles in these ecosystems on climate, and strategies for sustainably managing ecosystems in future. Learning will be achieved via lectures and videos, practicals and independent study.

20 credits
Foundations of Computer Science

The course consists of (around) 10 blocks of 2-3 weeks work each. Each block develops mathematical concepts and techniques that are of foundational importance to computing. Lectures and problem classes will be used. The intention is to enthuse about these topics, to demonstrate why they are important to us, to lay the foundations of their knowledge and prepare students for future computing courses. It is not expected that the course will cover ALL of the maths that is needed later either in terms of depth or scope.

20 credits
Introduction to Algorithms and Data Structures

Algorithms and algorithmic problem solving are at the heart of computer science. This module introduces students to the design and analysis of efficient algorithms and data structures. Students learn how to quantify the efficiency of an algorithm and what algorithmic solutions are efficient. Techniques for designing efficient algorithms are taught, including efficient data structures for storing and retrieving data. This is done using illustrative and fundamental problems: searching, sorting, graph algorithms, and combinatorial problems such as finding the shortest paths in networks.

10 credits
Elementary Logic

The course will provide students with knowledge of the fundamental parts of formal logic. It will also teach them a range of associated formal techniques with which they can then analyse and assess arguments. In particular, they will learn the languages of propositional and first-order logic, and they will learn how to use those languages in providing formal representations of everyday claims. They will also learn how to use truth-tables and truth-trees.

10 credits
Introduction to Astrophysics

One of four half-modules forming the Level-1 Astronomy course, PHY104 aims to equip students with a basic understanding of the important physical concepts and techniques involved in astronomy with an emphasis on how fundamental results can be derived from fairly simple observations. The module consists of three sections:

(i) Basic Concepts, Fluxes, Temperatures and Magnitudes;

(ii) Astronomical Spectroscopy;

(iii) Gravitational Astrophysics.

Parts (i), (ii) and (iii) each comprise some six lectures. The lectures are supported by problems classes, in which you will learn to apply lecture material to the solution of numerical problems.

10 credits
The Solar System

One of the four half-modules forming the Level 1 astronomy course, but may also be taken as a stand-alone module. PHY106 covers the elements of the Solar System: the Sun, planets, moons and minor bodies. What are their structures and compositions, and what dothey tell us about the formation and history of the Solar System?

10 credits
Our Evolving Universe

The course provides a general overview of astronomy suitable for those with no previous experience of the subject. The principal topics covered are (1) how we deduce useful physical parameters from observed quantities, (2) the structure and evolution of stars, (3) the structure of the Milky Way, and the classification, structure and evolution of galaxies in general, (4) an introduction to cosmology and (5) extrasolar plantets and an introduction to astrobiology. All topics are treated in a descriptive manner with minimal mathematics.

10 credits
Social Psychology I

This module will provide an overview of the fundamentals of social psychology. The module will introduce and explain key theories and research, and their application, for understanding social psychological phenomena. Content is organised around two themes: How people think (Semester 1), and how people feel and behave (Semester 2). The module will include lectures that will provide opportunities to learn how to critically evaluate social psychological research and theories, as well as to describe how social psychology theory can be applied to address real world issues.

20 credits
Cognitive Psychology I

This unit provides an overview of core components of cognition, and principles of their investigation. The module covers perception, attention, performance, cognitive neuroscience, language, learning, memory and reasoning. It introduces and explored key concepts, theoretical perspectives and foundational methods. Examples of key studies in cognitive psychology will be considered critically.

20 credits
Neuroscience and Clinical Psychology I

This unit aims to provide students with an understanding of the key principles within neuroscience and clinical psychology. The module will introduce students to the basic structure and function of the brain, techniques and assessments used within neuroscience and clinical psychology, and an awareness of the ethical issues. The module will cover the aetiology, development, assessment and treatment of specific psychological and neurological disorders. Students will develop their knowledge, skills and understanding by attending lectures, engaging with activities/discussions within the lectures and engaging with the reading for this module.

20 credits

The content of our courses is reviewed annually to make sure it's up-to-date and relevant. Individual modules are occasionally updated or withdrawn. This is in response to discoveries through our world-leading research; funding changes; professional accreditation requirements; student or employer feedback; outcomes of reviews; and variations in staff or student numbers. In the event of any change we'll consult and inform students in good time and take reasonable steps to minimise disruption. We are no longer offering unrestricted module choice. If your course included unrestricted modules, your department will provide a list of modules from their own and other subject areas that you can choose from.

## Learning and assessment

### Learning

You'll learn through lectures, problems classes in small groups and research projects. Some modules also include programming classes.

We invest to create the right environment for you. That means outstanding facilities, study spaces and support, including 24/7 online access to our online library service.

Study spaces and computers are available to offer you choice and flexibility for your study. Our five library sites give you access to over 1.3 million books and periodicals. You can access your library account and our rich digital collections from anywhere on or off campus. Other library services include study skills training to improve your grades, and tailored advice from experts in your subject.

### Programme specification

This tells you the aims and learning outcomes of this course and how these will be achieved and assessed.

Find programme specification for this course

## Entry requirements

With Access Sheffield, you could qualify for additional consideration or an alternative offer - find out if you're eligible

Standard offer
Access Sheffield offer

The A Level entry requirements for this course are:
AAA
including Maths

The A Level entry requirements for this course are:
AAB
including A in Maths

A Levels + additional qualifications | AAB, including A in Maths + A in a relevant EPQ; AAB, including A in Maths + B in Further Maths AAB, including A in Maths + A in a relevant EPQ; AAB, including A in Maths + B in Further Maths

International Baccalaureate | 36, 6 in Higher Level Mathematics (Analysis and Approaches) 34 with 6 in Higher Level Mathematics

BTEC | D*DD in a relevant subject with Distinctions in Maths units DDD in a relevant subject with Distinctions in Maths units

Scottish Highers + 1 Advanced Higher | AAAAB + A in Maths AAABB + A in Maths

Welsh Baccalaureate + 2 A Levels | A + AA, including Maths B + AA, including Maths

Access to HE Diploma | 60 credits overall in a relevant subject with Distinctions in 39 Level 3 credits, including Mathematics units, + Merits in 6 Level 3 credits 60 credits overall in a relevant subject with Distinctions in 36 Level 3 credits, including Mathematics units, + Merits in 9 Level 3 credits

Mature students - explore other routes for mature students

English language requirements

You must demonstrate that your English is good enough for you to successfully complete your course. For this course we require: GCSE English Language at grade 4/C; IELTS grade of 6.5 with a minimum of 6.0 in each component; or an alternative acceptable English language qualification

Equivalent English language qualifications

Visa and immigration requirements

Other requirements
• We will give your application additional consideration if you have passed the Sixth Term Examination Paper (STEP) at grade 3 or above or the Test of Mathematics for University Admissions (TMUA) at grade 5 or above

We also accept a range of other UK qualifications and other EU/international qualifications.

## School of Mathematics and Statistics

Staff in the School of Mathematics and Statistics work on a wide range of topics, from the most abstract research on topics like algebraic geometry and number theory, to the calculations behind animal movements and black holes. They’ll guide you through the key concepts and techniques that every mathematician needs to understand and give you a huge range of optional modules to choose from.

The department is based in the Hicks Building, which has classrooms, lecture theatres, computer rooms and social spaces for our students. It’s right next door to the Students' Union, and just down the road from the 24/7 library facilities at the Information Commons and the Diamond.

## Why choose Sheffield?

### The University of Sheffield

A Top 100 university 2021
QS World University Rankings

Top 10% of all UK universities
Research Excellence Framework 2014

No 1 Students' Union in the UK
Whatuni Student Choice Awards 2019, 2018, 2017

### School of Mathematics and Statistics

3rd in the Russell Group for overall satisfaction

National Student Survey 2019

### Mathematics

92% overall satisfaction

National Student Survey 2020

### School of Mathematics and Statistics

There will always be a place for maths graduates in banking, insurance, pensions, and financial districts from the City of London to Wall Street. Big engineering companies still need people who can crunch the numbers to keep planes in the sky and trains running on time too. But the 21st century has also created new career paths for our students.

Smartphones, tablets, social networks and streaming services all use software and algorithms that need mathematical brains behind them. In the age of ‘big data’, everyone from rideshare apps to high street shops is gathering information that maths graduates can organise, analyse and interpret. The same technological advances have created new challenges and opportunities in cybersecurity and cryptography.

If the maths itself is what interests you, a PhD can lead to a career in research. Mathematicians working in universities and research institutes are trying to find rigorous proofs for conjectures that have challenged pure mathematicians for decades, or are doing the calculations behind major experiments, like the ones running on the Large Hadron Collider at CERN.

#### What if I want to work outside mathematics?

A good class of degree from a top university can take you far, whatever you want to do. We have graduates using their mathematical training in everything from teaching and management to advertising and publishing.

### "I've found that prospective employers always value the skills that maths students can bring to a role"

Hailey Pottinger MMath Mathematics

After graduating, Hailey joined the NHS Graduate Management Training Scheme. The mathematical and problem solving skills Hailey learned during her MMath degree helped her secure her place on the scheme, and led to her becoming an Operational Manager for Neurosciences at Sheffield Teaching Hospitals.

### "My work is mainly concerned with constructing graph algorithms and determining the computational complexity of computing them"

Chris Knapp MMath Mathematics

Chris' MMath at Sheffield was what inspired him to go on to do a PhD in combinatorics.

## Fees and funding

### Fees

The annual fee for your course includes a number of items in addition to your tuition. If an item or activity is classed as a compulsory element for your course, it will normally be included in your tuition fee. There are also other costs which you may need to consider.

Examples of what’s included and excluded

Depending on your circumstances, you may qualify for a bursary, scholarship or loan to help fund your study and enhance your learning experience.

Use our Student Funding Calculator to work out what you’re eligible for.

## Visit us

### University open days

There are four open days every year, usually in June, July, September and October. You can talk to staff and students, tour the campus and see inside the accommodation.

### Taster days

At various times in the year we run online taster sessions to help Year 12 students experience what it is like to study at the University of Sheffield.

### Applicant days

If you've received an offer to study with us, we'll invite you to one of our applicant open days, which take place between November and April. These open days have a strong department focus and give you the chance to really explore student life here, even if you've visited us before.

### Campus tours

Campus tours run regularly throughout the year, at 1pm every Monday, Wednesday and Friday.

## Apply for this course

Make sure you've done everything you need to do before you apply.

When you're ready to apply, see the UCAS website: