This module develops your knowledge and understanding of key statistical techniques, statistical software and project-based skills, working  

collaboratively with local partners on an applied project. You’ll learn through a mix of lectures, workshops and laboratory sessions. 

You’ll study topics such as: 

• Project-based statistics, from data collection to conclusions  

• Statistical programming  

• Data manipulation, summary and visualisation 

• Commonly used statistical techniques and statistical modelling 

• Working with employers as a data analyst  

• Consultancy and project management skills 

This module develops the skills required of a professional mathematician, including reading, thinking and working with mathematical and statistical ideas, and programming. In lectures, workshops and group tutorials, you’ll develop confidence and accuracy with foundational concepts and techniques, extending these to new topics which are essential for successful further study.   

 You’ll study topics such as: 

• Functions, solving equations and complex numbers 

• Calculus, analytical and numerical techniques for basic differential equations 

• Matrices and linear algebra 

• Core concepts of statistics  

• Probability and inferential statistics  

• Programming  

This module develops skills in applying both familiar and new mathematical techniques to solve everyday problems, including critical thinking, team work and understanding the roles of different team members. Through lectures, workshops and group tutorials, you’ll appreciate the role of mathematics and statistics in research and wider society. 

You’ll study topics such as: 

• Modelling principles and techniques  

• Matrix algebra 

• Linear simultaneous equations and vectors 

• Linear programming  

• Queuing systems 

• Probability  

• Ordinary differential and difference equations  

• Mathematics and statistics in real-world contexts 

• The role of ethics 

This module explores problem solving and mathematical thinking skills by introducing mathematical theory and abstraction. Through interactive workshops you’ll develop an appreciation of rigour and methods of mathematical proof. 

You’ll study topics such as: 

• Problem-solving strategies 

• Communicating solution methods with clear definitions and justifications 

• Connecting and applying prior learning and skills to new problems 

• Proof methods 

• Set theory and logic 

• Number bases 

• Modular arithmetic 

• Functions 

• Group and graph theories 

• Combinatorics 

This module broadens your experience of techniques and applications of calculus, including vector calculus, Fourier analysis, linear algebra and operational research. You’ll learn through lectures, tutorials and workshops. 

You’ll study topics such as: 

• Multiple integrals, double integration in Cartesian and polar co-ordinates 

• Change of order of integration and triple integration  

• Vector calculus gradient, divergence, curl, identities and directional derivative 

• Fourier analysis  

• Spaces isomorphic to Rn  

• Linear independence, bases, subspaces, rank and transformations 

• Eigenvectors, eigenvalues and abstract vector spaces  

• Simplex method 

• Constrained and unconstrained optimisation 

• Graph theory and networks  

Module Aim:  

To develop knowledge and understanding of different modelling techniques in a variety of contexts to enable the production and interpretation of model output in real world scenarios. 

Indicative content:  

• Continuous modelling with differential equations 

• Discrete modelling 

• Statistical modelling  

At least one of these will include an enhanced applied project.

The module will be delivered through workshop style teaching sessions and independent study. 

This module contributes to course cohesion by developing the core skills of mathematical modelling central to applied mathematics and integral to the core Level 6 modules. 

This module develops mathematical rigour and knowledge in an area of pure mathematics, enabling you to prove and apply theorems and discover properties of mathematical objects. You’ll explore both real and complex analysis through a mix of lectures and tutorials. 

You’ll study topics such as: 

• Upper and lower bounds 

• Inequalities 

• Convergence and divergence of sequences and series 

• Power series 

• Complex-valued functions 

• Cauchy-Riemann equations 

• Contour integration 

• Laurent series 

• Residues 

• Applications of contour integration  

This module develops your theoretical understanding and practical application of more advanced statistical techniques that are used widely in industry. You’ll also expand on techniques covered at level 4. 

You’ll study topics such as:  

• Statistical modelling and application 

• Model formulation and selection  

• Identification of issues 

• Non-linear models  

• Understanding the relevant theory 

• Probability and theory of statistical inference 

• Bayesian statistics 

This module develops your theoretical and practical expertise in a range of mathematical and statistical applications.  Through lectures, seminars, tutorials, workshops and lab sessions, you’ll specialise in your own area of interest to further your knowledge and enhance your mathematical and statistical skills. 

You’ll study topics such as:

• Modelling with partial differential equations 

• Mathematical biology 

• Fluid dynamics 

• Data science and statistics 

• Codes, cryptography and abstract algebra 

• Combinatorics and game theory 

• Mathematical physics 

• Mathematical finance 

This module applies tools developed throughout the degree to build mathematical models that tackle issues of sustainability. Through lectures, seminars, tutorials, workshops and lab sessions, you’ll specialise in areas of interest, further developing your theoretical and practical expertise in a range of mathematical and statistical applications.   

You’ll study topics such as: 

• The mathematics of sustainability 

• Mathematical biology 

• Fluid dynamics 

• Data science and Statistics 

• Codes, cryptography, and abstract algebra 

• Combinatorics and game theory 

• Mathematical physics 

• Mathematical finance 

Your individual final year project is the apex of your academic journey, offering a platform to apply the wealth of knowledge and skills gathered throughout your degree to real-world linked problems. This module requires your creativity, problem-solving capabilities, and the ability to navigate new material independently in whichever field you choose to specialise in. 

This module allows you to: 

• Undertake in-depth research in a topic of your choosing

• The opportunity to work alongside cutting-edge researchers 

• Create a body of work that can support you into further study, or work in a field that interests you

Develop solid foundations for undertaking a self-managed academic research project. On this module you will develop the skills and understanding you will need to complete your dissertation project to the highest level. Through lectures, guided reading and one-to-one discussions with your project supervisor you will design a design a path through to successful completion of an extensive research project including developing the project management skills you will need to achieve this. 

You’ll study topics such as 

• The life cycle of a project 

• Reviewing academic literature 

• Quality management 

• Project management techniques and tools 

• Research ethics 

• Intellectual property rights 

This module aims to give experience in the practice of engineering and related disciplines at a professional level. It involves planning, managing, executing and reporting a programme of work which will normally involve a mixture of experimental, theoretical and computational work together with a review of relevant previous work in the field.  

You’ll study topics such as: 

• Approaches to managing complex technical projects 

• Effective teamwork and management 

• Planning and coordinating a team-based activities 

• Roles in a team 

• Critical reflection 

This Project and Dissertation module represents the capstone in your learning journey. It is your chance to push the boundaries of knowledge, showcasing originality through major research. Dive into an intellectually rich master's-level research project, all guided by your chosen topic and your dedicated Sheffield Hallam dissertation supervisor. 

This module allows you to: 

• Develop your own original ideas on a topic of your choosing. 

• Work alongside active researchers and receive one-to-one guidance. 

• Contribute to the field of your choosing and advance it in a meaningful way. 

• Gain insight into the day-to-day activities of a research scientist. 

Engage with cutting-edge research in this wide-ranging module and fuel your independent exploration. Explore an advanced area of research of your choosing and work alongside an active researcher in that field. Through a range of taught sessions, directed reading and investigations you will forge an understanding of a currently active area of research, culminating in presenting your findings in the style of an academic paper suitable for publication. 

In this module provides you with: 

• The opportunity to further your understanding in a specialist topic 

• The chance to work as part of a research team on cutting-edge research 

• The opportunity to have your work published 

• The experience of being a professional researcher  

In this module you will cultivate the essential skills for preparing the ground for dissertation work. You will develop and plan an original piece of research, supported though taught sessions that impart theories and concepts as well as one-to-one instruction from a dedicated supervisor who is an active researcher in the field. This module is your foundation to developing the skills needed for high-quality research and scientific excellence. 

This module allows you to: 

• Dive into the world of research from the ground up. 

• Master the art of research planning to ensure you are producing high-quality work. 

• Learn the art of literature search and evaluation and develop a critical faculty to examine the work of others. 

• Improve your academic writing abilities, with the potential of developing publishable research.