Mathematics with Foundation Year

This module supports and broadens your learning through practical experiments and application of mathematical knowledge. As an engineer or mathematician you’ll need to develop a variety of experimental and transferable skills as part of your education and ongoing professional development.  

You’ll study topics such as: 

• Mechanical laboratory experiments 

• Electrical and electronic practical work and skills 

• Mathematical case studies with real-world problems 

• Town planning and traffic management  

• Monitoring natural phenomena 

• How to design experiments 

• How to deal with experimental errors 

• Scientific writing 

This module introduces you to core topics in science, physics and mathematics. You’ll develop an awareness of mathematics contexts and your ability to apply mathematics appropriately. 

You’ll study topics such as:  

• Numbers and order of operations 

• Algebra, mathematical functions and solving simple equations 

• Geometry including trigonometry of right-angled triangles 

• Vector addition and resolution 

• Technology for calculations and plot graphs  

• Ohm's Law and capacitance 

• LR, CR and LCR circuits  

• AC theory  

• SI units and motion in a straight line (rectilinear) 

• Forces, friction and equilibrium 

This module consolidates your previous learning, developing further essential skills in science, physics and mathematics. You’ll study mathematical, electrical and mechanical areas of the subject with a structured approach to problem solving.   

You’ll study topics such as:   

• Functions and product, quotient, chain rules, gradients, min/max problems 

• Integration by function, parts, substitution and integrals 

• Velocity and acceleration problems 

• Trigonometric graphs, equations and sine/cosine rules 

• Logarithmic and exponential functions and graphs 

• Inverse and simultaneous equations using matrices 

• Electronics for measurement, diodes, power supplies and sensors 

• Op amps, analogue to digital converters and microcontrollers  

• Circular motion, work, energy, power and simple harmonic motion 

• Specific and latent heat, changes of state, expansion/contraction 

This module studies the physical and chemical principles underpinning materials science, introducing the structure, processing and characteristics of engineering materials. You’ll explore different manufacturing techniques, associated equipment and tooling, while developing your presentation and information skills.  

You’ll study topics such as: 

• Atomic and electronic structure of atoms 

• Chemical reactivity and electronic structure 

• Ionic bonding, crystals, compounds and covalent bonding  

• Characteristics and examples of organic compounds 

• Metallic bonding and conservation of mass in chemical reactions 

• Metals, organic polymers, ceramics and composites  

• Health, safety and solidification processes  

• Hot and cold metal working processes 

• Ceramic and polymer processing 

• Machining processes 

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, including the impact of Artificial Intelligence (AI) and machine learning algorithms.

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 

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 broadens your experience of techniques and applications of calculus and linear algebra. 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 

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 

Module aim:    

The aim of this module is to enhance students’ professional development through the completion of and reflection on meaningful work placement(s).  

A work placement will provide students with opportunities to experience the realities of professional employment and experience how their course can be applied within their chosen industry setting. The placement will: 

• Allow student to apply the skills, theories and behaviours relevant and in addition to their course 
• Enable students to enhance their interpersonal skills in demand by graduate employers – communication, problem-solving, creativity, resilience, team work etc.  
• Grow their student network and relationship building skills. 
• Provide student with insights into the industry and sector in which their placement occurs 
• Help student make informed graduate careers choices. 

Indicative Content:  

In this module students undertake a sandwich placement (min 24 weeks / min 21 hours per week) which is integrated, assessed and aligned to their studies.  

Their personal Placement Academic Supervisor (PAS) will be their key point of contact during their placement and will encourage and support students to reflect on their experience, learning and contribution to the organisation they work for.  

To demonstrate gains in professional development, students will be required to share their progress, learning and achievements with their Placement Academic Supervisor and reflect on these for the summative piece of work. 

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 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 · Data science and Statistics · Fluid dynamics · Discrete mathematics · Programming with Mathematical applications.

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 authentic, discipline-specific 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 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, and undertake some initial work. Through guided reading and one-to-one discussions with your project supervisor you will 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 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 areas of interest, further developing your theoretical and practical expertise in a range of mathematical and statistical applications. You’ll study topics such as: · Fluid dynamics · Data science and Statistics · Codes, cryptography, and abstract algebra · Combinatorics and game theory · Mathematical physics · Mathematical finance