# Mathematics BSc (Hons)/MMath

## BSc (Hons)/MMath Mathematics

## MMath BSc Mathematics

## Overview

Mathematics has shaped societies for thousands of years – from the Ancient Babylonians to the present day. Continue the tradition of unpicking complex mathematical problems that could help monitor the spread of disease, predict the route of a cloud of ash from a volcano and forecast climate change.

Study core mathematical topics including analysis, algebra, calculus, statistics, operational research and modelling. Then shape your degree to your ambitions and interests in following years, by specialising in advanced principles such as financial modelling, non-linear dynamics and cosmology.

When you graduate, you’ll be in high demand, especially in the expanding technology, data and machine learning industries.

### BSc or MMath?

You can study this course as a 3-year Bachelor's degree (BSc) or a 4-year integrated Master's degree (MMath). The MMath allows you to achieve a Master’s level degree with just one extra year of undergraduate study, further enhancing your career prospects.

Course highlights

- Delve into topics including deterministic chaos, partial differential equations, health research and abstract algebra
- Learn from expert researchers such as Dr. Michael Gnacik, who provided data visualisation for the University's Covid testing programme as member of the Institute of Cosmology and Gravitation's Covid Response Team
- Develop coding skills in programming languages including Python
- Learn to use industry-standard mathematical, statistical and operational research software
- Apply your skills on optional work placements in the community, such as assisting math teachers in local schools

90% of graduates in work or further study 15 months after this course (BSc) (HESA Graduate Outcomes Survey 2018/19)

### Accreditation

This course is accredited by the Institution of Mathematics and Its Applications (IMA).

## Facilities and specialist software

### Maths Café

No problem is too small or too tough for our Maths Café tutors, who are on hand every day during term-time to help you if you get stuck or need something explained.

### Specialist mathematics software

Use advanced mathematical and statistical software such as Mathematica and MATLAB for high-level simulations of complex dynamical processes. You'll also get exclusive access to industry-standard statistical and operational research software (R and SPSS), IBM and Microsoft software (Azure Dev Tools for Teaching) and VMware.

## Entry requirements

### BSc (Hons) Mathematics entry requirements

##### Typical offers

- A levels – ABB–BBC
- UCAS points – 112–128 points to include an A level in Mathematics, or equivalent (calculate your UCAS points)

See full entry requirements and other qualifications we accept

##### English language requirements

- English language proficiency at a minimum of IELTS band 6.0 with no component score below 5.5.

See alternative English language qualifications

We also accept other standard English tests and qualifications, as long as they meet the minimum requirements of your course.

If you don't meet the English language requirements yet, you can achieve the level you need by successfully completing a pre-sessional English programme before you start your course.

### MMath Mathematics entry requirements

##### Typical offers

- A levels – AAA–ABB
- UCAS points – 128–144 points to include 40 points from an A level in Mathematics, or equivalent (calculate your UCAS points)

See full entry requirements and other qualifications we accept

##### English language requirements

- English language proficiency at a minimum of IELTS band 6.0 with no component score below 5.5.

See alternative English language qualifications

We also accept other standard English tests and qualifications, as long as they meet the minimum requirements of your course.

If you don't meet the English language requirements yet, you can achieve the level you need by successfully completing a pre-sessional English programme before you start your course.

Tessa Wildsmith graduated from Portsmouth with a mathematics degree, a Master's in maths, and a PGCE teaching qualification. She now teaches maths in a high school.

Find out more about Tessa's early love for algebra and how she's showing teenagers how beautiful maths can be.

My name is Tessa Wildsmith and I'm a teacher for both key stage four and key stage five for mathematics.

My dad did mathematics and he showed a love of it throughout my childhood. He introduced me to algebra when I was way too young. That has gone on throughout my life and him inspiring me to be better and to go on to see how beautiful maths can be. So his enthusiasm and love for it just inspired me, really.

When applying to university, I did have a look at some of the local universities. You're looking at somewhere that not only are you going to fit in but also is going to stretch you academically. Portsmouth did both.

The other thing, obviously, is the location. Being right by the sea means that if you have free time, it's lovely just to be able to go and sit by the sea front, collect your thoughts, have a think about your day or how you're going to go about your next assignment. It calms you so much to have that environment.

At the University of Portsmouth, I studied an undergraduate in mathematics and then went on to study a masters of research, which also looked into mathematics. The lecturers there were really welcoming, obviously knowledgeable as well, but they had a real love and passion of each of their individual subjects. To see the things that seem very abstract actually have a very real life application was incredible.

Following my masters, I went on to do the PGCE also at the University of Portsmouth. I just wanted to go into teaching because I've seen a bit of research, I've done a bit of research with my masters and then after that, I realised that I always thought about teaching. During university as well, I was often tutoring other fellow students and helping them with it and that satisfaction you get from seeing lightbulb moments with people, especially with maths, because it seems something that for some people is very unattainable.

To unlock a passion in students, you just need to show them why you love it. You know some of the things you teach them, even if they don't apply in real world concepts later on, they will still remember. They actually will remember as a satisfying thing or something that brought them some joy. But the thing that motivates me most is the students, because when you go into a room and they're excited for your lesson or they're excited to see you or they're excited to learn, that's going to drive you constantly because that isn't something that dissipates.

My time at university definitely did change me. It did build my confidence a lot. It created the enthusiasm that I have now because of seeing people who inspired me more so. If someone is thinking of going to university, I would definitely say if your passionate about something, go. I don't think there's any drawbacks to opening up your mind to new concepts, ever.

## Careers and opportunities

Mathematics is more than just number crunching.

A degree in mathematics shows that you have the ability to think analytically and conveys an intellectual maturity that many employers look for when they hire staff.

The demand for mathematics graduates is increasing too. The Council for the Mathematical Sciences predicts more than 7 million people in the UK will need mathematical science skills in 2030 – an increase of 900,000 compared to 2009.

### Graduate destinations

Our graduates have worked for companies such as:

- NATS (National Air Traffic Services)
- TSB
- Oakbrook Finance Ltd
- NHS
- Carnival UK
- The Guide Dogs for the Blind Association
- Portsmouth Grammar School

### What jobs can you do with a mathematics degree?

Our graduates now work in roles including:

- research analyst
- service reliability engineer
- accountant
- mathematics teacher
- credit risk analyst
- data scientist
- accounts payable clerk
- service reliability engineer

### Placements (optional)

After your second year, you can do an optional work placement year to get valuable longer-term work experience in the industry.

A placement year gives you an advantage over other graduates who may understand theory but won't have the experience of applying their learning to a working environment. We’ll help you secure a work placement that fits your aspirations, and you’ll get mentoring and support throughout the year.

#### Potential roles

Previous students have taken placement roles such as:

- innovation and infrastructure specialist
- counter terrorism and security
- student research analyst

#### Potential destinations

They've completed placements at organisations including:

- IBM
- Defence Science and Technology Laboratory
- British Telecom

**Undergraduate Ambassador Scheme**

In year 3, you can do a 5-day (or 10 half-day) placement in a local school or college, acting as a role-model for Primary to A Level students interested in pursuing Science, Technology, Engineering and Mathematics (STEM) subjects.

Develop your confidence in communicating your knowledge of mathematics and your understanding of teaching methods and adapting to individual student needs.

The course mentors were always really supportive. I loved the lecture style lessons and I was so lucky to be able to complete the Undergraduate Ambassador Scheme in Year 3... Studying pure maths has allowed me to be a subject specialist within my department, meaning not only can I teach KS3 and KS4, but also KS5.

## What you'll study

Each module on this course is worth a certain number of credits.

In each year, you need to study modules worth a total of 120 credits. For example, four modules worth 20 credits and one module worth 40 credits.

### Modules

#### Core modules

###### What you’ll do

You'll explore ways in which calculus underpins much of modern science.

###### What you’ll learn

When you complete this module successfully, you'll be able to:

- Compute limits, derivatives, and integrals of functions
- Use differential calculus to study the behaviour of functions
- Use integral calculus to compute areas
- Determine convergence of infinite series
- Use infinite series in differentiation and integration

###### Teaching activities

- 23 x 2-hour lectures
- 23 x 1-hour seminars

###### Independent study time

We recommend you spend at least 131 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a set exercise (40% of final mark)
- an exam (10% of final mark)
- a 90-minute written exam (50% of final mark)

###### What you’ll learn

When you complete this module successfully, you'll be able to:

- Extract the algorithms in simple repetitive tasks
- Implement algorithms in a high-level programming language (Python)
- Analyse simple algorithms and their convergence properties
- Solve calculus and algebra problems numerically

###### Teaching activities

- 15 x 2-hour lectures
- 23 hours of practical classes and workshops

###### Independent study time

We recommend you spend at least 147 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a set coursework exercise (15% of final mark)
- a set of 30-minute in-class tests (35% of final mark)
- a 1-hour written exam (50% of final mark)

###### What you'll do

You'll cover topics including Gaussian elimination, matrices, vector spaces and eigentheory. You'll also meet applications such as differential equations, conic sections, graphs and networks.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Solve a linear system of equations, including the case of infinitely many solutions
- Describe the solution of linear systems in geometrical terms such as lines and planes
- Develop the algebra of matrices and vectors including determinants and dot products
- Find the eigenvalues and eigenvectors of a matrix
- Use matrices to represent and interpret linear transformations
- Analyse the vector space properties (such as basis and dimension) of certain sets

###### Teaching activities

- 46 x 1-hour Lectures
- 23 x 1-hour Seminars

###### Independent study time

We recommend you spend at least 131 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- 3x 40-minute in-class tests (30% of final mark)
- 2x 10-minute oral assessment and presentations (0% of final mark)
- a 2-hour written exam (70% of final mark)

###### What you'll do

You'll study different types of proof, learn to identify the circumstances in which they are useful, and practise the skills needed for finding proofs. You'll also learn about logic, set theory, complex numbers and elementary properties of integers.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Construct clear, logical arguments demonstrating the difference between experimental evidence and proof
- Manipulate elementary mathematical constructs and complex numbers
- Demonstrate an understanding of cryptographic systems and techniques by enciphering and deciphering messages

###### Teaching activities

- 23 x 2-hour lectures
- 23 x 1-hour seminars

###### Independent study time

We recommend you spend at least 131 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 90-minute set exercise exam (50% of final mark)
- a 90-minute written exam (50% of final mark)
- a 10-minute oral assessment and presentation (0% of final mark, pass mark of 40)

###### What you'll do

You'll cover models such as linear difference equations, fractals and multivariable problems, and reflect on their applications to subjects including biology, ecology, epidemiology and physics/astronomy.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Formulate mathematical models using algebraic equations/inequalities, difference equations and ordinary differential equations (ODEs)
- Formulate and solve linear programming models using graphical methods
- Solve and interpret the solutions to linear 1st and 2nd order difference equations, e.g. in biology and economics
- Solve and interpret the solutions to 1st and 2nd order ODEs with application to real world problems, e.g. in mechanics
- Demonstrate familiarity with numerical techniques and their applications to mathematical modelling

###### Teaching activities

- 23 x 2-hour lectures
- 11 hours of practical classes and workshops

###### Independent study time

We recommend you spend at least 143 hours studying independently. This is around 8.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a set exercise using the Maple TA software (40% of final mark)
- a 90-minute written exam (60% of final mark)

###### What you'll do

You'll apply your understanding of statistical theory to techniques used widely in business and social science.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Interpret, summarise and present data clearly using a variety of methods
- Identify and apply standard probability models
- Test hypotheses about population parameters (means, proportions, correlations) using inferential methods
- Fit and test simple linear regression models to data
- Use appropriate software to analyse data

###### Teaching activities

- 23 x 2-hour lectures
- 20 hours of tutorials
- 18 hours of practical classes and workshops

###### Independent study time

We recommend you spend at least 116 hours studying independently. This is around 7 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- an 80-minute set exercise exam (20% of final mark)
- a set exercise (20% of final mark)
- a 2-hour written exam (60% of final mark)

#### Core modules

###### What you'll do

You'll work in a group to select a problem, then produce and present a report on your solutions.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Identify and apply mathematical techniques to solve a problem
- Use high-level software to model and analyse problems
- Work in and lead a team
- Communicate mathematical findings in written and oral form
- Identify and demonstrate your skills, priorities and constraints in the context of career decision-making

###### Teaching activities

- 16 x 1-hour lectures
- 16 x 1-hour seminars
- 30 hours of supervised time in studio/workshop

###### Independent study time

We recommend you spend at least 138 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- 2 x 40-minute exams (30% of final mark)
- 2 x coursework assignments (60% of final mark)
- 1 x oral assessment and presentation (10% of final mark)

###### What you’ll do

You'll begin exploring Fourier series.

To choose this module, you should have taken *Mathematical Foundations* and *Calculus I* core modules, and be familiar with the basics of calculus.

###### What you’ll learn

When you complete this module successfully, you'll be able to:

- Determine the gradient, divergence, curl, and expressions involving these operators
- Evaluate line, surface and volume integrals
- Apply the integral theorems of vector calculus
- Find the Fourier series of a function
- Solve linear ordinary differential equations using standard analytical techniques including complementary function plus particular integral, series solutions and Laplace transform
- Interpret the solution of linear ordinary differential equations

###### Teaching activities

- 46 hours of lectures
- 23 x 1-hour seminars

###### Independent study time

We recommend you spend at least 131 hours studying independently. This is around 4 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 50-minute set exercise exam (20% of final mark)
- a set coursework exercise (20% of final mark)
- a 2-hour written exam (60% of final mark)

###### What you'll do

To choose this module, you should have taken the Mathematical Foundations and Calculus I core modules in year 1.

###### What you'll learn

When you complete this module successfully, you'll be able to:- Construct simple proofs and counter examples
- Give clear definitions and state basic theorems of analysis
- Illustrate simple complex mappings in the complex plane
- Demonstrate your understanding of the properties of standard functions of complex variables (including continuity, differentiability, series representation and integration)
- Apply the techniques of complex analysis to evaluate derivatives and integrals, and to solve appropriate problems

###### Teaching activities

- 22 x 2-hour lectures
- 22 x 1-hour tutorials

###### Independent study time

We recommend you spend at least 134 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a set coursework exercise (50% of final mark)
- a 90-minute set exercise exam (50% of final mark)

#### Optional modules

###### What you'll do

To choose this module, you need to take the *Mathematical Foundations and Linear Algebra* modules in year 1, to gain knowledge of complex numbers and linear algebra (particularly vector spaces, bases, dimension and matrices) and experience in mathematical proofs.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Apply appropriate terminology and techniques involving different algebraic structures to their solutions
- Construct simple proofs and counter examples for a wide set of given mathematical propositions
- Give clear definitions and statements of basic results in Abstract Algebra
- Conceptualise the notion of a group by using the group axioms to construct relevant proofs and by describing structural properties
- Conceptualise the notion of a group and its categorical properties by constructing proofs of structural properties
- Display your familiarity with sets, general abstract objects, and their correspondences

###### Teaching activities

- 36-hours of lectures
- 24-hours of tutorials

###### Independent study time

We recommend you spend at least 128 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a coursework exercise (50% of final mark)
- a 2-hour written exam (50% of final mark)

###### What you’ll do

You'll get the opportunity to put into practice your learning from the first two years of the degree and improve your chances of securing a professional level role upon graduation.

###### What you’ll learn

When you complete this module successfully, you'll be able to:

- Evaluate your learning, personal development and future career opportunities
- Describe tasks undertaken and responsibilities held in the course of (self) employment
- Differentiate your employability as graduates, as a result of the placement experience

###### Teaching activities

- 5 x 1-hour seminars
- 195 hours of placement

###### Independent study time

N/A

###### Assessment

On this module, you'll be assessed through a 4,000-word portfolio project (100% of final mark).

###### What you'll do

You'll enter at the appropriate level for your existing language knowledge. If you combine this module with language study in your first or third year, you can turn this module into a certificated course that is aligned with the Common European Framework for Languages (CEFRL).

###### What you'll learn

When you complete this module:

- You'll have improved your linguistic skills in Arabic, British Sign Language, Italian, Japanese, Mandarin, French, German or Spanish
- You'll be prepared for Erasmus study abroad

###### Teaching activities

- 12 x 2-hour seminars

###### Independent study time

We recommend you spend at least 176 hours studying independently. This is around 10 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- coursework (100% of final mark)

###### What you'll do

You'll develop practical programming skills (Python) and apply them creatively, using industry standard computer tools.

To choose this module, you need to show knowledge of calculus and stochastic methods.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Model and solve financial problems mathematically
- Simulate and analyse financial scenarios using computer tools
- Apply advanced analysis techniques to model financial market

###### Teaching activities

- 16 x 2-hour lectures
- 12 x 2-hour practical classes & workshops

###### Independent study time

We recommend you spend at least 144 hours studying independently. This is around 8.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a set coursework exercise (20% of final mark)
- a set of 1-hour in-class tests (20% of final mark)
- a 2-hour written exam (60% of final mark)

###### What you'll do

You'll then study linear and nonlinear differential and difference equations in the context of methods and techniques of dynamical systems.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Model simple mechanical systems (for example a double pendulum) in terms of coordinates and velocities
- Derive a special function known as a ""Langrarian"", from which the equations of motion (a set of differential equations) are derived
- Simulate/solve these equations, taking advantage of any symmetry in the model, to predict the behaviour of the system
- Broaden the context of the study of differential/difference equations in general, both linear and nonlinear
- Use special techniques to describe the qualitative behaviour of the solutions to these equations

###### Teaching activities

- 23 x 2-hour lectures
- 23 x 1-hour seminars

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- 2 x coursework exercises (15% of final mark, each)
- a 2-hour written exam (70% of final mark)

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Understand the numerical solution of systems of linear and nonlinear equations
- Understand the numerical solution of differential equations
- Fit mathematical models, including differential equations, to data
- Estimate model parameters, and select models, using Bayesian methods
- Implement methods and visualize data using R or Python

###### Teaching activities

- 44 hours of lectures
- 5 x 1-hour tutorials
- 17 hours of practical classes and workshops

###### Independent study time

We recommend you spend at least 134 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 45-minute test (25% of final mark)
- a 1,500-word coursework assignment (25% of final mark)
- a 90-minute exam (50% of final mark)

###### What you'll do

The knowledge you'll develop will help in future operational research topics such as simulation, planning, scheduling, forecasting, supply chain management and advanced modelling.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Model operational research problems
- Formulate and solve linear, nonlinear and dynamic programming models
- Formulate and solve game theory models

###### Teaching activities

- 18 x 2-hour lectures
- 10 x 1-hour tutorials

###### Independent study time

We recommend you spend at least 154 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 60-minute in-class test (30% of final mark)
- a 2-hour examination (70% of final mark)

###### What you'll do

You'll also apply your understanding of statistical methods to quality control systems. To choose this module, you need to take the Statistical Theory and Methods I module in year 1, or equivalent.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Formulate problems in statistical terms, apply appropriate analyses and interpret the results in terms of the problem
- Recognise, analyse and interpret results from simple designed experiments using ANOVA
- Fit, test and interpret multiple linear regression models
- Estimate and make inferences about parameters of statistical models using a variety of approaches
- Analyse bi-variate probability distributions
- Perform transformations of uni-variate and bi-variate random variables

###### Teaching activities

- 22 x 2-hour lectures
- 23 hours of practical classes and workshops

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- a 40-minute set exercise exam (10% of final mark)
- a 3-week set coursework exercise (30% of final mark)
- a 2-hour set exercise exam (60% of final mark)

###### What you'll do

You'll develop your understanding in celestial coordinate systems, telescope design, comparative planetology, stellar evolution, the formation and evolution of galaxies, and the dynamics and matter content Universe.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Derive and apply mathematical equations to solve astronomical problems
- Identify and apply physical principles underlying the properties and behaviour of planets, stars and galaxies
- Make astronomical observations and analyse the results with appropriate software

###### Teaching activities

- 12 x 2-hour lectures
- 12 x 2-hour seminars
- 12 x 2-hour practical classes and workshops
- 18 hours of external visits

###### Independent study time

We recommend you spend at least 110 hours studying independently. This is around 6.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- an 80-minute set practical exercise (50% of final mark)
- a 90-minute written exam (50% of final mark)
- an 18-hour practical skills coursework assessment (pass/fail)

#### Core modules - BSc (Hons)

###### What you'll do

You'll study solution techniques such as the heat conduction (or diffusion) equation, Laplace's equation, wave equations, and classifications of elliptic, parabolic and hyperbolic equations.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Classify partial differential equations and boundary conditions
- Solve partial differential equations using the method of characteristics, transform methods, numerical methods, separation of variables and Fourier series

###### Teaching activities

- 22 x 2-hour Lectures
- 11 x 2-hour Seminars

###### Independent study time

We recommend you spend at least 134 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 2-hour set exercise exam (100% of final mark)

#### Core modules - MMath

###### What you'll do

You'll study perturbation methods and Turing instability, and the software packages to apply them to contexts including biology, chemistry, physics and mathematics.

To choose this module, you need to take the Mechanics and Dynamics module in year two.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Recognise the solution behaviour of 1 to 3-dimensional nonlinear systems (fixed points, stability properties and bifurcation scenarios)
- Classify regular and chaotic regimes by applying analytical methods based on perturbation theory
- Perform numerical studies related to the long-term behaviour of realistic problems

###### Teaching activities

- 17 x 2-hour lectures
- 10 x 1-hour tutorials
- 4 hours of guided independent study

###### Independent study time

We recommend you spend at least 156 hours studying independently. This is around 9.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- 3 x set exercises (30% of final mark)
- a 2-hour written exam (70% of final mark)

###### What you'll do

You'll study solution techniques such as the heat conduction (or diffusion) equation, Laplace's equation, wave equations, and classifications of elliptic, parabolic and hyperbolic equations.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Classify partial differential equations and boundary conditions
- Solve partial differential equations using the method of characteristics, transform methods, numerical methods, separation of variables and Fourier series

###### Teaching activities

- 22 x 2-hour Lectures
- 11 x 2-hour Seminars

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- a 2-hour set exercise exam (100% of final mark)

###### What you'll do

You'll manage your own plan, from outline to dissertation, with supervision from relevant lecturers.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Locate and critically review relevant literature for your topic
- Synthesise information and ideas from multiple sources
- Write a formal, well-structured dissertation, including an abstract and appropriate conclusions
- Manage a project
- Evaluate and discuss your work

###### Teaching activities

- 18 hours of project supervision

###### Independent study time

We recommend you spend at least 182 hours studying independently. This is around 11 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 10-minute oral assessment and presentation (10% of final mark)
- a dissertation (90% of final mark) - approximately 35 pages including appendices, formulas, plots, and code

#### Optional modules - BSc (Hons)

###### What you'll do

You'll develop a foundation to support mathematical elements in your other modules as you work on practical examples. To choose this option, you need to take the Algebraic Structures and Discrete Mathematics module in year 2, or show basic knowledge about groups and other algebraic structures.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Construct proofs and counter examples for multiple mathematical propositions.
- Present your results and proofs to a wide audience on a whiteboard to practice exposition skills and master the subject matter
- Conceptualise the notion of a ring, and give clear definitions and statements of basic results involving rings
- Recover such basic results for integers and polynomials as the division algorithm or Bézout's identity
- Interpret the notion of a module or an algebra
- Demonstrate understanding of basic category theory that's at the heart of everything described above

###### Teaching activities

- 36-hours of lectures
- 24-hours of tutorials

###### Independent study time

We recommend you spend at least 128 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- 2 x 1,000-word coursework exercises (33% of final mark, each)
- a 1,000-word coursework exercise (34% of final mark)

###### What you'll do

You'll learn about data envelopment analysis and decision analysis, explore realistic case studies, and work toward optimal solutions for computationally difficult problems.

To choose this module, you need to take the *Statistical Theory and Methods I* module in year 1.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Use computer software to formulate and solve linear, integer programming models
- Formulate data envelopment analysis models
- Formulate and solve multiple decision analysis models
- Understand and use the discrete-event simulation process
- Interpret and report on the results of solutions of your models and processes

###### Teaching activities

- 29 hours of lectures
- 12 x 30-minute tutorials
- 13 hours of practical classes and workshops
- 3 x 1-hour lectures

###### Independent study time

We recommend you spend at least 149 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 2,000-word coursework exercise (50% of final mark)
- a 90-minute written exam (50% of final mark)

###### What you'll do

You'll focus on equity options and portfolio construction, exploring no-arbitrage pricing, the Black-Scholes partial differential equation, and hedging. To choose this module, you need to take the Calculus II and Mathematics for Finance modules in year 2 or an equivalent module covering basic interest rate structures and elementary stochastic processes.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Define and distinguish between various types of derivative contracts, deduce their future payoffs and analyse investment portfolios created from them
- Prove standard relations (parity) between the prices of different contracts under the assumption of fairness (no-arbitrage)
- Derive the famous Black-Scholes partial differential equation and learn how to solve it for various asset types
- Use stochastic processes to price options using risk-neutral valuation via change of measure and expectation
- Perform partial differential equation changes of variables and other solution methods for certain exotic options
- Put theory into practice by implementing numerical schemes on the computer

###### Teaching activities

- 11 x 1-hour tutorials
- 11 x 3-hour lectures
- 11 hours of practical classes and workshops
- 5 hours of guided independent study

###### Independent study time

We recommend you spend at least 156 hours studying independently. This is around 9.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 1,500-word coursework exercise (40% of final mark)
- a 2-hour written exam (60% of final mark)

###### What you'll do

To choose this module, Physics students need to take the Mathematical Physics (level 5) and Introduction to Modern Physics and Astrophysics (level 5) modules.

To take this module, Maths students need to take the Applied Mathematics (level 5) module.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Analyse the 4-dimensional spacetime formulation of Special Relativity
- Carry out basic calculations in tensor algebra and calculus, and apply these to physical problems
- Apply Einstein field equations to the calculation of the simplest exact and approximate solutions for relativistic stars and black holes and in cosmology, as well as in the weak field regime and for gravitational waves
- Analyse a problem and associate it with the physical and mathematical principle of General Relativity
- Apply the specific mathematical techniques of General Relativity to solve exercises and problems, conceptualising and generalising from previously seen problems
- Discuss the use of physical and mathematical principles and hypotheses in the solution of exercises and problems

###### Teaching activities

24 x 2-hour lectures

###### Independent study time

We recommend you spend at least 152 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- 3 x written assignments including essays (each worth 20% of the final mark)
- a 2-hour written exam (40% of final mark)

###### What you'll do

You'll consider the physics of stars, black holes and galaxies, and their formation mechanisms. To choose this module, you need to take the Mathematical Physics, and Introduction to Modern Physics and Astrophysics module.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Analyse fundamental physical processes in astrophysics, and apply them to the physics of stars, black holes and galaxies in multiple contexts
- Apply the physics of gravitational collapse to solve problems related to the formation of stars and galaxies, and compact objects
- Demonstrate your understanding of fundamental nuclear reactions and energetic balance, and evaluate the energetics of stars and galaxies
- Demonstrate your understanding of the quest for dark matter in galaxy formation and evolution and evaluate the observational evidence

###### Teaching activities

- 24 x 2-hour lectures

###### Independent study time

We recommend you spend at least 152 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 2-hour written exam (100% of final mark)

###### What you'll do

You'll study perturbation methods and Turing instability, and the software packages to apply them to contexts including biology, chemistry, physics and mathematics.

To choose this module, you need to take the Mechanics and Dynamics module in year two.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Recognise the solution behaviour of 1 to 3-dimensional nonlinear systems (fixed points, stability properties and bifurcation scenarios)
- Classify regular and chaotic regimes by applying analytical methods based on perturbation theory
- Perform numerical studies related to the long-term behaviour of realistic problems

###### Teaching activities

- 17 x 2-hour lectures
- 10 x 1-hour tutorials
- 4 hours of guided independent study

###### Independent study time

We recommend you spend at least 156 hours studying independently. This is around 9.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- 3 x set exercises (30% of final mark)
- a 2-hour written exam (70% of final mark)

###### What you'll do

You'll manage your own plan, from outline to dissertation, with supervision from relevant lecturers.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Locate and critically review relevant literature for your topic
- Synthesise information and ideas from multiple sources
- Write a formal, well-structured dissertation, including an abstract and appropriate conclusions
- Manage a project
- Evaluate and discuss your work

###### Teaching activities

- 18 hours of project supervision

###### Independent study time

We recommend you spend at least 182 hours studying independently. This is around 11 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 10-minute oral assessment and presentation (10% of final mark)
- a dissertation (90% of final mark) - approximately 35 pages including appendices, formulas, plots, and code

###### What you'll do

You'll produce projects that work toward solving open-ended problems, and present your work to other students.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Appraise and compare relevant journal articles and research papers
- Critically evaluate theoretical approaches to specific problems
- Apply current mathematical software to advanced numerical techniques
- Independently research a mathematical topic
- Communicate information and arguments effectively

###### Teaching activities

- 23 x 2-hour lectures

###### Independent study time

We recommend you spend at least 154 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- 3 x 1,000-word coursework exercises (30% of final mark, each)
- a 10-minute oral assessment and presentation (10% of final mark)

###### What you'll do

You'll learn about game theory and its application in logistics, network flow, revenue and inventory management, and scheduling. To choose this module you need to show a general knowledge of Operational Research techniques.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Design and solve game theory models and study their efficiency in logistics
- Formulate and solve network flow and revenue management problems
- Formulate and solve inventory management, planning and scheduling models

###### Teaching activities

- 16 x 2-hour lectures
- 12 x 1-hour tutorials

###### Independent study time

We recommend you spend at least 154 hours studying independently. This is around 9.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 1-hour exam (30% of final mark)
- a 2-hour exam (70% of final mark)

###### What you'll do

You'll explore advanced regression modelling, modern statistical learning methods, the use of open source statistical tools, and forecasting methodologies. To choose this module, you need basic knowledge of probability, calculus and linear algebra.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Apply statistical learning techniques to business problems, and interpret your results
- Use Python and/or R language to apply statistical learning techniques
- Demonstrate understanding of the bias variance trade-off and cross validation
- Fit and test general linear models to numerical and categorical data
- Fit a variety of predictive models to real world data
- Demonstrate understanding of advanced techniques such as regularisation, nonlinear models and clustering

###### Teaching activities

Scheduled Activities (Hours)

- 24 x 2-hour lectures
- 24 hours of practical classes and workshops

###### Independent study time

We recommend you spend at least 128 hours studying independently. This is around 8 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a set of practical coursework problems (40% of final mark)
- a 90-minute written exam (60% of final mark)

###### What you'll do

You'll explore multiple procedures for data analysis, use the statistical language and software environment R to model data, and examine the strengths and weaknesses of various study designs. To choose this module, you need to take the Statistical Theory and Methods I module in year 1.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Formulate and employ statistical methods commonly used in the study of epidemiology
- Construct lifetables and compare survival patterns in population subgroups
- Conceptualize the basic principles underpinning the design and analysis of clinical trials
- Employ a variety of multivariate techniques.
- Formulate the principles relating to questionnaire design and validation.
- Use R language to apply the learnt statistical techniques

###### Teaching activities

- 44-hours of lectures
- 10-hours of practical classes and workshops

###### Independent study time

We recommend you spend at least 150 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a coursework exercise (40% of final mark) - a set of exercises to solve partly using R
- a 2-hour exam (60% of final mark)

###### What you'll do

You'll apply these to subjects such as earthquakes, disease spread, financial markets or population dynamics, and demonstrate your understanding of the wider applications of mathematics.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Apply distributions of random discrete and continuous random variables
- Determine the probability of the extinction of branching processes
- Solve the gambler's ruin problem
- Solve partial differential equations that arise in birth-death processes
- Apply appropriate techniques to analyse continuous time stochastic processes

###### Teaching activities

- 17 x 2-hour of lectures
- 12 x 1-hour tutorials

###### Independent study time

We recommend you spend at least 154 hours studying independently. This is around 9.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 3-hour written exam (100% of final mark)

###### What you'll do

Over ten half-days, you'll be mentored by a maths teacher as you gain experience of teaching mathematics, leading special projects and offering classroom support. To choose this module, you need to show you know the fundamental concepts of basic probability, calculus and linear algebra.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Demonstrate your understanding of teaching mathematics, and of educational theories and debates
- Work in a challenging and unpredictable working environment
- Communicate difficult principles or concepts, whether you're speaking one-to-one or to an audience
- Reflect on stereotypes of mathematics and mathematicians, and how to combat them

###### Teaching activities

- 9 x 2-hour practical classes and workshops
- 20 hours of placement

###### Independent study time

We recommend you spend at least 182 hours studying independently. This is around 11 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a set coursework exercise (100% of final mark)

#### Optional modules - MMath

###### What you'll do

You'll develop a foundation to support mathematical elements in your other modules as you work on practical examples. To choose this option, you need to take the Algebraic Structures and Discrete Mathematics module in year 2, or show basic knowledge about groups and other algebraic structures.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Construct proofs and counter examples for multiple mathematical propositions.
- Present your results and proofs to a wide audience on a whiteboard to practice exposition skills and master the subject matter
- Conceptualise the notion of a ring, and give clear definitions and statements of basic results involving rings
- Recover such basic results for integers and polynomials as the division algorithm or Bézout's identity
- Interpret the notion of a module or an algebra
- Demonstrate understanding of basic category theory that's at the heart of everything described above

###### Teaching activities

- 36-hours of lectures
- 24-hours of tutorials

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- 2 x 1,000-word coursework exercises (33% of final mark, each)
- a 1,000-word coursework exercise (34% of final mark)

###### What you'll do

You'll learn about data envelopment analysis and decision analysis, explore realistic case studies, and work toward optimal solutions for computationally difficult problems.

To choose this module, you need to take the *Statistical Theory and Methods I* module in year 1.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Use computer software to formulate and solve linear, integer programming models
- Formulate data envelopment analysis models
- Formulate and solve multiple decision analysis models
- Understand and use the discrete-event simulation process
- Interpret and report on the results of solutions of your models and processes

###### Teaching activities

- 29 hours of lectures
- 12 x 30-minute tutorials
- 13 hours of practical classes and workshops
- 3 x 1-hour lectures

###### Independent study time

We recommend you spend at least 149 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 2,000-word coursework exercise (50% of final mark)
- a 90-minute written exam (50% of final mark)

###### What you'll do

You'll focus on equity options and portfolio construction, exploring no-arbitrage pricing, the Black-Scholes partial differential equation, and hedging. To choose this module, you need to take the Calculus II and Mathematics for Finance modules in year 2 or an equivalent module covering basic interest rate structures and elementary stochastic processes.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Define and distinguish between various types of derivative contracts, deduce their future payoffs and analyse investment portfolios created from them
- Prove standard relations (parity) between the prices of different contracts under the assumption of fairness (no-arbitrage)
- Derive the famous Black-Scholes partial differential equation and learn how to solve it for various asset types
- Use stochastic processes to price options using risk-neutral valuation via change of measure and expectation
- Perform partial differential equation changes of variables and other solution methods for certain exotic options
- Put theory into practice by implementing numerical schemes on the computer

###### Teaching activities

- 11 x 1-hour tutorials
- 11 x 3-hour lectures
- 11 hours of practical classes and workshops
- 5 hours of guided independent study

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- a 1,500-word coursework exercise (40% of final mark)
- a 2-hour written exam (60% of final mark)

###### What you'll do

To choose this module, Physics students need to take the Mathematical Physics (level 5) and Introduction to Modern Physics and Astrophysics (level 5) modules.

To take this module, Maths students need to take the Applied Mathematics (level 5) module.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Analyse the 4-dimensional spacetime formulation of Special Relativity
- Carry out basic calculations in tensor algebra and calculus, and apply these to physical problems
- Apply Einstein field equations to the calculation of the simplest exact and approximate solutions for relativistic stars and black holes and in cosmology, as well as in the weak field regime and for gravitational waves
- Analyse a problem and associate it with the physical and mathematical principle of General Relativity
- Apply the specific mathematical techniques of General Relativity to solve exercises and problems, conceptualising and generalising from previously seen problems
- Discuss the use of physical and mathematical principles and hypotheses in the solution of exercises and problems

###### Teaching activities

24 x 2-hour lectures

###### Independent study time

We recommend you spend at least 152 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- 3 x written assignments including essays (each worth 20% of the final mark)
- a 2-hour written exam (40% of final mark)

###### What you'll do

You'll consider the physics of stars, black holes and galaxies, and their formation mechanisms. To choose this module, you need to take the Mathematical Physics, and Introduction to Modern Physics and Astrophysics module.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Analyse fundamental physical processes in astrophysics, and apply them to the physics of stars, black holes and galaxies in multiple contexts
- Apply the physics of gravitational collapse to solve problems related to the formation of stars and galaxies, and compact objects
- Demonstrate your understanding of fundamental nuclear reactions and energetic balance, and evaluate the energetics of stars and galaxies
- Demonstrate your understanding of the quest for dark matter in galaxy formation and evolution and evaluate the observational evidence

###### Teaching activities

- 24 x 2-hour lectures

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- a 2-hour written exam (100% of final mark)

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Understand the numerical solution of systems of linear and nonlinear equations
- Understand the numerical solution of differential equations
- Fit mathematical models, including differential equations, to data
- Estimate model parameters, and select models, using Bayesian methods
- Implement methods and visualize data using R or Python

###### Teaching activities

- 44 hours of lectures
- 5 x 1-hour tutorials
- 17 hours of practical classes and workshops

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- a 45-minute test (25% of final mark)
- a 1,500-word coursework assignment (25% of final mark)
- a 90-minute exam (50% of final mark)

###### What you'll do

You'll produce projects that work toward solving open-ended problems, and present your work to other students.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Appraise and compare relevant journal articles and research papers
- Critically evaluate theoretical approaches to specific problems
- Apply current mathematical software to advanced numerical techniques
- Independently research a mathematical topic
- Communicate information and arguments effectively

###### Teaching activities

- 23 x 2-hour lectures

###### Independent study time

We recommend you spend at least 154 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- 3 x 1,000-word coursework exercises (30% of final mark, each)
- a 10-minute oral assessment and presentation (10% of final mark)

###### What you'll do

You'll learn about game theory and its application in logistics, network flow, revenue and inventory management, and scheduling. To choose this module you need to show a general knowledge of Operational Research techniques.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Design and solve game theory models and study their efficiency in logistics
- Formulate and solve network flow and revenue management problems
- Formulate and solve inventory management, planning and scheduling models

###### Teaching activities

- 16 x 2-hour lectures
- 12 x 1-hour tutorials

###### Independent study time

We recommend you spend at least 154 hours studying independently. This is around 9.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 1-hour exam (30% of final mark)
- a 2-hour exam (70% of final mark)

###### What you'll do

You'll explore advanced regression modelling, modern statistical learning methods, the use of open source statistical tools, and forecasting methodologies. To choose this module, you need basic knowledge of probability, calculus and linear algebra.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Apply statistical learning techniques to business problems, and interpret your results
- Use Python and/or R language to apply statistical learning techniques
- Demonstrate understanding of the bias variance trade-off and cross validation
- Fit and test general linear models to numerical and categorical data
- Fit a variety of predictive models to real world data
- Demonstrate understanding of advanced techniques such as regularisation, nonlinear models and clustering

###### Teaching activities

Scheduled Activities (Hours)

- 24 x 2-hour lectures
- 24 hours of practical classes and workshops

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- a set of practical coursework problems (40% of final mark)
- a 90-minute written exam (60% of final mark)

###### What you'll do

You'll explore multiple procedures for data analysis, use the statistical language and software environment R to model data, and examine the strengths and weaknesses of various study designs. To choose this module, you need to take the Statistical Theory and Methods I module in year 1.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Formulate and employ statistical methods commonly used in the study of epidemiology
- Construct lifetables and compare survival patterns in population subgroups
- Conceptualize the basic principles underpinning the design and analysis of clinical trials
- Employ a variety of multivariate techniques.
- Formulate the principles relating to questionnaire design and validation.
- Use R language to apply the learnt statistical techniques

###### Teaching activities

- 44-hours of lectures
- 10-hours of practical classes and workshops

###### Independent study time

We recommend you spend at least 150 hours studying independently. This is around 9 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a coursework exercise (40% of final mark) - a set of exercises to solve partly using R
- a 2-hour exam (60% of final mark)

###### What you'll do

You'll apply these to subjects such as earthquakes, disease spread, financial markets or population dynamics, and demonstrate your understanding of the wider applications of mathematics.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Apply distributions of random discrete and continuous random variables
- Determine the probability of the extinction of branching processes
- Solve the gambler's ruin problem
- Solve partial differential equations that arise in birth-death processes
- Apply appropriate techniques to analyse continuous time stochastic processes

###### Teaching activities

- 17 x 2-hour of lectures
- 12 x 1-hour tutorials

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- a 3-hour written exam (100% of final mark)

###### What you'll do

Over ten half-days, you'll be mentored by a maths teacher as you gain experience of teaching mathematics, leading special projects and offering classroom support. To choose this module, you need to show you know the fundamental concepts of basic probability, calculus and linear algebra.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Demonstrate your understanding of teaching mathematics, and of educational theories and debates
- Work in a challenging and unpredictable working environment
- Communicate difficult principles or concepts, whether you're speaking one-to-one or to an audience
- Reflect on stereotypes of mathematics and mathematicians, and how to combat them

###### Teaching activities

- 9 x 2-hour practical classes and workshops
- 20 hours of placement

###### Independent study time

###### Assessment

On this module, you'll be assessed through:

- a set coursework exercise (100% of final mark)

#### Core modules

###### What you'll do

You'll present and defend your research via written dissertation and oral presentation, followed by a question and answer session.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Use best practice when conducting academic research, including conducting, documenting and presenting research, as well as soft skills such as good time management.
- Understand ethical expectations when conducting research, such as avoiding plagiarism and other forms of academic misconduct.
- Carry out original research in pure, applied, or industrial mathematics, using methods such as analytical or numerical calculations.
- Report and defend the results and conclusions of your research, verbally and in writing.

###### Teaching activities

- 24 hours of project supervision
- 24 hours of seminars

###### Independent study time

This is the only module you will be committed to in the second teaching block, so you can devote your whole time to independent study; roughly 30 hours per week.

###### Assessment

On this module, you'll be assessed through:

- A 10 minute presentation (5%)
- A 30 minute "viva" type assessment (15%)
- A 7,500-word dissertation (80% of final mark)

###### What you'll do

This module will develop key topics in algebra and geometry at a level appropriate to the final year of this integrated Master's course.

###### What you'll learn

It is expected the specific syllabus details may vary from one year to the next depending on the lecturer's expertise, however the following learning outcomes are indicative:

- Calculate the Gauss curvature of a 2-dimensional manifold
- Generate and solve in special cases the geodesic equations
- Demonstrate an understanding of, and apply in specific cases, the Gauss-Bonnet theorem
- Demonstrate an understanding of, and apply in specific cases, the Poincaré-Hopf index theorem

###### Teaching activities

- 44-hours of lectures

###### Independent study time

We recommend you spend at least 156 hours studying independently. This is around 10 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- two, 1,500-word coursework reports (each worth 50% of the final mark)

###### What you'll do

Modern analysis is a central branch of mathematics with origins going back to the beginning of the 20th century. It is the mathematical basis of many areas of pure and applied mathematics, from differential equations to quantum mechanics.

We'll cover both linear algebra and topology at a fundamental level with a strong emphasis on infinite dimensional linear spaces. Differential equations arise in various applications but this module will focus on the methods used to solve them rather than the context. However, we will then apply the methods to specific scenarios with particular emphasis on the research that takes place within the department.

The aim of this module is to introduce the required machinery that leads to the theory of Hilbert spaces, and will approach the topic from a final year integrated Master's level.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Develop the theory of modern analysis and recognise important examples relevant in practice
- Express advanced integration and differentiation problems in the language of modern analysis
- Use the theory of modern analysis to analyse and study solutions of integration and differentiation problems
- Use the theory of modern analysis to perform sensitivity analysis of solutions

###### Teaching activities

- 44 hours of lectures

###### Independent study time

We recommend you spend at least 156 hours studying independently. This is around 10 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 1,500-word coursework report (30% of final mark)
- a 2-hour exam (70% of final mark)

#### Optional modules

###### What you'll do

This module is designed to give you an applied knowledge of significant data and text analytics methods.

You'll get hands-on experience using data and text mining toolkits and learn how data mining, as a tool, can be used for a range of applications.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Demonstrate a comprehensive understanding of current advanced methods and techniques in data and text analytics
- Design and implement data mining based applications to solve real-world problems
- Critically analyse and evaluate the performance of different data mining techniques for text analysis, and analyse and interpret the data mining results

###### Teaching activities

- 11-hours of lab time
- 11-hours of timetabled lectures

###### Independent study time

We recommend you spend at least 178 hours studying independently. This is around 11 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 3,000-word coursework report (100% of the final mark)

###### What you'll do

We'll study the applications of quantum field theory in curved spacetime, such as black hole evaporation, inflationary fluctuations, and the cosmological constant problem.

The module will encourage you to develop a critical and reflective knowledge and understanding of the subject, independent thinking, analytical and creative problem-solving.

###### What you'll learn

When you complete this module successfully, you'll be able to:

- Perform basic calculations of particle production using quantum field theory in curved space-time
- Discuss the thermodynamics of black holes and why they evaporate
- Perform basic calculations of scalar field dynamics driving inflation in the very early universe and derive primordial power spectra from inflation

###### Teaching activities

- 28-hours of lectures (pre-recorded)
- 22-hours of tutorials (2-hours per week, live)

###### Independent study time

We recommend you spend at least 150 hours studying independently. This is around 9.5 hours a week over the duration of the module.

###### Assessment

On this module, you'll be assessed through:

- a 1500 word coursework report (40% of final mark)
- a 2,000 word coursework report (60% of final mark)

We use the best and most current research and professional practice alongside feedback from our students to make sure course content is relevant to your future career or further studies.

Therefore, some course content may change over time to reflect changes in the discipline or industry and some optional modules may not run every year. If a module doesn’t run, we’ll let you know as soon as possible and help you choose an alternative module.

Get an introduction to mathematics at Portsmouth from Professor Daniel Thomas, Head of the School of Mathematics and Physics, and colleagues. Explore our facilities and equipment, and discover more about your prospects as a maths graduate.

**Daniel Thomas: **What excites me most about university education is that it is right at the interface between research and teaching. Newly acquired skills and knowledge get passed on to the next generation directly, to you.

The University of Portsmouth is providing mathematics staff and students just with the right space in the right environment to do exactly that.

Our research, as well as our teaching, are concentrated in this building in the Lion Gate Building.

We will now move on to our lecture theatre where Dr. Marianna Cerasuolo will tell us more about the facilities we have in this building.

**Marianna Cerasuolo: **In the first year, all of our students take compulsory modules in core subjects which are necessary to become very good mathematicians. In the second and third year, they have a wide variety of options they can choose.

In particular, they can decide either to stay on straight mathematics, so what we call the BSc Mathematics, or to take different, more specialised paths. For example, mathematics for finance and management or mathematics with statistics.

We have also other types of options like astrophysics or cosmology and general relativity, or they can decide to do operational research and logistics. Actually, we have a very strong research group who works on this particular subject.

So since the first year, our students learn that mathematics in its entirety has lots of real life applications. They also learn to work together as a team, and that makes them very valuable for companies once they finish their degree with us.

**Daniel Thomas: **The nice thing about our school is that the staff offices are right next to the lecture theatre and the computer lab. We have an open door policy because we want to support your learning the best we can. You can pop in our staff office any time during the day and ask our staff about the lectures or about the course material, any questions about mathematics that you may have.

We will now move on to our computer lab where Dr. James Burridge, reader in statistical physics, will tell you about the facilities we have.

**James Burridge: **In my research, I use tools of probability, physics, and machine learning to build models of language, and to understand what we can learn about people from the way they speak. My models use many different kinds of data, including detailed geographical information, large scale linguistic surveys and audio.

Using big data to model the real world, identifying patterns and making predictions are commercially valuable skills. Some people say they are driving a fourth industrial revolution. Here at Portsmouth, we will teach you the mathematics of modelling and prediction, which can be applied to problems in biology, health care and a whole range of commercial applications.

Using computer labs like this one, we will teach you state of the art machine learning techniques to solve real world problems. These can include recognising emotions from speech data, predicting and classifying images and modelling behaviour.

**Daniel Thomas: **The Technology Learning Centre at the ground floor of Lion Gate Building is a perfect space for students to study, to learn, to meet or just to hang out. We also use the space to offer our daily tutorials, the maths cafe, where our mathematics staff are providing tutorials to our mathematics students, where you can ask any questions about mathematics.

We look forward to welcoming you at the University of Portsmouth to discover the beauty of mathematics with us.

### Teaching

Teaching methods on this course include:

- Lectures
- Seminars
- Independent study

You can access all teaching resources on Moodle, our virtual learning environment, from anywhere with a web connection.

For more about the teaching activities for specific modules, see the module list above.

Teachers are always willing to help and make the best effort to be in contact with you. Be it via email or even in person. There's even the Maths Café which provides help every day.

### How you're assessed

You’ll be assessed through:

- Written exams
- Practical exams
- Coursework
- In-class tests

You’ll be able to test your skills and knowledge informally before you do assessments that count towards your final mark.

You can get feedback on all practice and formal assessments so you can improve in the future.

The way you’re assessed will depend on the modules you select throughout your course. Here's an example from a previous year of how students on this course were typically assessed:

**Year 1 students**: 65% by written exams and 35% by coursework**Year 2 students**: 58% by written exams and 42% by coursework**Year 3 students**: 68% by written exams, 2% by practical exams and 30% by coursework**Year 4 students (MMath only)**: 100% by coursework

' I have had a really positive relationship with my project leader, Dr Maria Pickett. She has helped me tremendously over the last couple of years and has offered me lots of individual support.'

**Mark Howarth, BSc (Hons) Mathematics graduate**

## How you'll spend your time

One of the main differences between school or college and university is how much control you have over your learning.

At university, as well as spending time in timetabled teaching activities such as lectures, seminars and tutorials, you’ll do lots of independent study with support from our staff when you need it.

### A typical week

We recommend you spend at least 35 hours a week studying for your Mathematics degree. You’ll be in timetabled teaching activities such as lectures, practical classes and workshops for about 19 hours a week. The rest of the time you’ll do independent study such as research, reading, coursework and project work, alone or in a group with others from your course. You'll probably do more independent study and have less scheduled teaching in years 2 and 3 (and year 4 if you do the MMath), but this depends on which modules you choose.

Most timetabled teaching takes place during the day, Monday to Friday. Optional field trips may involve evening and weekend teaching or events. There’s usually no teaching on Wednesday afternoons.

### Term dates

The academic year runs from September to June. There are breaks at Christmas and Easter.

## Supporting your learning

The amount of timetabled teaching you'll get on your degree might be less than what you're used to at school or college, but you'll also get support via video, phone and face-to-face from teaching and support staff to enhance your learning experience and help you succeed. You can build your personalised network of support from the following people and services:

#### Types of support

Your personal tutor helps you make the transition to independent study and gives you academic and personal support throughout your time at university.

As well as regular scheduled meetings with your personal tutor, they're also available at set times during the week if you want to chat with them about anything that can't wait until your next meeting.

You'll have help from a team of faculty learning support tutors. They can help you improve and develop your academic skills and support you in any area of your study in one-on-one and group sessions.

They can help you:

- master the mathematics skills you need to excel on your course
- understand engineering principles and how to apply them in any engineering discipline
- solve computing problems relevant to your course
- develop your knowledge of computer programming concepts and methods relevant to your course
- understand and use assignment feedback

All our labs and practical spaces are staffed by qualified laboratory support staff. They’ll support you in scheduled lab sessions and can give you one-to-one help when you do practical research projects.

As well as support from faculty staff and your personal tutor, you can use the University’s Academic Skills Unit (ASK).

ASK provides one-to-one support in areas such as:

- academic writing
- note taking
- time management
- critical thinking
- presentation skills
- referencing
- working in groups
- revision, memory and exam techniques

If you have a disability or need extra support, the Additional Support and Disability Centre (ASDAC) will give you help, support and advice.

Our online Learning Well mini-course will help you plan for managing the challenges of learning and student life, so you can fulfil your potential and have a great student experience.

You can get personal, emotional and mental health support from our Student Wellbeing Service, in person and online. This includes 1-2-1 support as well as courses and workshops that help you better manage stress, anxiety or depression.

If you require extra support because of a disability or additional learning need our specialist team can help you.

They'll help you to:

- discuss and agree on reasonable adjustments
- liaise with other University services and facilities, such as the library
- access specialist study skills and strategies tutors, and assistive technology tutors, on a 1-to-1 basis or in groups
- liaise with external services

Library staff are available in person or by email, phone or online chat to help you make the most of the University’s library resources. You can also request one-to-one appointments and get support from a librarian who specialises in your subject area.

The library is open 24 hours a day, every day, in term time.

The Maths Cafe offers advice and assistance with mathematical skills in a friendly, informal environment. You can come to our daily drop-in sessions, develop your mathematics skills at a workshop or use our online resources.

If English isn't your first language, you can do one of our English language courses to improve your written and spoken English language skills before starting your degree. Once you're here, you can take part in our free In-Sessional English (ISE) programme to improve your English further.

## Course costs and funding

### Tuition fees (2022 start)

**UK/Channel Islands and Isle of Man students**– £9,250 per year (may be subject to annual increase)**EU students**– £9,250 a year (including Transition Scholarship – may be subject to annual increase)**International students**– £17,000 per year (subject to annual increase)

#### Funding your studies

Find out how to fund your studies, including the scholarships and bursaries you could get. You can also find more about tuition fees and living costs, including what your tuition fees cover.

Applying from outside the UK? Find out about funding options for international students.

### Additional course costs

These course-related costs aren’t included in the tuition fees. So you’ll need to budget for them when you plan your spending.

### Additional costs

Our accommodation section shows your accommodation options and highlights how much it costs to live in Portsmouth.

You’ll study up to 6 modules a year. You may have to read several recommended books or textbooks for each module.

You can borrow most of these from the Library. If you buy these, they may cost up to £60 each.

We recommend that you budget £75 a year for photocopying, memory sticks, DVDs and CDs, printing charges, binding and specialist printing.

If your final year includes a major project, there could be cost for transport or accommodation related to your research activities. The amount will depend on the project you choose.

## Apply

### How to apply

To start this course in 2021, apply through UCAS. You'll need:

- the UCAS course code – G100 (BSc) or GG10 (MMath)
- our institution code – P80

If you'd prefer to apply directly, use our online application form:

You can also sign up to an Open Day to:

- Tour our campus, facilities and halls of residence
- Speak with lecturers and chat with our students
- Get information about where to live, how to fund your studies and which clubs and societies to join

If you're new to the application process, read our guide on applying for an undergraduate course.

### How to apply from outside the UK

See the 'How to apply' section above for details of how to apply. You can also get an agent to help with your application. Check your country page for details of agents in your region.

To find out what to include in your application, head to the how to apply page of our international students section.

If you don't meet the English language requirements for this course yet, you can achieve the level you need by successfully completing a pre-sessional English programme before you start your course.

#### Admissions terms and conditions

When you accept an offer to study at the University of Portsmouth, you also agree to abide by our Student Contract (which includes the University's relevant policies, rules and regulations). You should read and consider these before you apply.

- Subject area
- Mathematics and Physics

**Discover Uni course data – BSc**

**Discover Uni course data – MMath**