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Group theory is one of the great simplifying and unifying ideas in modern mathematics. It was introduced in order to understand the solutions to polynomial equations, but only in the last one
hundred years has its full significance, as a mathematical formulation of symmetry, been understood. It plays a role in our understanding of fundamental particles, the structure of crystal lattices and the geometry of molecules.

In this module we build on material from Linear Algebra II and will begin by revising the simple axioms satisfied by groups and begin to develop basic group theory by reference to some elementary
examples. We will analyse the structure of 'small' finite groups, and examine examples arising as groups of permutations of a set, symmetries of regular polygons and regular solids, and groups of
matrices. We will develop the notions of homomorphism, normal subgroups and quotient groups and study the First Isomorphism Theorem and its application.

We will also examine how the notion of a permutation group can be generalized to that of a group action on a set, and will show how to use this in certain counting problems arising in combinatorics. We will also see how to use group actions to prove strong results about the structure of finite groups. We shall study Sylow’s Theorems and some of their applications.

Group theory is one of the great simplifying and unifying ideas in modern mathematics. It was introduced in order to understand the solutions to polynomial equations, but only in the last one
hundred years has its full significance, as a mathematical formulation of symmetry, been understood. It plays a role in our understanding of fundamental particles, the structure of crystal lattices and the geometry of molecules.

In this module we build on material from Linear Algebra II and will begin by revising the simple axioms satisfied by groups and begin to develop basic group theory by reference to some elementary
examples. We will analyse the structure of 'small' finite groups, and examine examples arising as groups of permutations of a set, symmetries of regular polygons and regular solids, and groups of
matrices. We will develop the notions of homomorphism, normal subgroups and quotient groups and study the First Isomorphism Theorem and its application.

We will also examine how the notion of a permutation group can be generalized to that of a group action on a set, and will show how to use this in certain counting problems arising in combinatorics. We will also see how to use group actions to prove strong results about the structure of finite groups. We shall study Sylow’s Theorems and some of their applications.

Group theory is one of the great simplifying and unifying ideas in modern mathematics. It was introduced in order to understand the solutions to polynomial equations, but only in the last one
hundred years has its full significance, as a mathematical formulation of symmetry, been understood. It plays a role in our understanding of fundamental particles, the structure of crystal lattices and the geometry of molecules.

In this module we build on material from Linear Algebra II and will begin by revising the simple axioms satisfied by groups and begin to develop basic group theory by reference to some elementary
examples. We will analyse the structure of 'small' finite groups, and examine examples arising as groups of permutations of a set, symmetries of regular polygons and regular solids, and groups of
matrices. We will develop the notions of homomorphism, normal subgroups and quotient groups and study the First Isomorphism Theorem and its application.

We will also examine how the notion of a permutation group can be generalized to that of a group action on a set, and will show how to use this in certain counting problems arising in combinatorics. We will also see how to use group actions to prove strong results about the structure of finite groups. We shall study Sylow’s Theorems and some of their applications.

This module will be first offered in the 2019/20 academic year.

This module will provide a basic grounding in navigation guidance and control with particular aspects on the processing of the signals involved and overall system integration.

This module will be first offered in the 2019/20 academic year.

This module will provide a basic grounding in navigation guidance and control with particular aspects on the processing of the signals involved and overall system integration.

Hacking for MoD (H4MoD) is an interdisciplinary and entrepreneurial module that provides you with the opportunity to learn from the Ministry of Defence (MoD) and Intelligence Community (IC) to better address the nation’s emerging threats and security challenges. The delivery of the module is supported by the Common Mission Project (The Common Mission Project UK), a charity that works in partnership with the UK Government. This is a practical and applied module with students working in teams to engage directly with complex, real world problems proposed by the UK government sponsors (problem owners sourced by the Common Mission Project). H4MoD covers policy, economics, technology, national security, and any area required to address the problem posed by sponsors.

You will be assigned to a team and provided with a range of relevant methodological tools and techniques to solve a problem assigned to you. As you progress through the module, you along with your team will be required to identify and validate customer needs. You will be required to continually build iterative prototypes to demonstrate that you have understood the problem and provide appropriate solutions. Teams take a hands-on approach, requiring close engagement with actual military, the Ministry of Defence and other government agency end-users, using their real-world challenges.

The goal is to give you a framework to test solution hypotheses using a start-up model with all the real-world pressures and demands in an early-stage start-up, recognising that you are working within the constraints of a classroom and a limited amount of time. This module is designed to give the experience of working as a team and turn an idea into a solution for real-world problems faced by the Ministry of Defence and Intelligence Community.

This module aims to simulate start-ups and entrepreneurship in the real world, which includes the need to take conceptually-sound decisions amidst uncertainty, challenging deadlines, and often conflicting input.
The module is based on the Hacking for DefenceTM (H4D) programme initially developed at Stanford University (http://hacking4defense.stanford.edu) and is an education initiative sponsored by the U.S. Defence Accelerator, and National Security Innovation Network (NSIN). In the UK, Hacking for Ministry of Defence (H4MoD) is funded by the Ministry of Defence.

Note for students considering taking this module:

This module requires a significant time commitment which includes working with a government sponsor for your assigned problem and gathering primary data on it. In addition to classroom time and engaging in group discussions, the module’s demands include engagement with the lecture and other resources, course reading and an average of 10 interviews per week per student team. You are required to be available for a session of interview training as well as any team meetings.

The aims and learning objectives of this module are focussed on developing a set of skills that you will be able to apply in a variety of professions. The problems assigned to students are curated by the Hacking for MoD module team to ensure that they provide you with the scope needed for the module, and that they match the student skills.

The number of students on this module is limited. Once you sign up for the module, you are making a commitment to all stakeholders (including the government agencies that are sponsoring the problems for the module as well as your fellow team members) involved in making this module a success. Dropping out is unfair to your fellow students who did not get into the module and also appears unprofessional to the government sponsors involved.

It seems clear that people’s lives can go well or badly. But what is it for one’s life to go well? Does it consist in feeling good more often than feeling bad? Or getting most of what you want? Or does it consist in achievement, friendship, knowledge and a variety of other disparate things? It is highly tempting to think that your happiness matters for how well your life goes. But this raises further questions: what is happiness? Can it be measured? Is it a sensible goal for public policy? This module aims to explore questions such as these.

It seems clear that people’s lives can go well or badly. But what is it for one’s life to go well? Does it consist in feeling good more often than feeling bad? Or getting most of what you want? Or does it consist in achievement, friendship, knowledge and a variety of other disparate things? It is highly tempting to think that your happiness matters for how well your life goes. But this raises further questions: what is happiness? Can it be measured? Is it a sensible goal for public policy? This module aims to explore questions such as these.

It seems clear that people’s lives can go well or badly. But what is it for one’s life to go well? Does it consist in feeling good more often than feeling bad? Or getting most of what you want? Or does it consist in achievement, friendship, knowledge and a variety of other disparate things? It is highly tempting to think that your happiness matters for how well your life goes. But this raises further questions: what is happiness? Can it be measured? Is it a sensible goal for public policy? This module aims to explore questions such as these.

It seems clear that people’s lives can go well or badly. But what is it for one’s life to go well? Does it consist in feeling good more often than feeling bad? Or getting most of what you want? Or does it consist in achievement, friendship, knowledge and a variety of other disparate things? It is highly tempting to think that your happiness matters for how well your life goes. But this raises further questions: what is happiness? Can it be measured? Is it a sensible goal for public policy? This module aims to explore questions such as these.