Module finder

This module is designed for students in their third year and aims to introduce the basic concepts and techniques of Galois theory, building on earlier work at level 2. As such, it will provide an introduction to core concepts in rings, fields, polynomials and certain aspects of group theory.

Galois theory arose out of attempts to generalize to polynomials of higher degree the well-known formula for the roots of a quadratic polynomial. This turns out to be possible for cubic and quartic polynomials but impossible for polynomials of degree five or more. This impossibility result is one of the main applications of Galois theory. Further applications to be considered are ruler-and-compass constructions; for instance, we determine all natural numbers n for which the regular n-gon can be constructed.

Much of this beautiful and fascinating theory was discovered by the French mathematician and revolutionary Évariste Galois, shortly before he was killed in a duel in 1832, aged twenty. It has
considerably influenced the development of Algebra and is nowadays a basic tool also in Number Theory and (Algebraic) Geometry. For instance, it features prominently in the famous proof of Fermat's Last Theorem by Andrew Wiles in the 1990s.

The main theorem of Galois theory gives a correspondence between the intermediate fields of a finite extension L/K of fields on the one hand and the subgroups of the automorphism group G = Aut (L / K) on the other hand. In particular, this module will introduce the concepts of rings and fields including, for example, the notions of polynomial rings, ideals, quotient rings and homomorphisms, building on material from MATH2046 Algebra and Geometry. Some group theory is also assumed, such as normal subgroups, quotient groups, and familiarity with permutation groups. These topics are all covered in MATH2003 Group Theory, which is also a pre-requisite for this module.

On successful completion of the module the students should be able to:
• show familiarity with the concepts of ring and field, and their main algebraic properties;
• correctly use the terminology and underlying concepts of Galois theory in a problem-solving context;
• reproduce the proofs of its main theorems and apply the key ideas in similar arguments;
• calculate Galois groups in simple cases and to apply the group-theoretic information to deduce results about fields and polynomials.

One of the pre-requisites for MATH3078 and MATH6156

Games design and development is an increasingly important and sophisticated topic, that draws together many of the core aspects of Computer Science and Software Engineering. This course introduces students to the fundamentals of game design, gives them practical experience in developing games within an industry-leading contemporary games framework, and encourages students to consider the wider possibilities of digital entertainment through non-linear narratives and innovative gaming forms.

Games design and development is an increasingly important and sophisticated topic, that draws together many of the core aspects of Computer Science and Software Engineering. This course introduces students to the fundamentals of game design, gives them practical experience in developing games within an industry-leading contemporary games framework, and encourages students to consider the wider possibilities of digital entertainment through non-linear narratives and innovative gaming forms.

In the Game Mechanics module, you will delve into the concepts of game mechanics, exploring both mechanics as actions and mechanics as rules. This module combines theoretical understanding with practical application through various hands-on activities.

In the Game Mechanics module, you will delve into the concepts of game mechanics, exploring both mechanics as actions and mechanics as rules. This module combines theoretical understanding with practical application through various hands-on activities.

In the Game Pitching and Presenting module, you will take the work you are undertaking in the Game Project Proposal module and pitch and present your idea to your peers and staff at regular intervals during the various stages of development. The structure of these presentations and pitches will be determined by staff and will follow a pattern that allows you to use this process to inform and support the creation of a strong project proposal. By the end of the module, you will have a series of presentations and materials documenting the process of idea generation and refinement, closely linked to the work within the Games Project Proposal module.

In the Game Pitching and Presenting module, you will take the work you are undertaking in the Game Project Proposal module and pitch and present your idea to your peers and staff at regular intervals during the various stages of development. The structure of these presentations and pitches will be determined by staff and will follow a pattern that allows you to use this process to inform and support the creation of a strong project proposal. By the end of the module, you will have a series of presentations and materials documenting the process of idea generation and refinement, closely linked to the work within the Games Project Proposal module.

In the Games Project Proposal module, you will work to develop a unique game idea for the module Major Project – Unique Impact Games. The game proposal you develop will start as an individual effort, but you will have the option to form teams around each proposal, encouraged to do so organically. The module will include workshops on how to form a proposal around the concept of a unique impact game, with each workshop building on previous techniques to produce a unique game idea that you will take into production as a solo designer/developer or in your team. The proposed game must be a complete game experience, not just a technical demo, and should have a unique experience and concept that can be conveyed in a finished game. You will be encouraged to think big, lean on your passions, developmental and current needs, and create a project you will make, market, and release in the module Major Project – Unique Impact Games.

In the Games Project Proposal module, you will work to develop a unique game idea for the module Major Project – Unique Impact Games. The game proposal you develop will start as an individual effort, but you will have the option to form teams around each proposal, encouraged to do so organically. The module will include workshops on how to form a proposal around the concept of a unique impact game, with each workshop building on previous techniques to produce a unique game idea that you will take into production as a solo designer/developer or in your team. The proposed game must be a complete game experience, not just a technical demo, and should have a unique experience and concept that can be conveyed in a finished game. You will be encouraged to think big, lean on your passions, developmental and current needs, and create a project you will make, market, and release in the module Major Project – Unique Impact Games.

In the Game Worlds module, you will embark on a series of creative projects focused on generating and refining ideas for imaginative worlds and settings. This module combines field trips, workshops, and various design and art methodologies to help you create compelling game worlds and associated materials.