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Graph theory was born in 1736 with Euler’s solution of the Königsberg bridge problem, which asked whether it was possible to plan a walk over the seven bridges of the town without re-tracing one’s steps. Euler realised that the problem could be rephrased in terms of a graph whose vertices corresponded to the four regions of the city, and whose edges corresponded to the seven bridges each joining a pair of the regions.

With this rephrasing, we can view this problem of walking through Königsberg as a (significantly more tractable) problem of navigation in the corresponding diagram (or graph), which is straightforward to resolve.

Graph theory is a stand-alone branch of mathematics that has links across the mathematical spectrum, from parts of pure mathematics such as abstract algebra and topology, to parts of mathematics focusing on applications such as operational research and computation, through to other areas of science such as chemistry, biology and electronics.

In this module, we introduce the basic concepts of graph theory, focusing primarily on finite graphs. These include numerical invariants of graphs and methods for calculating them; how to navigate through graphs (including the method that lies behind the resolution of the Königsberg problem discussed above); vertex and edge colourings of graphs and other numerical invariants of graphs; the conditions under which a graph is planar; and the introductory elements of the theory of random graphs.

Graph theory was born in 1736 with Euler’s solution of the Königsberg bridge problem, which asked whether it was possible to plan a walk over the seven bridges of the town without re-tracing one’s steps. Euler realised that the problem could be rephrased in terms of a graph whose vertices corresponded to the four regions of the city, and whose edges corresponded to the seven bridges each joining a pair of the regions.

With this rephrasing, we can view this problem of walking through Königsberg as a (significantly more tractable) problem of navigation in the corresponding diagram (or graph), which is straightforward to resolve.

Graph theory is a stand-alone branch of mathematics that has links across the mathematical spectrum, from parts of pure mathematics such as abstract algebra and topology, to parts of mathematics focusing on applications such as operational research and computation, through to other areas of science such as chemistry, biology and electronics.

In this module, we introduce the basic concepts of graph theory, focusing primarily on finite graphs. These include numerical invariants of graphs and methods for calculating them; how to navigate through graphs (including the method that lies behind the resolution of the Königsberg problem discussed above); vertex and edge colourings of graphs and other numerical invariants of graphs; the conditions under which a graph is planar; and the introductory elements of the theory of random graphs.

This module is designed for MMath and MPhys students in their fourth year, and builds directly upon MATH3006 Relativity, Blackholes and Cosmology.

Gravitational waves are tiny ripples in space-time, first predicted by Einstein himself in 1916. These "wrinkles in the spacetime curvature" carry information from the most violent events in the Universe - from colliding black holes, collapsing stars, to the birth of the Universe itself. Exactly one hundred years after Einstein’s prediction, after many decades of searching, scientists announced that they had finally detected these waves, from two black holes colliding at a distance of over one billion light years from Earth.

This module aims to introduce you to the many issues involved in understanding gravitational waves and their generation from astrophysical sources. It will give you an insight into one of the hottest topics in modern research, and an insight into what has been described as the “greatest scientific achievement of the century.”

This module is designed for MMath and MPhys students in their fourth year, and builds directly upon MATH3006 Relativity, Blackholes and Cosmology.

Gravitational waves are tiny ripples in space-time, first predicted by Einstein himself in 1916. These "wrinkles in the spacetime curvature" carry information from the most violent events in the Universe - from colliding black holes, collapsing stars, to the birth of the Universe itself. Exactly one hundred years after Einstein’s prediction, after many decades of searching, scientists announced that they had finally detected these waves, from two black holes colliding at a distance of over one billion light years from Earth.

This module aims to introduce you to the many issues involved in understanding gravitational waves and their generation from astrophysical sources. It will give you an insight into one of the hottest topics in modern research, and an insight into what has been described as the “greatest scientific achievement of the century.”

This module is designed for MMath and MPhys students in their fourth year, and builds directly upon MATH3006 Relativity, Blackholes and Cosmology.

Gravitational waves are tiny ripples in space-time, first predicted by Einstein himself in 1916. These "wrinkles in the spacetime curvature" carry information from the most violent events in the Universe - from colliding black holes, collapsing stars, to the birth of the Universe itself. Exactly one hundred years after Einstein’s prediction, after many decades of searching, scientists announced that they had finally detected these waves, from two black holes colliding at a distance of over one billion light years from Earth.

This module aims to introduce you to the many issues involved in understanding gravitational waves and their generation from astrophysical sources. It will give you an insight into one of the hottest topics in modern research, and an insight into what has been described as the “greatest scientific achievement of the century.”

This module is designed for MMath and MPhys students in their fourth year, and builds directly upon MATH3006 Relativity, Blackholes and Cosmology.

Gravitational waves are tiny ripples in space-time, first predicted by Einstein himself in 1916. These "wrinkles in the spacetime curvature" carry information from the most violent events in the Universe - from colliding black holes, collapsing stars, to the birth of the Universe itself. Exactly one hundred years after Einstein’s prediction, after many decades of searching, scientists announced that they had finally detected these waves, from two black holes colliding at a distance of over one billion light years from Earth.

This module aims to introduce you to the many issues involved in understanding gravitational waves and their generation from astrophysical sources. It will give you an insight into one of the hottest topics in modern research, and an insight into what has been described as the “greatest scientific achievement of the century.”

Many writers have penned essays about fiction and memoir: E.M. Forster, Virginia Woolf, Henry James, Edith Wharton, Italo Calvino, Vladimir Nabokov, Milan Kundera, A.L. Kennedy, A.S. Byatt, to name just a famous few. Indeed, it seems essential at some point for authors to write critically about creative writing. What makes a novel, memoir, or story work?

Interestingly, writers don’t necessarily put pen to paper about their own work. Instead, they write about the authors who influenced them, both those from decades before and those working contemporaneously. Sometimes this results in critical essays that examine the craft and themes of a classic writer’s work, giving us knowledge of how fiction works in general. Other times, writers respond to influences with a new piece of creative writing.

T.S. Eliot is paraphrased as saying: “Good Writers Borrow, Great Writers Steal”. In this module, we will look at how writers steal: how they draw upon other writers for knowledge about craft and for inspiration. We will look at two pairings of creative work, seeing how a contemporary writer responded creatively to a classic book. We will also look at related critical essays by writers about those works. In doing so, we will go backward to examine a writer’s influences; inward to a writer’s own writing; and forward to the writers they have influenced, analysing as we do so ideas of theme, structure, inspirations, and the craft of character, place, and narrative.

Many writers have penned essays about fiction and memoir: E.M. Forster, Virginia Woolf, Henry James, Edith Wharton, Italo Calvino, Vladimir Nabokov, Milan Kundera, A.L. Kennedy, A.S. Byatt, to name just a famous few. Indeed, it seems essential at some point for authors to write critically about creative writing. What makes a novel, memoir, or story work?

Interestingly, writers don’t necessarily put pen to paper about their own work. Instead, they write about the authors who influenced them, both those from decades before and those working contemporaneously. Sometimes this results in critical essays that examine the craft and themes of a classic writer’s work, giving us knowledge of how fiction works in general. Other times, writers respond to influences with a new piece of creative writing.

T.S. Eliot is paraphrased as saying: “Good Writers Borrow, Great Writers Steal”. In this module, we will look at how writers steal: how they draw upon other writers for knowledge about craft and for inspiration. We will look at two pairings of creative work, seeing how a contemporary writer responded creatively to a classic book. We will also look at related critical essays by writers about those works. In doing so, we will go backward to examine a writer’s influences; inward to a writer’s own writing; and forward to the writers they have influenced, analysing as we do so ideas of theme, structure, inspirations, and the craft of character, place, and narrative.

This module covers recent developments in electronic devices that reduce energy consumption, generate power, or advance the distribution of power. Together these devices are playing an essential role in reducing our dependence on fossil fuels.

The module provides an introduction to both the fundamentals of energy generating electronic devices and the systems that can be implemented using such devices. The concepts will be explained in detail for photovoltaic devices but the analogy for thermo-electric devices is evident. The module covers the fundamental theoretical foundations , manufacturing and practical limitations. System integration with the grid is also introduced with key concepts such as smart grids, smart meters, microgrids and storage being covered in the course.

As part of this module, students will learn to use PC1D, a quasi-one-dimensional finite-element program for modelling semiconductor devices that is used frequently in university research groups and industrial R&D labs around the world for simulating photovoltaic devices.

This module covers recent developments in electronic devices that reduce energy consumption, generate power, or advance the distribution of power. Together these devices are playing an essential role in reducing our dependence on fossil fuels.

The module provides an introduction to both the fundamentals of energy generating electronic devices and the systems that can be implemented using such devices. The concepts will be explained in detail for photovoltaic devices but the analogy for thermo-electric devices is evident. The module covers the fundamental theoretical foundations , manufacturing and practical limitations. System integration with the grid is also introduced with key concepts such as smart grids, smart meters, microgrids and storage being covered in the course.

As part of this module, students will learn to use PC1D, a quasi-one-dimensional finite-element program for modelling semiconductor devices that is used frequently in university research groups and industrial R&D labs around the world for simulating photovoltaic devices.