Philosophy and Mathematics (BA)

The notion of limit and convergence are two key ideas on which rest most of modern Analysis. This module aims to present these notions building on the experience gained by students in first year Calculus module. The context of our study is: limits and co...

The 17th and 18th centuries, a period of great intellectual and social upheaval, saw the rise of Modern Philosophy. In continental Europe, the 'Rationalism' of Descartes, Spinoza and Leibniz argued for the capacity of reason to arrive at knowledge and und...

The theory and methods of Statistics play an important role in all walks of life, society, medicine and industry. They enable important understanding to be gained and informed decisions to be made, about a population by examining only a small random sampl...

Differential equations occupy a central role in mathematics because they allow us to describe a wide variety of real-world systems. The module will aim to stress the importance of both theory and applications of differential equations. The module begin...

You might watch a stunning film, hear a delightful song, enjoy a beautiful sunset, read a dreadful poem, attend an elegant dance, or see a garish building. Experiences like this can stimulate thoughts and feelings of great depth, and provide pleasure or d...

Epistemology is dedicated to questions about the nature and structure of knowledge and justified belief. Some central questions in epistemology include: - What is knowledge? Why is it valuable? - To gain knowledge from a reliable source, does one n...

Ethics of Global Poverty examines the duties of affluent people towards those living in poverty around the world. Among the questions we will examine are: What obligations do we have to help strangers in need? What bases might such obligations have? Are s...

This module involves the ethical evaluation of public policies. Note that it is not primarily concerned with how public policies are made and implemented, nor with non-ethical assessment of them, such as how effective they are in achieving their aims. The...

Over the last four hundred years progress in understanding the physical world (theoretical physics) has gone hand in hand with progress in the mathematical sciences, so much so that the terms applied mathematics and theoretical physics have come to be alm...

Geometry has grown out of efforts to understand the world around us, and has been a central part of mathematics from the ancient times to the present. Topology has been designed to describe, quantify, and compare shapes of complex objects. Together, geome...

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 for...

Among philosophers in the modern era, Immanuel Kant is widely acknowledged as the most important, original and influential. His challenging book, Critique of Pure Reason, asks what we can know about the nature of reality at the most fundamental level. Can...

Building on the intuitive understanding and calculation techniques from Linear Algebra I, this module introduces the concepts of vector spaces and linear maps in an abstract, axiomatic way. In particular, matrices are revisited as the representation of a ...

Ever since Aristotle, philosophers have been interested in developing formal systems of logic to refine our ability to distinguish valid from invalid arguments and to further our understanding of the nature of logic and validity. The aim of this module is...

We all make moral judgments and think about moral questions. For instance, you might think that torture is typically wrong but wonder whether it may sometimes be right. Whereas normative ethics tries to answer these questions, metaethics is concerned with...

Metaphysics is the study of what kinds of things there and what they are like in the most general terms. We have both a common sense picture of the world and a scientific picture of the world, and sometimes these two appear to conflict. Part of the job of...

Moral philosophy is concerned with questions of right and wrong, good and bad, virtue and vice. Such questions are familiar: can it be right to lie to someone to avoid hurting their feelings? Is it okay to favour my friends and family, or should I be impa...

Can there be a proof that God exists? Or might phenomena such as suffering serve to show that an omniscient, omnipotent and omnibenevolent being cannot exist? Such questions are central to the philosophy of religion; attempting to answer them leads us to ...

We build our world on scientific knowledge, in fact we stake our lives on it. Every time we board a train, send an email or take a medical drug we reaffirm our trust in the products of science. But what, if anything, gives science the authority it seems t...

Philosophy of mind explores questions about the nature of the mind and mental states – states such as perceptual experiences, beliefs, desires, and emotions. What is the mind? Is it an immaterial substance? Is it the brain? Is it something like a computer...

For all mathematics students, this project is compulsory. The module will consist of some discussion elements in semester 1 that will aid the development of The project typically entails a weekly visit to a supervisor who advises and assists the student i...

Students taking this module undertake research on a philosophical topic of their choice (subject to approval by the Department), and write a dissertation of 8,000 words on that topic.

Modelling fluid flow requires us first to extend vector calculus to include volumes that change with time. This will allow us to rephrase Newton’s second law of motion, that the force is equal to the time derivative of the linear momentum, in a way that ...

Partial Differential Equations (PDEs) occur frequently in many areas of mathematics. This module extends earlier work on PDEs by presenting a variety of more advanced solution techniques together with some of the underlying theory.

Philosophy flourished in classical India for well over a millennium, with figures in this tradition producing works that are on a par with those of figures in ancient Greece and late antique and medieval Europe. In fact, figures in classical India contri...

The aim of this module is to familiarise you with several important, but competing, theories of justice. Such theories give guidance on important questions of distributive justice (who ought to get what, when and why?), and provide, to varying degrees, gr...

We are all familiar with fictions from Romeo and Juliet to Jaws, from The Hobbit to Harry Potter. Despite this familiarity, the nature of fiction and of our engagement with it appears puzzling. On the one hand, fictional characters do not exist. On the ot...

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 ...

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 ...

This module is an introduction to functional analysis on Hilbert spaces. The subject of functional analysis builds on the linear algebra studied in the first year and the analysis studied in the second year. The module introduces the concept of Hilbert...

Many classes of problems are difficult to solve in their original domain. An integral transform maps the problem from its original domain into a new domain in which solution is easier. The solution is then mapped back to the original domain with the inver...

Biology is undergoing a quantitative revolution, generating vast quantities of data that are analysed using bioinformatics techniques and modelled using mathematics to give insight into the underlying biological processes. This module aims to give a flavo...

Reading the works of Friedrich Nietzsche is both exciting and troubling. He sets out to undermine the basis of many of our beliefs about values. Christianity, he believed, has had a powerfully negative effect on the potential of human beings. His method o...

Introduce the students to the practical application of a relatively wide spectrum of numerical techniques and familiarise the students with numerical coding. Often in mathematics, it is possible to prove the existence of a solution to a given problem, ...

The module introduces the operational research approach for modelling and solving engineering and management problems.

A variety of OR techniques are covered in lectures and assessed by examination. Workshops develop skills with computer modelling software (discrete-event simulation and linear programming). Other skills that are developed within the module are group w...

Module Contents: This module discusses continuous optimization problems where either the objective function or constraint functions or both are nonlinear. It explains optimality conditions, that is, which conditions an optimal solution must satisfy. It in...

The science of psychology and the project of artificial intelligence raise profound philosophical issues as they attempt to understand, simulate and even go beyond human thought. Some concern the kind of explanation that these ventures seek: If we underst...

In this module you will explore some major philosophical questions related to sex. We will begin by considering the nature of sex, discussing a range of theories of sex including the traditional view of sex as essentially connected to reproduction and “pl...

Socrates wants to cross a river and comes to a bridge guarded by Plato, who says: “Socrates, if you say something true, I will permit you to cross. But if you speak falsely, I shall throw you into the water.” Socrates answers: “You will throw me into the ...

The aims of this module are to explore some central issues about the relationship between action, reason, and ethics. Questions we shall consider may include: What is an action? What is it to act intentionally? What are reasons for action? Do all, some, o...

This is a module principally on Einstein's general theory of relativity, a relativistic theory of gravitation which explains gravitational effects as coming from the curvature of space-time. It provides a comprehensive introduction to material which is cu...

We seem to know our own minds - our beliefs, desires, intentions, thoughts, feelings and sensations - in a distinctively secure and immediate way, without having to rely on observation of our own behaviour. Such self-knowledge seems different from knowled...

The climate crisis is one of the most urgent issues facing humanity. Climate change is having an increasing impact on individual lives, and on social and political relations and institutions. This module examines the moral and political philosophical issu...

It is commonplace to hear people say such things as, ‘You shouldn’t believe that God exists—look at all the evil in the world’, or ‘You ought to believe that there is life on other planets—it’s entirely probable’, and the like. These judgements concerning...

In the first part of this module we build on multivariate calculus studied in the first year and extend it to the calculus of scalar and vector functions of several variables. Line, surface and volume integrals are considered and a number of theorems inv...

Wittgenstein is the most important philosopher of the twentieth century. He offers a sustained critique of many of the most common assumptions underlying much contemporary philosophy of mind and language. He explores, among other things, the questions of ...