Mathematics and Philosophy BSc/BA (Hons)

About the course

Mathematics

This programme builds a firm basis of understanding in areas of mathematics of fundamental importance, making it an interesting study in its own right. In addition, it develops applications of mathematics highly supportive of studies in business, computing, economics, engineering and the sciences. Initially, various A level mathematics topics are refreshed and extended. The second year develops deeper insight into this work, with the Joint study route introducing additional skills, and the Major developing computer techniques. The final year applies the knowledge and skills previously acquired to the solution of practical problems drawn from a wide variety of areas.

Philosophy

As well as personal fulfilment, this course gives you transferable analytical skills that are valuable in a wide range of careers. Philosophy offers you the opportunity of studying a subject which is personally rewarding, whilst at the same time developing transferable skills which are highly valued by employers: the ability to identify and analyze problems, to understand alternative solutions and their merits, and to make intelligent and well articulated judgments. The introductory courses include issues in ethics, knowledge and metaphysics, the philosophy of religion and the philosophy of science. The courses do not aim to provide ready made solutions to the problems that are posed but to look for means by which difficult and puzzling questions can be tackled systematically and objectively. The second and final years include detailed studies of a wide range of areas and topics, including: Greek philosophy; Kant; continental philosophy; contemporary Anglo-American philosophy; logic and reasoning; metaphysics; philosophy of science, and of mind; moral and political philosophy.

Why choose this course?

• This subject in our university has a long tradition of teaching useful and relevant mathematics at degree level in ways that are understandable.
• It provides an intellectual training that will enable you to become clearer and more systematic in the expression of your own ideas and in the critical assessment of those of others.
• It assumes no prior knowledge of the subject while the first year offers introduction to essay writing skills, critical analysis and debate by in the introduction to philosophy module.

Study routes

• Part Time,
• Sandwich,
• Full Time,

Locations

• University of Hertfordshire, Hatfield

Careers

This programme gives you flexibility in your studies at university resulting in flexibility in your choice of career at the end of your course. You will acquire a much broader base of knowledge and experience that could really widen your employment opportunities. Graduates have found employment in diverse roles such as computer programmers, design engineers, management development specialists, accountants and project managers. Over 72% of our graduates had entered employment six months after graduation, and a further 17% had gone on to further study or training.

Teaching methods

You experience a wide variety of learning styles when you study on the programme. During your time with us we will develop your capacity for self-learning and your interpersonal skills. We particularly emphasise the importance of structured research; well-prepared written and verbal presentations; and computer literacy. Alongside elements of standard lectures, seminars, tutorials and laboratories, you also learn through case studies, individual and group projects and other student centred activities. In your final year you will normally have the opportunity to practice your self-learning and interpersonal skills by undertaking a Major project or dissertation.

Work Placement

You will have the opportunity to take a paid work placement or study abroad for a year between your second and final years, extending your degree from a three year to a four year qualification. You will not be required to pay tuition fees for this year and you will gain excellent experience that sets you apart from the crowd in the graduate jobs market.

Study Abroad

You can study in most European countries, USA, Canada, Mexico, Brazil, Chile, Uruguay, South Africa, Russia, China, Korea, Japan, Malaysia, Singapore, Thailand and Australia. You will study a programme of taught modules and/or project work with one of our partner universities, which will complement your studies on the Joint Honours Programme. You may need to study the language of your chosen country in your first and second years. Depending on where you choose to study you may be eligible to apply for certain grants, scholarships and financial support to help finance your study abroad experience.

Work Placement

A work placement provides you with an excellent opportunity to gain valuable experience and put your theoretical knowledge and understanding from your studies in to practice.

Our Careers and Placements service will help you to develop your CV and support you through the application process for a wide range of placement opportunities in a variety of sectors and organisations.

Structure

Year 1

Core Modules

• Introduction to Philosophy

  You will gain a basic training in how to read and write essays in philosophy, while exploring perennial questions such as: Can we know right from wrong? How, if at all, can we tell a good act from a bad one? Is ethics merely a matter of personal opinion? What is knowledge? Can we reliably gain it, and if so how? Can we be certain of anything? What is pessimism? Is it justified? Are we really free? Do we need God in order for lives to be truly meaningful?

• Reason and Persuasion

  We live in a world of persuasion. Advertisers would persuade us to buy their products while politicians press their policies on us. In personal life too, others want us to see things their way. We, of course, want others (colleagues, friends and family) to agree with us, to be persuaded by our arguments. Rhetoric is the art of persuasive speech and writing. It has been studied both for academic interest and for its practical, business and legal usefulness since ancient times. This module will explore the reasons why some persuasive efforts work while others do not. It will develop your ability to judge when you ought to be persuaded by the arguments of others and to present your own views in a way that increases their persuasive force.

• Philosophy of Film and Literature

  The central theme of the module is to investigate what it is possible for film and literature to represent. How do we establish what is true in a fiction? Can the impossible happen in fiction? How, if at all, do we manage to engage with fictions that we take to be metaphysically or morally problematic (such as H.G.Wells' The Time Machine or Vladimir Nabokov's Lolita)? In what sense can film and literature explore not only how things actually are but how things could have been? Is there a difference between what can be represented in film and what can be represented in literature? We tackle these questions by engaging with various films and works of literature to see how they fit within a philosophical framework for thinking about them.

• Mathematical Techniques 1 (L1)

  On entry students will have different mathematical knowledge and this module has been designed to standardise their mathematical knowledge. The module will initially review core areas of A-Level Mathematics which will be extended to improve students' knowledge. You will learn the standard mathematical techniques in calculus, matrices and vectors.

• Linear Algebra and Analysis

  You will learn fundamental ideas and language on which the rest of mathematics is based. The module also investigates the idea of tending to a limit, on which calculus is based, and some of the ideas of linear algebra which occur throughout mathematics.

• Small Group Tutorial

  The module will require students to attempt a range of problems, mostly of a mathematical nature, broadly in the students' subject area. Some problems will be associated with other specific taught modules on the programme, while others will have a synoptic role sitting across several modules. The work will challenge students to develop problem solving skills that enable them to approach unfamiliar as well as familiar problems.

Optional

Year 2

Core Modules

• Mathematical Techniques 2

  You will learn how to integrate functions of two and three variables along plane and space curves and how to evaluate multiple integrals of such functions. You will learn about gradient, divergence and curl. You will be able to obtain Fourier series expansions of simple functions and perform calculations involving functions of a complex variable.

• Differential Equations

  This module employs a variety of mathematical methods and techniques to explore, describe and predict the behaviour of scientific, industrial and engineering phenomena. The subject appeals to individuals interested in applying their mathematical interests and skills to real-word problems. In this module, we will focus on ordinary differential equations. The emphasis is on the development of methods important in applications. Topics include:- Theory and applications of first, second and higher order differential equations, The Laplace transform methods, Systems of linear differential equations.

• Numerical Methods

  You discover how to use numerical methods to solve mathematical problems, and to discuss relative performance of different methods in terms of accuracy and efficiency. You also learn about the theoretical background to the methods. Refer to the teaching plan for a more detailed description.

Optional

• Themes in Plato's Republic

  If you could get away with morally unjust behaviour, why should you act morally? What would an 'ideal society' be like? What is the relationship between justice in the individual, and justice in society? This course investigates several major themes in Plato's philosophy. After an introduction to the importance of Socrates and the nature of Socratic enquiry, we shall focus predominantly upon the Republic - one of the most important texts in the history of western thought - in which the above questions are central. The course will aim to show connections between Plato's metaphysics and theory of knowledge, and his ethics, political thought and philosophy of art and literature. Students will develop their skills in reading, assessing and advancing arguments.

• The Right and The Good

  Is happiness the only thing of value? According to Utilitarianism, my moral duty is to promote happiness. What do we mean by "happiness"? If our moral duty is to promote happiness does this mean that we are justified in adopting any means, including killing, that might promote happiness? Kant is one philosopher who considers that we should value human beings in their own right and this introduces constraints on what we are morally justified in doing. We have duties to assist and also not to harm other human beings. We study these two theories by looking at Mill's ‘Utilitarianism’ and Kant's ‘Groundwork of the Metaphysics of Morals’. Application of these theories to moral dilemmas chosen by students will form the topic of the presentation. For example, is it ever morally right to use violence or terrorism in the pursuit of peace? Should we ever assist anyone to commit suicide?

• Philosophy of Mind

  What are mental states? How do they relate to human actions? What is consciousness? Is there a real difference between the mental and the physical? This course explores philosophical approaches to understanding the nature of mind which range from dualism to strong forms of materialism. Students will be trained in the use of relevant terminology and will develop their skills in reading, assessing and advancing arguments. Students will be assessed on their knowledge and understanding of at least two approaches/issues in the philosophy of mind, their use of relevant terminology and their ability to produce structured arguments, which anticipate possible replies, in the form of essays.

• Logic and Language

  Should you study logic? Mephistopheles has no doubts: Make use of time, its course so soon is run,/[...]/I counsel you, dear friend, in sum,/That first you take collegium logicum [the logic class]. (Goethe, Faust). Logic can be a lot of fun, like chess, poker, cross-words or sudoku. It provides some conceptual tools that are very helpful in order to clarify your ideas and to develop convincing arguments. Logic is also crucial in order to understand much contemporary philosophy, which relies heavily on many of its technical notions. Mephistopheles is wrong, however, in one final respect: logic is really a defence against the dark arts. The course will teach you to fight vagueness, obscurity, imprecision, fallacies and those who rely on them to cast rhetorical spells.

• Knowledge and Discovery

  What kind of justification is required to be able to say not just that we believe something but that we know it? Must we be able to cite reasons for believing something before we can be said to know it, or is it enough for those beliefs to have been generated in a reliable way? Must knowledge rest on a foundation that is immune from error, or are beliefs justified by being part of a network of mutually supporting beliefs? We shall discuss the extent to which the particular observations we make give us reason to believe (or disbelieve) general claims about the world and, further, what counts as a good explanation for why that thing has happened. We shall consider not just beliefs about those things we can see with our own eyes but whether there is any reason to believe in those things which we cannot observe directly (e.g., the very small and the very distant).

• Philosophy of Art

  We go to museums, read novels, listen to music, talk about art. But what is art? In this module, we survey the main theories of art throughout history, observing as we go along, that while each theory has added to our understanding of art, it has not defined it once and for all. At the end of the survey, we shall ask whether a comprehensive definition is possible, or even necessary to our understanding of art. The survey will take us through passages from authors such as Plato, Aristotle, Tolstoy, Hume, Kant, Collingwood, Wittgenstein, Danto, Dickie and Wollheim. We will ask ourselves: Is art is a matter of personal taste or are there intersubjective criteria in the determination of art? Where is the boundary between art and craft? How is art related to morality? Is Tracy Emin's My Bed art; if so, is it good art? What makes anything art?

• Social and Political Philosophy

  We tackle fundamental questions concerning how our society should function and what implications this has for the individual. How should goods (e.g. property, services, rights, liberties, power) be distributed in society? On what basis can some people claim ownership of property? Should goods be distributed on the basis of desert, entitlement or some notion of equality? On what basis can someone 'in authority' tell me what (or what not) to do? And if I don't do as they say, on what basis can I be punished for it? What are rights? Do we have them naturally or are they all conferred on us by an institution? Do all humans have rights or are children and/or the mentally impaired to be excluded? Do future generations of people have rights? Can these notions extend to non-human animals or the environment in general? And what are our obligations in each of these cases?

• Metaphysics

  Metaphysics asks the most general questions about the most fundamental features of the world. How should we understand space, time and causation? Does time flow? Does the future already exist? Is space a substance? Is it possible for me to do something now so as to affect what happened in the past? What are things and what does it take for them to persist over time? What is it for things to have properties, such as being red? What are properties? Do they exist in the same way that the things that have them do? What else exists? Does reality extend beyond what is actual?

Year 3

Core Modules

Optional

• Year Abroad

  A Study Abroad year is an optional additional year that increases the length of the Honours degree award to a four-year full-time degree. The additional year comprises an agreed programme of study in a partner institution abroad with whom the University of Hertfordshire has an institutional agreement. The programme of study will support, supplement and extend the more usual three-year programme. Success in the third year will be recognised in the title of the award, but does not carry additional credit towards the Honours programme. A student would normally confirm the intention to study abroad during the first ten weeks of study at Level 2. This will enable a place to be negotiated at a host institution and the Study Programme and learning contract to be arranged and agreed.

• Professional Placement

  Supervised work experience provides students with the opportunity to set their academic studies in a broader context, to gain practical experience in specific technical areas and to strengthen their communication and time-management skills. It greatly assists them in developing as independent learners, so that they are able to gain the maximum benefit from the learning opportunities provided at level 3 of the programme.

• Year Abroad

  The Year Abroad will provide students with the opportunity to expand, develop and apply the knowledge and skills gained in the first two taught years of the degree within a different organisational and cultural environment in a partner academic institution. The host institution will appoint a Programme Co-ordinator who will oversee the student's programme during the Year Abroad and will liaise with the appointed UH Supervisor.

Year 4

Core Modules

• Linear Optimisation

  You learn to tease out the relevant information from business problems and to develop linear models to represent them. A number of different solution methods are developed and used to solve these problems. You will develop the ability to interpret the results in management terms and how to handle changes in the data after the problem has been solved. You also learn about other practical difficulties involved in the process. Refer to the teaching plan for a more detailed description.

• Boundary Value Problems

  You will learn how to solve one and two-dimensional boundary-value problems both analytically and numerically. Through practical sessions you will use suitable numerical software to investigate the numerical processes. Refer to the teaching plan for a more detailed description.

Optional

• Philosophy Project

  You will have the opportunity to develop your research skills through the largely independent study of a particular topic in philosophy of your choice, which must be approved by your supervisor. You will receive guidance from your supervisors in the form of suggestions about reading and about the structure and development of the project. Supervisors also provide critical feedback on material that is submitted. No conditions are placed on the choice of topic, so long as it falls within the general discipline of philosophy, and a member of the philosophy staff has the relevant expertise to provide the appropriate supervision. If you are intending to pursue a project you must identify your area of interest and are required to complete and submit a form by the end of the academic year prior to that in which you intend to begin your project.

• Kierkegaard, Philosophy and Religion

  What makes a human life worthwhile? What form would philosophy have to take effectively to communicate genuine ethical or religious insight? What does it really mean to live an 'aesthetic', 'ethical' or 'religious' life? Kierkegaard tackled these questions through a series of literary-philosophical texts published under a variety of bizarre pseudonyms. This module considers central aspects of Kierkegaard's thought, focusing upon issues related to ethics, religion and philosophical communication. After an introduction to the importance of 'indirect' communication in existential matters, we shall investigate in some detail the 'aesthetic', 'ethical' and 'religious' modes of life. The central texts will be Either/Or and Fear and Trembling.

• Aristotle P

  Is there a method to philosophy? Are we rational animals? Do all living things have a purpose? What is the good life or is there more than one? Is ethics primarily concerned with virtue? These questions, which are still of relevance today, will be explored by an examination of Aristotle's central works.

• Representation and Consciousness

  Cognitive science seeks to scientifically explain, or at least shed light, on how and why agents behave as they do. Yet it has met with some serious obstacles in trying to understand the nature of representation and conscious experience. This module introduces and examines various proposals about how these phenomena might be scientifically understood, at least in principle. It asks such questions as: Is cognition really a form of symbol manipulation? Do these symbols have any representational content? Are they about anything in the world? If so, what accounts for this? Is there any real prospect for a scientific theory of consciousness or do all ‘objective’ accounts necessarily leave something out?

• Nietzsche, Genealogy and Morality

  Nietzsche famously claimed that 'God is dead'. But what does he mean by this? What ramifications would the 'death of God' have for morality and human flourishing? What would a 'Nietzschean' view of self and world look like? And what religious responses to Nietzsche's challenge are possible? With these questions in mind, this module investigates key aspects of Nietzsche's thought. Typically, after an introduction to his styles of philosophizing, the 'hermeneutics of suspicion', and his 'moral perfectionism', we shall focus upon his influential critique of morality. We shall investigate his account of ressentiment, guilt and 'bad conscience', alongside central Nietzschean ideas such as the will to power, eternal recurrence and 'self-overcoming'. We'll also consider some possible critical responses to his worldview. The central text will be On the Genealogy of Morality.

• Philosophy of Language

  Marks, sounds and gestures can all have meaning. But what is it for them to have meaning and how do they manage to have it? Is the meaning of my words to be analysed in terms of my intentions to communicate with another or the conventions I subscribe to when using words? In what way is meaning related to truth and my being warranted in asserting what I say? What other things can we do with words than state truths? How should we understand metaphorical uses of language? How do names and descriptions in particular manage to pick out objects in the world? Are some things I say true solely in virtue of the meanings of the words I use? Is there anything that fixes what it is that I do mean when I use words, or is meaning, to some extent, indeterminate? Can a study of language tell us anything about reality?

• Wittgenstein's Philosophy

  Ludwig Wittgenstein is one of the greatest philosophers of the twentieth century. Much of today's philosophical thinking has been inspired by or has developed in response to his work. His first published work - the Tractatus Logico-Philosophicus - provides, for some, an inspiration for powerful anti-metaphysical programmes. For others, it offers refined tools for doing metaphysics in a new, more fertile way. He himself came to reject aspects of his early work. How his approach evolved can only be fully understood by considering his early programme in the light of his second great masterpiece, Philosophical Investigations. This module does just that by introducing important aspects of Wittgenstein's philosophy in their historical and ideological contexts. The module will explore a range of topics such as: the nature of language and thought and their relations to reality; meaning and use; understanding and intentionality; following a rule; the possibility of a private language; the nature of philosophy.

• Understanding Minds

  What is the basis of our everyday ability to understand reasons for actions? Do we make sense of other minds by using theories, by imaginatively adopting the other's perspective, by creating narratives or by all of the above? Are such capacities built-in or acquired? How do they develop during childhood? These questions are central in much of today's philosophy of mind, cognitive science, anthropology, developmental psychology and a host of other disciplines. There is considerable debate about what lies at the basis of these so-called folk-psychological abilities. This module will introduce these debates and explore their relevance for philosophy and for other disciplines in the humanities and sciences.

• Philosophy of Information

  From laptops to iphones, from emails to GPS, we live in an ever expanding infosphere, which is posing unprecedented problems and reshaping old philosophical issues. What is knowledge in the age of Google and Wikipedia? What is the nature of personal identity after Facebook? Is it right to download copyrighted material? The philosophy of information (PI) provides the conceptual foundations to approach these and similar questions. It investigates the conceptual nature and basic principles of information, including its dynamics, utilisation, and sciences, and elaborates information-theoretic and computational solutions to philosophical problems. The course offers an accessible approach to the foundations for this new philosophical subject. It describes what the philosophy of information is, its problems, approaches, and methods. It offers a grasp of the complex nature of the various concepts and phenomena related to information, and it seeks to answer several key theoretical questions of great philosophical interest, arising from the investigation of information. No previous knowledge of the topic, of any mathematics or computer science is required or expected.

• Virtues, Vices and Ethics

  There has been a revival of interest in 'virtue ethics' in recent decades, and it is typically presented as a third major approach to contemporary moral philosophy, alongside consequentialist and Kantian deontological theories of ethics. We shall briefly discuss this context and the work of some important recent virtue theorists. But the primary focus of this module will be a body of writing by contemporary philosophers on specific personal virtues and, where appropriate, corresponding vices. We shall thus bring philosophical reflection to bear on such 'everyday' issues as pride, humility, gratitude, love, compassion, hope, patience, forgiveness and trust.

• Kant's Critical Philosophy

  "Kant made me sick." This was Bertrand Russell's reaction to the philosophy of Immanuel Kant. Much of the philosophy written in the Western tradition in the last two centuries is in some way a reaction to or development of Kant's 'Copernican revolution' in philosophy. Kant's main work, the Critique of Pure Reason, develops and defends two thoughts. First, our empirical experience is structured and conditioned by what we bring to it, so the problem of epistemology is the adequacy of our preconceptions. Second, there are limits to what pure reason can achieve, and much philosophy is a hopeless attempt to answer questions that lie beyond reason's powers. Kant argued that it is in the nature of reason to attempt more than it can achieve. Moreover, reason is sovereign over itself, and therefore must police its own boundaries. It is therefore always caught in a tension between transgressing its limits and enforcing them.

Fees & funding

Fees 2013

UK/EU Students

Full time: £8,500 for the 2013 academic year

International Students

Full time: £9,500 for the 2013 academic year

Discounts are available for International students if payment is made in full at registration

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Scholarships

• National Scholarship Programme

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Other financial support

Find out more about other financial support available to UK and EU students

Living costs / accommodation

The University of Hertfordshire offers a great choice of student accommodation, on campus or nearby in the local area, to suit every student budget.

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How to apply