External summary

Philosophy has been at the core of Western intellectual life for at least 2,500 years and is central to our understanding of the world and of our place in and interaction with it. Philosophy provides the tools whereby the presuppositions of all areas of intellectual and practical activity may be systematically and critically examined. While there are different approaches that philosophers have taken, characteristic of Philosophy is the emphasis on the use of argument, critical enquiry, rigour in reasoning, and clarity of expression, including the making of pertinent distinctions.

As the historic home of David Hume and Adam Smith, the city of Edinburgh is a fitting place to study philosophy. The University, too, has a strong historic connection to the subject, counting Adam Ferguson and Sir William Hamilton among its former students. Edinburgh has one of the UK’s largest Philosophy departments and the Philosophy Society attracts high-profile speakers. An advantage of the four- year course at Edinburgh is that it is structured in such a way that students cover the basics of Western Philosophy and have the opportunity and time to specialize in the areas of most interest.

Studying Mathematics the University of Edinburgh gives you a broad introduction to the subject and the flexibility to study topics that interest you within and outside Mathematics. Mathematics is a study of number and pattern. It can be pursued both for its own internal fascination and also as a central tool for Science and Technology, as well as the Social Sciences.

Educational aims of programme

• a thorough knowledge of the ideas and arguments employed by the main philosophers of past and present, studied through their texts, and an understanding of the main areas of Philosophy and an appreciation of the significance of these in world culture
• a knowledge of specific areas of philosophy or philosophers in yet greater depth, for example, mathematical logic, philosophy of language, philosophy of mathematics, philosophy of psychology, philosophy of religion, philosophy of science, Wittgenstein, aesthetics, philosophy of law, applied ethics
• how philosophical problems may be generated by conceptual or foundational issues in other areas of inquiry
• the skills required not only to understand philosophical debates but also to take part in such debates constructively and intelligently
• be able to describe synchronic and diachronic phenomena and processes in language.
• be able to use of the computational package MAPLE to solve mathematical problems
• write simple programmes using MAPLE
• use LaTeX to produce mathematical documents
• acquire active-learning and transferable skills (e.g. study skills, information retrieval skills, information technology skills, communication skills, group work skills)
• be equipped to deal with complex data in a variety of realms
• have the possibility of exploring areas in which the concerns of the two subject areas overlap, e.g. formal logic, mathematical logic
• transferable skills of use in virtually every area of employment, including everything requisite for fostering independent critical thinking, self-directed research and sustained analytical activity

Programme outcomes: Knowledge and understanding

On completion of the programme, students will have acquired a good knowledge and understanding of:

• the problems, theories, and arguments of the main areas of philosophy, specifically: metaphysics, epistemology, logic, philosophy of mind, philosophy of science and moral philosophy. Joint Honours students will have studied most of these areas in less depth and some in considerable depth. The achievement of increasing depth is intimately related to student progression.
• the views and arguments of some of most important philosophers of the past, including: Plato, Aristotle, Descartes, Locke, Berkeley, Hume, Kant, and Mill
• the works of historical philosophers not simply as self-contained bodies of doctrine but as attempts to solve real philosophical problems. In the pre-honours years this is achieved by studying historical philosophers in the context of problem-oriented courses
• single and several variable calculus, including applications of the differentiation and integration of functions of a single or several variables in a variety of contexts
• convergence of real sequences and series, including the application of tests for convergence
• rigorous definitions of analytic concepts such as limits and continuity
• complex numbers
• geometry in two and three dimensions, including conics in the plane and the use of vectors
• elementary group theory as an illustration of abstract mathematics
• matrices and their application to the solution of systems of linear equations
• notions of linearity, including linear independence and dependence, bases, dimension and linear maps between finite-dimensional spaces
• solution of linear programming problems using the simplex method
• first order ODEs and their use in the modeling of problems
• use of Fourier series
• selected areas of Mathematics and Statistics of a more advanced nature representing important branches of the subjects.

Programme outcomes: Graduate attributes - Skills and abilities in research and enquiry

Throughout the course of the programme, students acquire key philosophical abilities, including the ability to:

• analyse a text and reconstruct its arguments, to find its premises, and the inferences drawn from them
• be able to distinguish between validity and soundness, and to assess arguments for both
• distinguish relevant from irrelevant considerations in argument
• look for counter-examples to general claims
• use examples appropriately in support of general claims
• construct clearly organized arguments
• make careful distinctions
• be sensitive to ambiguity and multiplicity of meanings
• understand and appreciate the significance of new ideas
• to assess critically the presuppositions and methods of familiar ways of thinking within and outwith Philosophy and Mathematics
• make a principled choice between the use of qualitative and quantitative modes of enquiry
• analyse a mathematical argument and understand its logical structure
• formulate a rigorous mathematical proof
• read and assimilate an unfamiliar piece of mathematics or statistics
• apply mathematical and statistical knowledge to model and solve real-life problems

Programme outcomes: Graduate attributes - Skills and abilities in personal and intellectual autonomy

• analytical thinking skills—the abilities to understand difficult pieces of text, to reconstruct arguments and views, to assimilate and explain difficult ideas.
• critical thinking skills—the abilities to draw conclusions from positions or bodies of data, to question arguments and (wherever appropriate) to show their flaws, to generate alternative ideas and new solutions to problems
• independent thinking skills—the abilities to approach a problem with an open mind and to address problems with an original approach, and the confidence to rely on one’s own intellectual capacities
• independent working skills—the ability to motivate oneself, to plan one’s own work, and to set one’s own goals and deadlines

Programme outcomes: Graduate attributes - Skills and abilities in communication

Students should acquire skills that can be used in a wide variety of intellectual contexts and forms of employment. These include:

• written communication skills — students should be able to construct a lengthy, coherent piece of prose that constitutes a well-structured argument or investigation
• oral communication skills — students should be able to explain their ideas to others in a discussion
• being able to take part in a debate, keeping to the goal of the discussion, maintaining the thread of argument, to be able to argue their point forcefully and to disagree with others while showing respect for their opinions and without causing or taking offence

Programme outcomes: Graduate attributes - Skills and abilities in personal effectiveness

• the confidence to rely on one’s own intellectual capacities
• the ability to motivate oneself, to plan one’s own work, and to set one’s own goals and deadlines
• ability to apply philosophical and mathematical skills and techniques to issues arising out with subject area
• the ability to work autonomously
• time and priority management skills
• construct clearly organized arguments
• understand and appreciate the significance of new ideas

Programme outcomes: Technical/practical skills

Students should acquire skills that can be used in a wide variety of intellectual contexts and forms of employment. These include:

• computing skills — the ability to use computers for word-processing, information storage and for retrieving information from the world wide web
• use of libraries—the ability to use libraries for the recovery of information, and related research skills, including the ability to discriminate between different sources of information, suggested readings, and so on
• correct use of the internet for research

Programme structure and features

Full details of the degree programme and structure can be seen at <http://www.drps.ed.ac.uk>

Courses are taught through a combination of lectures and tutorials. Optional courses in Years 3 and 4 are taught through seminars.

Progression Requirements – Students are normally expected to have gained 120 credits at the end of Year

Teaching and learning methods and strategies

Years 1 and 2

Philosophy courses in Years 1 and 2 are taught by a combination of lectures and tutorials. Typically, for each course, a student attends three one-hour lectures and one one-hour tutorial per week. Lectures introduce and explain ideas relevant to the course, and tutorials provide an opportunity for students to discuss and clarify these ideas in a small group setting.

Mathematics courses ...

Students may also take courses outside Philosophy and Mathematics in subject areas of their choosing. The teaching methods of these courses are determined by the relevant subject area.

Years 3 and 4

Philosophy courses in Years 3 and 4 are taught primarily by weekly two-hour seminars. The seminar format puts strong emphasis on group discussion and student participation. Often seminars are based on pre-assigned readings which students are expected to read in preparation for the seminar. For some courses, students may give a short presentation to the class on an assigned topic.

Mathematics courses ...

In Year 4, students are required to satisfy a dissertation requirement in either Philosophy or Mathematics. This provides an opportunity for students to undertake extended, independent research, under the supervision of an appropriate member of staff.

Facilities

The main university library houses extensive holdings in both philosophy and mathematics, including online access to journal articles and a growing number of online books. A second smaller library, shared between Philosophy and Psychology, houses philosophy materials for use by staff, graduates and Honours students and offers further study space.

Assessment methods and strategies

Philosophy courses in Years 1 and 2 are assessed by a combination of essays and exams. In most cases, a course will have one 1500-word mid-term essay, worth 25% of the overall mark for the course, and one end-of-term exam, worth 75%. In Years 3 and 4, there is greater variation in assessment methods between courses. The most commonly used methods are essays and exams, but different courses may combine these in different ways. Other assessment methods used in some cases include take-home exams and class presentations.

Mathematics courses ...

Career opportunities

Other items

• all students are assigned a Director of Studies on admission to the degree programme, who oversees the course of the student’s degree programme, offers advice on academic matters (including degree-progression)
• student opinion is actively sought through participation in Staff-Student Liaison Committees, through the election of class- and tutorial-representatives, and by the wide circulation and review of detailed student questionnaires each semester.  In addition, Philosophy student representatives are invited to attend, and to contribute to, selected Philosophy subject-area meetings.
• students are encouraged to take the opportunity to study abroad in their third year. Consultation with staff before leaving helps to advise students on the most appropriate courses to take while away
• mathematics offers support throughout the degree, which includes MathsBase, our popular walk-in help centre for first-year students
• in later years students can use the MathsHub, a student-run facility that is both a social centre and a work space
• the main university library houses extensive holdings in Philosophy and mathematics, including online access to journal articles and a growing number of online books.  A second smaller library, shared with Psychology, houses Philosophy materials for use by staff, graduates and Honours students and offers further study space.  The Philosophy Society (in consultation with staff) is also working to create a dedicated store of course materials tailored to the reading-lists and guidance contained in course guides
• Edinburgh MathSoc is run by Edinburgh University maths students. It has two main functions, academic and social. It runs a programme of popular lectures and organises many social events throughout the year