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BA Hons Mathematics and Philosophy

Mode of Study: Full Time Department: Mathematics and Statistics
UCAS Code: GV15 Duration/Length: 3 Year(s)
QAA Subject Benchmark: Mathematics, Statistics and Operational Director of Studies: Not known
Total Credit Points: 360 Credit Points Year 2: 120
Credit Points Year 3: 120

Educational Aims: Knowledge, Understanding and Skills

  • This joint degree scheme gives students the opportunity to explore the historical and methodological links between mathematics and philosophy. Mathematics has made an important contribution to many branches of philosophy, whilst philosophy has had a significant positive input into the development of mathematics by challenging its foundations and opening up prospects of new theories with abstract ontology. By studying both subjects, students develop a capacity for logical method, critical reasoning and abstract thought. These aspects are particularly relevant in studying pure mathematics, where proof is of central importance.

    Through joint study of these disciplines, students can benefit from:

    • intellectual development in both subjects and the fertile area between them;
    • a strong demand for graduates with these theoretical and practical skills in many areas of employment.

    While permitting only a narrower scope for study of specialist subjects in mathematics and computing, this joint degree scheme meets the educational aims of the BSc Mathematics and BA Philosophy.


    The Department's educational aims are to:

    • create a teaching and learning environment which supports all students in reaching their full potential in their study of mathematics at BSc level;
    • offer a high-quality teaching and learning programme, informed by staff research, designed to provide adequate preparation for postgraduate studies or employment involving a similar high level of knowledge and skills.

    The explicit aims of this programme are to:

    • provide students with analytical techniques and problem-solving skills that can be applied systematically and creatively in many types of employment, especially those involving logical skills, decision-making in complex circumstances, or advanced skills of numeracy;
    • offer modules of study which, individually and collectively, enable students to appreciate both the theoretical and problem-solving aspects of mathematics, and encourage students to show self-direction and originality in tackling problems;
    • provide students with enough core material, of sufficient depth and variety, in the first two levels of study that they are adequately prepared and informed for subsequent study in either or both of pure mathematics and statistics;
    • provide a programme of study that allows students to specialise in either pure mathematics or statistics, or to take a coherent blend of each, at the third level of study of a BSc;
    • maintain a programme of study that introduces the background of current research in pure mathematics and statistics;
    • produce alumni recognised for the distinctive value of their education on this programme.


    The Department of Politics, Philosophy and Religion aims to provide all students with high quality teaching, utilising its excellence in scholarship and research. Teaching and learning in the department are based on a wide-ranging understanding of the discipline. We seek to produce graduates with a strong knowledge of their subject area who are characterised by well-developed leadership skills, the ability to make a positive difference to society and a willingness to take the initiative in their jobs and communities.

    The programme aims to:

    • develop students subject specific knowledge about the themes, concepts and events that have shaped the contemporary philosophical scene;
    • enable students to engage in debate on matters of philosophy;
    • encourage students in thinking critically and independently about philosophical issues;
    • be aware of a range of different theoretical and methodological perspectives within philosophical studies and to be able to apply their general understanding to real world examples;
    • generate a broad understanding of the range of areas of investigation in philosophical studies by offering a wide range of substantive topics from which students can choose;
    • develop students cognitive, time management and transferable skills through a variety of learning environments and modes of assessment;
    • offer high quality teaching, informed by staff research, which helps students realise their creative and academic potential;
    • enhance student internationalisation and employability;
    • develop students' high level skills in problem solving, the application of knowledge, analysis and critical reflection, oral and written communication, independent learning, negotiation and influence, time management, work organisation and the application of modern technologies.

Learning Outcomes: Knowledge, Understanding and Skills

  • This joint degree allows students to appreciate both:

    • the different methodological approaches that characterise the two disciplines, and
    • a deeper understanding of both mathematics and philosophy, developed by the complementary approaches of the two disciplines.

    The students on this degree scheme are likely to develop all the general knowledge, understanding and skills of those taking single honours degrees in mathematics or philosophy, and many of the subject-specific ones too, though within each subject this will be over a narrower range of material, given the fewer modules they take in each department.


    Subject-specific knowledge, understanding and skills

    On completing the programme students should have acquired:

    • An understanding of and competence in the key ideas and techniques, and knowledge of the statement and proof of key results, both within the core areas of real and complex analysis, linear and abstract algebra, and probability and statistics, and in the more advanced topics chosen in the third year of study;
    • An appreciation of the progressive and hierarchical structure of mathematical knowledge;
    • An understanding of mathematical notation, and an ability to use it correctly and coherently;
    • An appreciation of the importance of proof, generalization and abstraction in the logical development of formal theories;
    • An ability both to follow and correctly to construct mathematical proofs of appropriate degrees of complexity;
    • An understanding of the mathematical and contextual basis of statistics as a science, and an appreciation of the statistical paradigm, linking design and conduct of experiments and observations with data analysis,modelling and inference;
    • Experience of implementing the statistical paradigm in a range of general applications;
    • An ability to read and comprehend mathematical literature at an appropriate level;
    • An ability to use computers and specialist software to investigate and solve practical mathematical problems.

    General knowledge, understanding and skills

    On completing the programme students should have acquired:

    • An ability to learn from various styles of presentation of material;
    • An ability to apply previously acquired knowledge to new situations, both to gain understanding and to solve problems;
    • An ability to use information skills to gain access to library and IT resources effectively in researching topics;
    • An ability to produce documents which accurately and effectively communicate scientific material to the reader;
    • An ability to make presentations based on prepared material;
    • An ability to work effectively both independently and as part of a small group;
    • An ability to work to deadlines, and experience in time management when working to a range of deadlines.


    Subject-specific knowledge, understanding and skills

    On successful completion of this scheme of study students will be able to:
    • Demonstrate a broad knowledge of philosophy in the analytical tradition together with deeper knowledge in some particular fields;
    • Demonstrate a broad knowledge of the themes, concepts and events that have shaped the contemporary philosophical scene;
    • Engage in debate on matters of philosophy, and use philosophical techniques of analysis and argumentation;
    • Think critically and independently about philosophical issues;
    • Demonstrate awareness of a range of different theoretical and methodological perspectives within philosophical studies and apply their general understanding to real world examples;
    • Demonstrate familiarity with the range of areas of investigation in philosophical studies;
    • Recognise and critically analyse problems, methodological errors, rhetorical devices, unexamined conventional wisdom and unnoticed assumptions;
    • Interpret texts from a variety of ages and philosophical traditions sensitively and to critically assess arguments in such texts.

    General knowledge, understanding and skills

    On successful completion of this scheme of study students will be able to:

    • Demonstrate cognitive and transferable skills;
    • Demonstrate enhanced internationalisation and employability;
    • Summarise and compare conceptually based theoretical arguments, constructing, developing and defending valid arguments, recognising invalid arguments;
    • Assimilate information from taught material with independent reading and produce written work that demonstrates their understanding of those materials;
    • Communicate ideas to others, articulating underlying issues in all kinds of debate, and making presentations based on prepared material and participate effectively in small group contexts;
    • Review unfamiliar ideas and ways of thinking with an open mind, and show willingness to change their minds where appropriate;
    • Use library and IT resources effectively in the preparation of written work;
    • Work independently under supervision and guidance;
    • Manage their time effectively.

Learning and Teaching Strategies and Methods: Knowledge, Understanding, Skills

  • The primary method of instruction is the lecture. Lectures are used to teach key concepts and offer learning guidance.

    All lecture courses in the Department of Mathematics and Statistics are supported by weekly problem-solving classes. Students are set weekly assignments which are marked and returned, with feedback, by tutors who are either academic staff or graduate teaching associates. This assessment is designed to be formative, but a small amount of summative credit is awarded. Regular computer lab sessions, especially in the first two years, are used to teach the programming language R and train students to solve problems using software. The labs are designed to complement the lecture courses and problem-solving classes.

    The Department of Mathematics and Statistics offers a dedicated Project Skills course, MATH390, optional for this scheme of study, which carries 15 credits at Level 6 and is taught in the third term of Year 2 and the first term of Year 3. Students are trained to use the mathematical typesetting software LaTeX, write scientific reports, enhance their communication skills and deliver oral presentations. Working in small groups, the students are asked to write and present a substantial report on an advanced topic in mathematics or statistics.

    In philsophy, the PPR department's aim is to integrate learning and teaching with the research culture of the department.

    In Part I, students are given a gentle introduction to the theoretical foundations of philosophy, and begin to understand what is meant by critical enquiry in academia. Students learn the basic essay writing skills that will enable them to produce high quality course work in subsequent years. They are also encouraged to become independent as learners. Teaching principally takes the form of lectures and seminars (with groups of up to 15 students), as well as a significant amount of independent study.

    Part II builds on the theoretical foundation and requires students to develop a broader and deeper understanding of the subject area. Depending on their choice of modules, students can gear their learning to focus deeply on a particular area (theoretical or issue based) on which to specialise, or they can chose to gain an increased breadth of understanding through choosing more diverse modules. Teaching principally takes the form of lectures and seminars (with groups of up to 15 students), as well as a significant amount of independent study. Students can also choose to develop their independent research skills through doing a supervised dissertation in the final year.

    Weekly lectures provide students with a basic framework for understanding the issues raised by the course material. Independent study and the ability to discuss ideas with others is facilitated by interactive, student-oriented seminars of groups of up to 15. Course materials include outlines and lecture handouts. Course outlines provide information about intended learning outcomes, the aims of the course, a list of lecture and seminar topics and a reading list. Lecture handouts, where used, typically indicate the main points of lectures, suggested detailed reading, and usually include material for the associated seminar. Independent learning and researching and preparing for lectures, seminars and assessments are an integral part of the learning experience.

Assessment Strategy and Methods: Knowledge, Understanding and Skills

  • Testing of knowledge and understanding is conducted through a range of formative and summative assessment methods. The assessment strategy reflects the progressive nature of the subject and moves from testing simple skills and methods through to more complex arguments and independent projects. Work in Year 1 is usually based closely on lecture material and includes basic skills in mathematical techniques, the understanding and application of simple abstract concepts and an appreciation of the role of proof. As the level of study progresses, the work becomes more demanding and requires a firm understanding of the main theoretical approaches and methodological techniques in core topic areas, and a developing experience of transferring these skills to new problems.

    In Year 1 all courses are assessed by a combination of written examination and coursework, in equal proportions. Coursework includes weekly assessed work, end-of-module tests, computer lab work and short project work.

    In Year 2 the majority of courses are assessed by a combination of written examination and coursework, with the examination allocated the majority of marks.

    In Year 3 the majority of courses are assessed by a combination of written examination and coursework, with the examination allocated the majority of marks. However, one optional course (MATH390) is assessed entirely through coursework and continual assessment, and there is the option to offer a substantial dissertation (PPR.399) in philosophy.

    Examinations are designed to test the learning objectives. The guiding philosophy is to reward students for what they know rather than penalise them for what they do not know. Formal examinations provide experience of single-minded concentration, critical time-management, preparation skills and working under pressure.

    Essays and other written assignments require independent research, the use of library skills and the attainment of in-depth subject specific knowledge. Students are expected to demonstrate an ability to synthesise their reading into a coherent argument, make appropriate use of evidence and draw on relevant theoretical and conceptual issues in order to produce an answer that will demonstrate a degree of independent thinking and critical judgement.

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