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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 Management: Not Defined 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

  • Educational Aims

    This joint degree scheme gives students the opportunity to 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.



    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/BA level;
    • To offer a high-quality teaching and learning programme, informed by staff research, designed to train students in preparation for a wide range of postgraduate education and employment.


    The aims of the BSc/BA Mathematics programme are:

    • To provide students with analytical techniques and problem-solving skills that can be applied in many types of employment, especially those involving logical skills, decision-making in complex circumstances, or advanced skills of numeracy;
    • To offer modules of study which, individually and collectively, enable students to appreciate both the theoretical and problem-solving aspects of mathematics;
    • To 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;
    • To provide a programme of study that allows students to specialize in either pure mathematics or statistics, or to take a coherent blend of each at the third level of study of a BSc/BA;
    • To maintain a programme of study that introduces the background of current research in pure mathematics and statistics;
    • To produce alumni recognised for the distinctive value of their education on this programme.



    Philosophy was one of the founding disciplines of the University, and philosophy teaching programmes have always reflected the ideals of cross-disciplinary collaboration that is distinctive of the academic culture at Lancaster.  

    Philosophy teaching at Lancaster aims to develop learners interest in and knowledge of philosophy in a structured and progressive way by:

    • Pursuing the Universitys commitment to provide high quality teaching and learning programmes, reflecting and drawing upon excellence in research and scholarship and designed to meet the educational and vocational needs of students.
    • Reflecting the Universitys planning statement aim to enable students on all courses to learn independently, to understand complex problems, to adopt a critical approach to their subject, to appreciate the wider context of their specialist knowledge and methodology, and to communicate what they learn to others.
    • Offering an undergraduate programme that is designed to give students a broad knowledge of philosophy within the analytical tradition, and to provide skills in thinking, argumentation and analysis in the context of deeper knowledge of particular fields of philosophy
    • Providing a supportive learning environment within which students have the opportunity to reach their academic potential
    • Enabling students to develop transferable skills in argumentation and the critical analysis of problems which prepare students for both employment and further study and training after graduation

Learning Outcomes: Knowledge, Understanding and Skills

  • Intended Learning Outcomes

    The programme specifications and outcomes for the BSc Mathematics and BSc Philosophy degree apply equally to this joint degree. The two benchmarking statements and programme specifications define the distinctive outcomes from this degree. It encourages students to develop the mathematical skills helpful in appreciating certain areas of philosophy such as Logic, and the philosophical underpinning of the foundations of mathematics.


    The students on this degree should develop all the general knowledge, understanding and skills of the Mathematics and Philosophy degree schemes, and many of the subject-specific ones too, though in both subjects over a narrower range of material given that fewer modules are taken 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 level of study;
    • An appreciation of the 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.



    Knowledge and Understanding

    • A broad knowledge of philosophy in the analytical tradition together with deeper knowledge in some particular fields
    • The ability to question ideas concerning the nature of reality, value and experience that play a pervasive role in understanding the world and ourselves
    • The ability to use philosophical techniques of analysis and argumentation



    Intellectual Skills

              Avoid confusion in the presentation of more difficult ideas and more complex argumentation.

              Synthesise a wide range of ideas and arguments into a single coherently structured written presentation. At Level 3, students should be able to structure longer pieces of work in the form of dissertations.

              Grasp at least some of the main dimensions of a philosophical problem at issue in such a way as to support the beginnings of critical independent thought about it. At Level 3, independent critical thought should be developed further in dissertations.

              Maintain throughout a limited study that claims are open to test and evaluation. At Level 3, students should be able to maintain critical awareness throughout dissertations.

              Work with a sharp sense of validity and invalidity in relations to complex lines of argumentation.

              Draw intelligently on ones own reading, writing and thinking on a range of challenging contributions made by others. At Level 3, students should demonstrate detailed study of selected areas of philosophy in dissertations.

              Read and have a good understanding of at least some aspects of some challenging contributions to the problem at issue.

              Work with a sense of relevance in relation to a limited project as a whole both in choice of reading and presenting argument. At Level 3, this should be sustained over the length of a dissertation.


    Transferable Skills

    • To be able to articulate underlying issues in all kinds of debate;
    • To construct, develop and defend a valid argument, and to recognise an invalid argument;
    • To recognise and critically analyse problems, methodological errors, rhetorical devices, unexamined conventional wisdom and unnoticed assumptions;
    • To interpret texts from a variety of ages and traditions sensitively and to critically assess arguments in such texts;
    • To review unfamiliar ideas and ways of thinking with an open mind, and show willingness to change their minds where appropriate
    • To communicate complicated issues clearly and concisely.


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