Lancaster University

Educational Aims

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 MSci level;
• To 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 aims of the MSci Mathematics/USA-Canada 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;
• To 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;
• 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 enable students to experience a programme of study at level three at a North American University which is comparable with and complementary to Lancaster level three modules;
• To enable students to learn about a different higher education system and a different society and culture, and to encourage students to develop confidence and success as independent learners;
• To provide a programme of study that allows students to specialise in pure mathematics at the third and fourth levels of study of an MSci, during which students must take a range of modules at level four that require both greater technical maturity and increased self-directed learning in comparison with that needed at BSc/BA level; to maintain a programme of study that leads directly into current research in pure mathematics;
• To produce alumni recognised for the distinctive value of their education on this programme.

Intended Learning Outcomes

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 and fourth levels of study;
• An appreciation of the hierarchical structure of mathematical knowledge;
• An understanding of mathematical notation, and an ability to use it correctly, coherently and fluently;
• An appreciation of the importance of proof, generalization and abstraction in the logical development of formal theories, and familiarity with and mastery of several examples of such a development, one of which is studied in detail through a substantial project;
• An ability both to follow and correctly to construct mathematical proofs of appropriate degrees of complexity, which require a synthesis of several separate results;
• 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 and from supervised private study, and to assimilate material from several sources;
• An ability to apply previously-acquired knowledge to new situations, both to gain understanding and to solve complex problems requiring a synthesis of several techniques;
• An ability to use information skills to gain access to library and IT resources effectively in researching topics;
• An ability to produce a range of documents which accurately and effectively communicate scientific material to the reader, and experience in doing this in a substantial dissertation;
• 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;
• An enhanced degree of self-reliance and confidence in independent study through the experience of the teaching and assessment methods that are used at North American universities.