Mathematics Project

BUEM039D7 (60 credits)

Aims

• To give students the opportunity of undertaking a sustained, independent investigation into a specific topic in mathematics, related to one or more of the areas studied in the MSc programme, such as algebra or combinatorics.
• To give students practice in academic research, writing up and presenting the results and conclusions of an investigation in a report where the problem, final results and conclusions can be understood and appreciated by a mathematics graduate, and which includes sufficient technical detail for the proofs and arguments to be verified by a specialist in the field.
• To give students practice in the oral presentation of the background, results and conclusions of an investigation in a way that may be understood by mathematics graduate who has not necessarily specialised in the topic being studied.

Structure

The dissertation gives students the opportunity to identify and, with some guidance, carry out a research project in an area of mathematics related to one or more topics encountered on the MSc programme. Completely new work (such as the discovery and proof of a previously unknown theorem) would be very unusual at this level, however application of known results in different areas, or synthesis of existing academic research to produce a coherent analysis of a particular problem, would be acceptable kinds of project. Each student is required to submit a project proposal at the beginning of the second year of study and a supervisor is then allocated. Once project and supervisor are agreed, and an initial meeting has taken place, students are expected, over the remainder of the autumn term, to complete:

1. background reading on the project area and on the mathematical theory and techniques required;
2. assemble relevant journal papers, and locate and becoming familiar with the necessary software (both for doing and for typesetting mathematics);
3. final specification of the questions that are of interest and can feasibly be investigated in the time.

Seminars on research methods in mathematics will be arranged to help students with these tasks. At the end of the autumn term in the second year, each student is required to give a 10 minute oral presentation, giving the relevant background to their project, the problem to be investigated, and progress to date. A written progress report is required by the end of the spring term and the final project report of between 6,000 and 10,000 words must be submitted by September 1st at the end of the two years of study. Individual oral presentations of 25 to 30 minutes, including 5 minutes for questions, are then scheduled to be completed by September 30th. Throughout the duration of the project, students are advised to discuss progress and obtain feedback from their supervisor on three/four occasions after the initial meeting, including feedback on the preliminary project presentation, the written progress report, and a draft plan and at most one draft section of the final project report.

Assessment

80% of the marks for the module are for the dissertation (submitted at the end of Year 2). 5% are for the initial ten minute oral presentation (Autumn Term Year 2), 5% for the written progress report (Spring Term Year 2) and 10% for the final oral presentation (End of Year 2).

Learning Outcomes

• Knowledge and understanding of, and the ability to use, mathematical techniques.
• Knowledge and understanding of a range of results in mathematics.
• Familiarity with and ability to work with academic writing of mathematics.
• A deeper understanding of several topics in mathematics.
• Ability to comprehend and evaluate conceptual and abstract material.
• Ability to devise rigorous mathematical proofs.
• Ability to understand and apply mathematical reasoning in several different areas of mathematics.
• Problem-solving skills, including the ability to assess problems logically and to approach them analytically.
• Ability to transfer knowledge and expertise from one context to another.
• Ability to work in a largely self-directed or autonomous manner.
• Communicate conclusions and the knowledge and rationale underpinning these, to specialist and non-specialist audiences, clearly and unambiguously.
• Ability to learn independently using a variety of media.
• Ability to complete work in a limited time period.
• Time-management and organizational skills.
• Ability to work professionally with a considerable degree of independence.
• Ability to carry out academic work such as collation and synthesis of existing sources on a particular topic.
• Ability to complete a substantial piece of work at a high academic level.