Advanced Interdisciplinary Mathematics - 2019 entry

This module follows on from Fundamentals of Interdisciplinary Mathematics. Continuing to work in small groups, you will integrate more advanced mathematical, computational and statistical modelling tools with key questions and issues from scientific and engineering applications. You will also broaden your understanding of scientific questions and engineering challenges and the relevance of modern mathematics to their solution.

Pre-requisite modules: "Fundamentals of Interdisciplinary Mathematics" (ECM1911 or ECM1913), or “Mathematics of the Environment (ECM2911), or equivalent

In this module you will continue to develop the interdisciplinary perspective to mathematical sciences. Your learning will follow a three-stage cycle of colloquia, followed by group work, followed by presentation or poster session: Contemporary, expert-led colloquia will address state of the art issues from ecology, environmental science, and renewable energy; Each colloquium will be followed by break out-sessions with you working in small groups, with guidance from the module leader and classroom assistants to further your understanding of modelling and computing in MATLAB. Finally, you will present findings from the group work back to peers for discussion. Each of these three stages will be repeated three times to extend your knowledge of the underlying science and the relevant mathematical, statistical and computational approaches. You will also gain important experience of planning and carrying out research projects both independently and within groups.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 Apply and develop advanced mathematical skills to model and analyse natural and technological phenomena;

2 Abstract key issues in engineering, environmental and life sciences into advanced mathematical concepts;

Discipline Specific Skills and Knowledge:

3 Collect and archive data;

4 Develop more sophisticated models for processes in ecology, renewable energy and social interactions;

Personal and Key Transferable / Employment Skills and Knowledge:

5 Work successfully in small groups;

6 Communicate to specialists and non-specialists both orally and in written form;

7 Engage in group work.

The syllabus is developed around three colloquia. These colloquia are delivered by experts from the engineering, environmental and life sciences. The exact details of each colloquium will vary from year to year because one key aim is to address contemporary issues from a mathematical sciences perspective. These colloquia will be representative of the scope of the engineering, environmental and life sciences and so will include colloquia from ecology; renewable energy and environmental sciences. To emphasise the interdisciplinary nature of the module, the focus of the colloquia will be on key scientific or engineering challenges. Each colloquia will then be followed by a lecture on mathematical and computational approaches to the challenges, which you will explore throughout the subsequent group work activity.

The learning and teaching will follow a 3-week cycle. Sample themes for purposes of illustration:

Weeks 1 – 3: Theme A. Optimal decision making for the energy economy:

To make renewable energy technologies cost-competitive and secure energy provision for consumers, efficiencies in the chain from generation, to distribution, to consumption have to be managed and optimised. This might be, e.g., at the level of the wind turbine, the electrical grid or smart efficient appliances within the internet of things. You will explore different routes of management and optimisation towards more sustainable energy. [1 hour colloquium, 1 hour lecture, 7 hours supported group work, 2 hours presentations and discussion].

Weeks 4 - 6: Theme B. Infectious diseases:

The spread of disease is influenced by network structure and susceptibility of the individual, and mortality/severity. The contact networks for different diseases may vary dramatically: vector-borne transmission, e.g. in Malaria, or one-to-one contact, e.g. in HIV. Similarly susceptibility and mortality also can vary substantially. You will explore simple mathematical models of disease transmission and network topology and apply the ideas to human or wildlife disease. [1 hour colloquium, 1 hour lecture, 7 hours supported group work, 2 hours presentations and discussion];

Weeks 7 – 9. Theme C. Co-operation and Conflict:

Individual opinions on various societal challenges are formed within social networks. Opinions spread and can heavily influence how communities develop solutions for these challenges. Also, the outcome of an individual's decisions will depend on the decisions of others. Depending on the circumstances, this can lead to either competitive or cooperative behaviours. Similarly, competitive and cooperative behaviours emerge in biology as a result of natural selection. You will develop an understanding of simple mathematical models (e.g. agaent-based models/ game theoretic models) and apply these to understand and stimulate social network behaviours and/ or cooperation and competition in a biological setting. [1 hour colloquium, 1 hour lecture, 7 hours supported group work, 2 hours presentations and discussion];

Weeks 10 & 11: Finalising Individual Project

To build on scientific themes and consolidate advanced MATLAB skills. [Independent study with 3 hours of academic support per week].

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

ELE – http://vle.exeter.ac.uk

Reading list for this module:

MATLAB:

McMahon, D., MATLAB Demystified

Higham, D., Higham, N., MATLAB Guide

Kharab, A., Guenther, R., An Introduction to Numerical Methods: A MATLAB Approach

Hahn, B.D., Essential MATLAB for Engineers and Scientists

Optimisation and Energy Systems:

Sørensen, B., Renewable Energy: Physics, Engineering, Environmental Impacts, Economy and Planning

Great Britain. Department of Trade and Industry, Our energy future: creating a low carbon economy

Greig, D.M., Optimisation

Infectious diseases:

Vynnycky, E., White, R.G., An Introduction to Infectious Disease Modelling

Cooperation and conflict:

Scott, J., Carrington, P.J. (eds.), The SAGE Handbook of Social Network Analysis

Newman, M.E.J., Networks: An Introduction

Grimm, V., Railsback, S.F., Individual-Based Modeling and Ecology

Reading list for this module: