ECM2911 - Mathematics of the Environment (2021)

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MODULE TITLEMathematics of the Environment CREDIT VALUE15
MODULE CODEECM2911 MODULE CONVENERDr Markus Mueller (Coordinator)
Number of Students Taking Module (anticipated) 20
DESCRIPTION - summary of the module content
Mathematics Matters. These words are often stated. In this module we put these words to the test. You will build core computational skills and use these to explore important societal themes from a mathematical perspective. A distinctive feature of the module is that each exploration starts with a plenary-style colloquium from an expert scientist or engineer. Then, working in small classroom-based guided group work sessions, you will develop and apply a variety of mathematical, statistical and computational techniques either, inspired by, or to analyse and dissect, the expert opinion. You will communicate the analyses from your group to your peers for discussion and report your findings.


Pre-requisite: A Level in Mathematics, or equivalent
AIMS - intentions of the module

The module has three interwoven aims: Develop core MATLAB skills; understand key societal themes from a mathematical and computational perspective; develop transferable skills including team-work, report writing and presentation skills. Inter-disciplinarity is key and throughout the module there will be ample opportunity to work alongside mathematical scientists to break down pre-conceived barriers between different areas of mathematics and different applications in science and engineering. Your learning will follow a “develop skills – apply skills – present skills” cycle.

Each cycle will combine lectures and computer lab sessions aimed at building-up quantitative skills, an introduction lecture to a research theme by an expert from science or engineering, and guided exploration of the scientific/engineering theme in groups, ending with a presentation or poster session. The cycle will be repeated across three skill sets/applications to offer a wide range of mathematical and computational skills and their application across a wide range of scientific themes.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

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

Module Specific Skills and Knowledge:

1 Listen critically to experts from science and engineering and assimilate imparted knowledge in mathematical terms;

2 Analyse contemporary scientific issues using mathematical, statistical and computational techniques;

Discipline Specific Skills and Knowledge:

3 Abstract scientific issues into logical mathematical form;

4 Synthesize a range of mathematical, statistical and computational techniques;

5 Develop evidenced-based reasoning;

Personal and Key Transferable/Employment Skills and Knowledge:

6 Engage in informed debate concerning key issues from the engineering, environmental and life sciences;

7 Engage with stakeholders from the engineering, environmental and life sciences;

8 Engage in group work with peers from different disciplines with different skill sets.

SYLLABUS PLAN - summary of the structure and academic content of the module
The syllabus has two key threads: A skills-based thread aimed at developing core MaATLAB skills and related mathematical and computational techniques; and an applications-based thread whereby skills are applied to key societal challenges*. The challenges are posed by an expert from engineering, environmental or life sciences. Learning and teaching will follow a 3-stage cycle. In each stage, you will work in teams to put applied mathematics and computational skills into practice in a real-world application. Each stage will conclude with a group presentation or poster session.
Weeks 1-3: Theme A. Climate Change Project
To include energy balance modelling, tipping points, hysteresis in the climate. [3x4 hours]
This theme will also introduce you to the following MATLAB skills: Getting started; Lists and arrays; 2D plotting; Extrapolation and interpolation; Loops, iteration and logic; Matrices and matrix algebra in MATLAB;
Weeks 4-7: Theme B. Natural Populations Project
To include population projection modelling, eigenvalue and eigenvector analysis of population growth trends, and mathematical approaches to population management. [3x4 hours]
You will continue to develop MATLAB skills, using iterative schemes to make projections, performing eigenvector and eigenvalue calculations, and use of 2D plotting to visualise population progression;
Weeks 8-10: Theme C. LiDAR and the Environment Project
To include data handling and manipulation and 3D visualisation. [3x4 hours]
You will gain experience of processing and visualising large data sets in MATLAB.
Weeks 11-12: Individual Project
To build on scientific themes and consolidate MATLAB skills, leading to an individual report. To assess your skills under ILOs 1-5 you will include a reflection on the quantitative skills applied to demonstrate your understanding of the modelling and computational aspects of the module. [Independent study with 3 hours of academic support per week].
*The exact details of each challenge may vary from year to year because one key aim is to address contemporary issues.
Scheduled Learning & Teaching Activities 44.00 Guided Independent Study 106.00 Placement / Study Abroad 0.00
Category Hours of study time Description
Scheduled Learning and Teaching Activities 10 Lectures and computer demos
Scheduled Learning and Teaching Activities 3 Colloquium-style lectures
Scheduled Learning and Teaching Activities 3 Peer-to-peer presentations
Scheduled Learning and Teaching Activities 28 Guided group work and independent study
Guided Independent Study 106 Wider reading and preparation


FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Minutes for Group Meetings (expected 2-3 meetings per theme) 500 words (or equivalent) per minutes document 1-8 Oral
Mock Quantitative Skills Test 40 minutes 2-4 Written/Computer-Based


Coursework 100 Written Exams 0 Practical Exams 0
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Three Group Presentations/Posters 33 Per Presentation: 10 min/ Per Poster: 500 words (or equivalent) 1-8 Oral and Written
Quantitative Skills Test 33 40 minutes 2-4 Written/Computer-based
Individual Report 34 2000 words (or equivalent) 1-7 Oral and Written


DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All Above Individual Report 3000 words (or equivalent) All August Ref/Def Period



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.

INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Basic Reading:


Web based and Electronic Resources:

Met Office Hadley Centre - UKCP18 Science Overview Report:

American Meteorological Society (AMS) - State of the Climate in 2015:

Intergovernmental Panel on Climate Change (IPCC) Reports - AR5 Synthesis Report:

Other IPCC Reports:

Other Resources:

Sanyal, J. & Lu, X.X. Application of Remote Sensing in Flood Management with Special Reference to Monsoon Asia: A Review, Natural Hazards (2004) 33: 283

Tarsi, K. & Tuff, T. (2012) Introduction to Population Demographics. Nature Education Knowledge 3(11):3

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set McMahon, D. MATLAB Demystified McGraw-Hill 2007 978-0071485517 [Library]
Set Gander, W. Learning MATLAB: A Problem Solving Approach Springer 2015 978-3319253275 [Library]
Set Higham, D. and Higham, N. MATLAB Guide 3rd SIAM 2017 978-1611974652 [Library]
Set Kharab, A. and Guenther, R.B. An Introduction To Numerical Methods: A MATLAB Approach Chapman & Hall 2012 978-1439868997 [Library]
Set Deffeyes, K.S. Beyond Oil: The View from Hubbert's Peak Hill & Wang 2006 978-0809029570 [Library]
Set Otto, S.P. and Day, T. A Biologist's Guide to Mathematical Modeling in Ecology and Evolution 1st Princeton University Press 2007 978-0691123448 [Library]
Set Campbell, J.B. and Wynne, R. Introduction to Remote Sensing 5th Guilford Press 2011 [Library]
ORIGIN DATE Wednesday 11 January 2017 LAST REVISION DATE Monday 22 February 2021
KEY WORDS SEARCH Interdisciplinary Mathematics and Statistics; Ecology; Environmental Science; Policy; Society; Scientific Computing with MATLAB