School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2019/20 Last Updated: 01 March 2020

MAT-20016 - Mathematical Modelling

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The aim of the module is to demonstrate how real-world problems can be modelled mathematically. To facilitate this aim, the module introduces a six-step mathematical modelling and problem-solving process.

(i) identifying a suitable problem from the particular real-world scenario;

(ii) make assumptions to simplify the problem;

(iii) classifying variables influencing the problem;

(iv) construct a mathematical model to determine interrelationships among the variables;

(v) solve and interpreting the model;

(vi) validate the model with real-world data.

(i) identifying a suitable problem from the particular real-world scenario;

(ii) make assumptions to simplify the problem;

(iii) classifying variables influencing the problem;

(iv) construct a mathematical model to determine interrelationships among the variables;

(v) solve and interpreting the model;

(vi) validate the model with real-world data.

apply the modelling cycle to real-world problems: 2,3

reflect on employability and transferable skills: 3

reflect on team working, independence, communication, decision-making and organization: 3

evaluate and apply theoretical and practical skills to real-world problems: 2,3

reflect on employability and transferable skills: 3

reflect on team working, independence, communication, decision-making and organization: 3

evaluate and apply theoretical and practical skills to real-world problems: 2,3

The aim of the module is to demonstrate how real-world problems can be modelled mathematically. The mathematical modelling process will be introduced through a six-step problem-solving approach: identifying a suitable problem from the particular real-world scenario, making assumptions to simplify the problem, classifying variables influencing the problem, constructing a mathematical model to determine interrelationships among the variables, solving and interpreting the model and finally validating the model with real-world data.

Mathematical tools that will be used in the model construction and solution process include: Ordinary Differential Equations and their solution methods, such as phase-plane analysis, Dimensional Analysis and Difference Equations.

The modelling ideas will be developed through novel and innovative case studies of real-world scenarios and through individual/group projects.

Mathematical tools that will be used in the model construction and solution process include: Ordinary Differential Equations and their solution methods, such as phase-plane analysis, Dimensional Analysis and Difference Equations.

The modelling ideas will be developed through novel and innovative case studies of real-world scenarios and through individual/group projects.

Lectures: 24 hours

Examples Classes: 12 hours

Preparation of coursework: 16 hours

Independent study: 98 hours

Examples Classes: 12 hours

Preparation of coursework: 16 hours

Independent study: 98 hours

Confidently model real-world problems mathematically: 2,1

Enhance theoretical and practical skills: 1,2

Enhance employability and transferable skills: 1

Enhance team working, independence, communication, decision-making and organization: 1,2

Enhance theoretical and practical skills: 1,2

Enhance employability and transferable skills: 1

Enhance team working, independence, communication, decision-making and organization: 1,2

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Two reflective pieces.

Two short reflective pieces. The first reflective piece covers "Principles of Time Management" and the second piece "Dealing with Difficult People". The word length of each piece is approximately 500 words.

Take-home assignments

Approximately two equally weighted take-home, written assignments. Each assignment consists of a set of questions with pre-allocated space for written solutions. The assignments are set at regular intervals across the semester. Students should expect to spend 12 hours across the semester on their assignments.

Three group projects spread across the semester

There will be three group projects. Project one (30%) requires a group report and short oral presentation; project two (30%) requires a poster presentation and report; project three (40%) requires a report. Project one is a 1 week-long learning activity, project 2 and 3 last 3 weeks each. Each report's length will not exceed ten sides of A4, not including appendices, but including figures and tables. Formatting guides will be provided.