School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2023/24 Last Updated: 13 February 2024

MAT-30051 - Mathematical Modelling

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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: linear and nonlinear ordinary differential equations and their solution methods, such as phase-plane analysis, and partial differential equations and their solution techniques, such as separation of variables and method of characteristics.

Computational tools will include programming using Python for the numerical solutions of ordinary and partial differential 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: linear and nonlinear ordinary differential equations and their solution methods, such as phase-plane analysis, and partial differential equations and their solution techniques, such as separation of variables and method of characteristics.

Computational tools will include programming using Python for the numerical solutions of ordinary and partial differential equations.

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

The aim of the module is to apply mathematics to a variety of practical and open-ended problems relevant to industry, commerce and the environment.

Specific skills in model development and refinement, computational, report writing and teamwork will be developed using individual/group projects and student-led group activities.

Specific skills in model development and refinement, computational, report writing and teamwork will be developed using individual/group projects and student-led group activities.

construct mathematical models for problems arising from real-world phenomena: 1,2,3

apply appropriate mathematical and computational techniques to formulate and interpret solutions of the mathematical models in the context of the real-world phenomena: 1,2,3

communicate mathematical results in a variety of formats including oral and poster presentations, and writing reports: 2,3

further enhance and articulate the employability and transferable skills that they have developed during their degree: 2,3

apply appropriate mathematical and computational techniques to formulate and interpret solutions of the mathematical models in the context of the real-world phenomena: 1,2,3

communicate mathematical results in a variety of formats including oral and poster presentations, and writing reports: 2,3

further enhance and articulate the employability and transferable skills that they have developed during their degree: 2,3

Lectures: 24 hours

Examples Classes: 12 hours

Collaborative working in groups outside classes: 30 hours

Independent preparation of coursework: 24 hours

Independent study: 60 hours

Examples Classes: 12 hours

Collaborative working in groups outside classes: 30 hours

Independent preparation of coursework: 24 hours

Independent study: 60 hours

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Take-home assignments

Two equally weighted take-home, written assignments which assess the theoretical, computational and practical aspects of this module. 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.

Extended Group Project (3 weeks)

Group project 1 focuses on constructing mathematical models using linear and nonlinear ordinary differential equations choosing from a given set of real-world problems. The groups have three weeks to complete this project. The groups will be formed randomly by the tutor and will have between 5-6 members each depending on the class size. The groups must communicate the results via a written report and poster presentation. The group's report will not exceed ten sides of A4 and a maximum of 5000 words, not including appendices, but including figures and tables. A separate submission must include a record of each group meeting via minutes. Formatting guides will be provided for writing the report; templates will be provided for the poster and writing the minutes. The poster presentation's length will not exceed ten minutes, not including questions. Each member must contribute to the presentation, but the questions can be answered by anyone. A group project mark will be allocated based on the report, poster presentation and the meeting minutes. Individual contributions to group work will be assessed using tutor-moderated self- and peer assessment. The peer assessment score will be used to scale the group project mark to allocate an individual project mark. The groups are expected to spend a maximum of 12 hours over the duration of this project.

Extended Group Project (3 weeks)

Group project 2 focuses on constructing mathematical models using partial differential equations choosing from a given set of real-world problems. This project will use more advanced mathematical and computational solution techniques, hence has a higher weighting compared to group project 1. The groups have three weeks to complete this project. The groups will be formed randomly by the tutor and will have between 5-6 members each depending on the class size. The groups may be different from group project 1. The groups must communicate the results via a written report and oral presentation. The group's report will not exceed ten sides of A4 and a maximum of 5000 words, not including appendices, but including figures and tables. A separate submission will include a record of collective decision making via minutes of meetings. Formatting guides will be provided for writing the report; templates will be provided for the oral presentation and writing the minutes. The oral presentation's length will not exceed ten minutes, not including questions. Each group member must take part in the presentation, but the questions can be answered by anyone. A group project mark will be allocated based on the report, oral presentation and the meeting minutes. Individual contributions to group work will be assessed using tutor-moderated self- and peer assessment. The peer assessment score will be used to scale the group project mark to allocate an individual project mark. The groups are expected to spend a maximum of 12 hours over the duration of this project.