MXB361 Aspects of Computational Science
To view more information for this unit, select Unit Outline from the list below. Please note the teaching period for which the Unit Outline is relevant.
| Unit code: | MXB361 |
|---|---|
| Prerequisite(s): | MXB261 |
| Assumed Knowledge: | Sound programming skills; sound achievement in Senior Mathematics B (or equivalent) is assumed knowledge. |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
| CSP student contribution | $555 |
| Domestic tuition unit fee | $3,324 |
| International unit fee | $4,296 |
Unit Outline: Semester 1 2024, Gardens Point, Internal
| Unit code: | MXB361 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | MXB261 |
| Assumed Knowledge: | Sound programming skills; sound achievement in Senior Mathematics B (or equivalent) is assumed knowledge. |
| Coordinator: | Godfrey Smith | godfrey.smith@qut.edu.au |
Overview
With the rapid development in computing hardware, algorithms, AI and their applications to advanced scientific problems that require computational solutions, there is a need for IT, Maths, Science and Engineering students to have a practical understanding of Computational Science. You will develop advanced knowledge and skills in computational techniques for solving real-world in numerical computing environments such as MATLAB. This unit aims to provide you with the knowledge to apply computational techniques for problem-solving in a variety of application areas you are likely to encounter in your early careers, whether in industry or in further study.
This unit will equip you with an understanding of different application areas requiring modern computational solutions, particularly as they relate to complex systems; you will have the opportunity to implement such computational techniques and analyse and interpret the resulting data.
Learning Outcomes
On successful completion of this unit you will be able to:
- Apply programming skills to implement various simulation algorithms for spatio-temporal simulations.
- Apply mathematical methods to predict and/or complement simulation results.
- Analyse, visualise and interpret simulation data with reference to real-world application and/or mathematical theory.
- Communicate scientific data in written and visual formats to scientific audiences.
Content
The weekly content of the unit is detailed below. This unit will focus on intuitive explanations and applications of the topics based on the approach and knowledge gained in pre-requisite unit MXB261. Module 1 is assessed in Assessment Item 1 (Problem Solving Task) and Module 2 is assessed in Assessment Item 2 (Project).
Module 1
- Revision of fundamental mathematical concepts, including partial derivatives, and difference (recurrence)-type equations. Revision of programming.
- Introduction to random walks on structured grids. Applications. How to simulate in MATLAB.
- Continuum limits: random walk to diffusion equation in 1D, 2D and 3D. Fundamental (Gaussian) solution to diffusion equation.
- Numerical solutions of ODEs: reminder of first order ODEs and some basic solutions, forward Euler, RK45, ode45 and similar in MATLAB.
- Introduction to finite difference methods for solving diffusion problems: central difference, forward in time, order of accuracy and CFL stability constraints.
Module 2
- Introduction to ODE systems: linear solution methods (eigenvalues/ eigenvectors for linear systems).
- Qualitative behaviour of ODE systems: stability analysis, bifurcation analysis, phase portrait construction.
- Stochastic differential equations: stochastic simulation – stochastic algorithms and differential equations (Euler-Maruyama method).
- Optimisation and root finding: gradient descent, Newton’s method, and inbuilt MATLAB versions.
- Fitting models to data – deterministic approaches: deterministic parameter estimation by optimization.
- Forecasting/prediction
Learning Approaches
This unit is available for you to study in either on-campus or online mode. You can expect to spend on average between 10 - 15 hours per week involved in preparing for and attending scheduled workshops, preparing and completing assessment tasks as well as independent study and consolidation of your learning.
This unit uses a theory-to-practice approach to engage you in your learning. Unit content will be introduced via lectures (2 hours each week), which will be followed by practical hands-on workshop (2 hours each week) designed to develop programming skills, problem-solving in both individual and team contexts. As a third year unit, you will expected to demonstrate your independent learning to find solutions to problems.
As with any unit requiring programming skills, you may need to devote additional hours each week to practice programming and analysis skills. If you are experiencing difficulty with the mathematics and/or programming required in this unit, you are encouraged to make contact with your teachers to get assistance. You are also reminded of the free Maths and IT programming support via the STIMulate peer program.
Feedback on Learning and Assessment
You will have a range of opportunities to receive feedback on your learning and progress in this unit including formative in-class individual or whole-of-class feedback on exercises conducted in class by teachers and peers as well as individual feedback on assessment tasks via a rubric and written feedback. Whole-of-class feedback will be provided by an announcement on the unit site in Canvas. Individual consultations with members of the teaching team can be arranged at a mutually convenient time. Marks and feedback for summative assessment items will be returned to the students within 10 working days from the due date of the assessment.
Assessment
Overview
This unit is assessed through a Problem Solving Task due mid-semester, and a Project due at the end of semester.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Problem Solving Task
The Problem Solving Task is designed to assess your learning across the topics of the first half of the unit.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Project
This applied project will provide you with the opportunity to demonstrate and integrate your learning from across the semester, with particular reference to the second half of the unit. You will be expected to program a computational solution to a problem, analyse the resulting data, and interpret the results that will be presented in a professional project report.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Academic Integrity
Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.
Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.
Resources
Various readings will be assigned, available online or at the QUT Library.
The required software is installed on computer labs, available as a download from QUT, or freely available as Open Source.
Students are not expected to purchase any software or other resources for this unit.
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres and computer laboratories. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp
Unit Outline: Semester 1 2024, Online
| Unit code: | MXB361 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | MXB261 |
| Assumed Knowledge: | Sound programming skills; sound achievement in Senior Mathematics B (or equivalent) is assumed knowledge. |
Overview
With the rapid development in computing hardware, algorithms, AI and their applications to advanced scientific problems that require computational solutions, there is a need for IT, Maths, Science and Engineering students to have a practical understanding of Computational Science. You will develop advanced knowledge and skills in computational techniques for solving real-world in numerical computing environments such as MATLAB. This unit aims to provide you with the knowledge to apply computational techniques for problem-solving in a variety of application areas you are likely to encounter in your early careers, whether in industry or in further study.
This unit will equip you with an understanding of different application areas requiring modern computational solutions, particularly as they relate to complex systems; you will have the opportunity to implement such computational techniques and analyse and interpret the resulting data.
Learning Outcomes
On successful completion of this unit you will be able to:
- Apply programming skills to implement various simulation algorithms for spatio-temporal simulations.
- Apply mathematical methods to predict and/or complement simulation results.
- Analyse, visualise and interpret simulation data with reference to real-world application and/or mathematical theory.
- Communicate scientific data in written and visual formats to scientific audiences.
Content
The weekly content of the unit is detailed below. This unit will focus on intuitive explanations and applications of the topics based on the approach and knowledge gained in pre-requisite unit MXB261. Module 1 is assessed in Assessment Item 1 (Problem Solving Task) and Module 2 is assessed in Assessment Item 2 (Project).
Module 1
- Revision of fundamental mathematical concepts, including partial derivatives, and difference (recurrence)-type equations. Revision of programming.
- Introduction to random walks on structured grids. Applications. How to simulate in MATLAB.
- Continuum limits: random walk to diffusion equation in 1D, 2D and 3D. Fundamental (Gaussian) solution to diffusion equation.
- Numerical solutions of ODEs: reminder of first order ODEs and some basic solutions, forward Euler, RK45, ode45 and similar in MATLAB.
- Introduction to finite difference methods for solving diffusion problems: central difference, forward in time, order of accuracy and CFL stability constraints.
Module 2
- Introduction to ODE systems: linear solution methods (eigenvalues/ eigenvectors for linear systems).
- Qualitative behaviour of ODE systems: stability analysis, bifurcation analysis, phase portrait construction.
- Stochastic differential equations: stochastic simulation – stochastic algorithms and differential equations (Euler-Maruyama method).
- Optimisation and root finding: gradient descent, Newton’s method, and inbuilt MATLAB versions.
- Fitting models to data – deterministic approaches: deterministic parameter estimation by optimization.
- Forecasting/prediction
Learning Approaches
This unit is available for you to study in either on-campus or online mode. You can expect to spend on average between 10 - 15 hours per week involved in preparing for and attending scheduled workshops, preparing and completing assessment tasks as well as independent study and consolidation of your learning.
This unit uses a theory-to-practice approach to engage you in your learning. Unit content will be introduced via lectures (2 hours each week), which will be followed by practical hands-on workshop (2 hours each week) designed to develop programming skills, problem-solving in both individual and team contexts. As a third year unit, you will expected to demonstrate your independent learning to find solutions to problems.
As with any unit requiring programming skills, you may need to devote additional hours each week to practice programming and analysis skills. If you are experiencing difficulty with the mathematics and/or programming required in this unit, you are encouraged to make contact with your teachers to get assistance. You are also reminded of the free Maths and IT programming support via the STIMulate peer program.
Feedback on Learning and Assessment
You will have a range of opportunities to receive feedback on your learning and progress in this unit including formative in-class individual or whole-of-class feedback on exercises conducted in class by teachers and peers as well as individual feedback on assessment tasks via a rubric and written feedback. Whole-of-class feedback will be provided by an announcement on the unit site in Canvas. Individual consultations with members of the teaching team can be arranged at a mutually convenient time. Marks and feedback for summative assessment items will be returned to the students within 10 working days from the due date of the assessment.
Assessment
Overview
This unit is assessed through a Problem Solving Task due mid-semester, and a Project due at the end of semester.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Problem Solving Task
The Problem Solving Task is designed to assess your learning across the topics of the first half of the unit.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Project
This applied project will provide you with the opportunity to demonstrate and integrate your learning from across the semester, with particular reference to the second half of the unit. You will be expected to program a computational solution to a problem, analyse the resulting data, and interpret the results that will be presented in a professional project report.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Academic Integrity
Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.
Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.
Resources
Various readings will be assigned, available online or at the QUT Library.
The required software is installed on computer labs, available as a download from QUT, or freely available as Open Source.
Students are not expected to purchase any software or other resources for this unit.
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres and computer laboratories. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp