MXB226 Computational Methods 1
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: | MXB226 |
|---|---|
| Prerequisite(s): | MXB103 and MXB106 |
| Equivalent(s): | MAB420, MXB222 |
| Assumed Knowledge: | MXB105 is assumed knowledge |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
Unit Outline: Semester 2 2027, Gardens Point, Internal
| Unit code: | MXB226 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | MXB103 and MXB106 |
| Equivalent: | MAB420, MXB222 |
| Assumed Knowledge: | MXB105 is assumed knowledge |
| Coordinators: | Qianqian Yang | q.yang@qut.edu.au Vivien Challis | vivien.challis@qut.edu.au |
Overview
This is an intermediate unit in Computational Mathematics. It covers the design and implementation of computational techniques for solving a range of problems in applied mathematics. These techniques will be analysed for important properties such as efficiency, stability, convergence and error. You will gain an appreciation for how your computational abilities acquired in MXB103 can be extended to more complex real-world scenarios.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of mathematical principles underpinning the discretisation of continuous problems into discrete approximations.
- Implement computational algorithms using MATLAB and synthesise individual components into high-level computational tools.
- Critically select and apply appropriate computational algorithms, including the use of specialised data structures, to solve practical problems.
- Engage communication skills through a combination of report writing, code documentation, group collaboration and individual problem-solving.
Content
The main topics that will be covered include: finite difference methods for models of heat conduction in two dimensions; direct and iterative methods for linear systems; efficient storage of sparse matrices; norms; approximation; numerical integration; numerical methods for ordinary differential equations.
Learning Approaches
This unit is available for you to study in either on-campus or online mode. You can expect to spend 10 - 15 hours per week involved in preparing for and attending scheduled classes, preparing and completing assessment tasks as well as independent study and consolidation of your learning.
This unit is strongly practical-based, with much of your learning taking place in the form of practical activities conducted in the computer lab. Here, you will have the opportunity to put in practice the theoretical knowledge you have gained from the weekly lectures. By implementing, experimenting with and profiling the relevant algorithms in MATLAB, you will gain an appreciation for the art and science of algorithm selection and design.
The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios. The emphasis will be on learning by doing, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning. You will work with experts and peers to develop effective methods/approaches for communicating, retrieving, evaluating and presenting information.
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments, student perusal of marked assessment pieces and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit learning outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: MATLAB Portfolio
The portfolio is comprised of a number of worksheets where you will implement the techniques discussed in lectures using MATLAB. There will be two submission dates in Weeks 5 and 12 of the semester, with each submission contributing 10% to your final grade. For the first submission date, you choose two worksheets to submit out of Practicals 1-4. For the second submission date, you choose two worksheets to submit out of Practicals 5-8.
For each worksheet you need to complete the specified tasks and insert all code and your reasoning into the MATLAB Live Script.
The use of generative artificial intelligence (GenAI) tools is prohibited during this assessment.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Case Study
The case study will consider a real-world application where spatial discretisation leads to a large, sparse, structured linear system of equations. You will derive this system, investigate and compare different methods for its solution using computational techniques, and gather data on the efficiency of each approach.
You are required to submit all your code, in the form of MATLAB functions and a single MATLAB script that calls your functions and exhibits your results.
You are also required to submit a report that introduces the problem, outlines the mathematical model, discusses your solution methodology, presents your results/findings/analyses and concludes your work. Your report must be typeset in a word processor or document preparation system such as Microsoft Word, Google Docs, LaTeX or similar.
The use of generative artificial intelligence (GenAI) tools is prohibited during this assessment.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Exam
This final invigilated examination will assess your learning over the course of the entire semester.
The use of generative artificial intelligence (GenAI) tools is prohibited during this assessment.
The examination will require attendance at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide local testing centre information.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
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.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
There is no set text for this unit.
There are many reference texts for this unit, many of which can be located in the library. There are also many online resources such as lecture notes and some e-books that can be found online. Example reference texts are listed below.
Resource Materials
Reference book(s)
Atkinson KE (1998) An Introduction to Numerical Analysis, Wiley
Bradie B (2006) A Friendly Introduction to Numerical Analysis, Pearson
Burden RL & Faires JD (2002) Numerical Analysis, 7th edition, PWS-KENT Publishing Company
Golub & van Loan (1996) Matrix Computatations, John Hopkins.
Kelley CT (1995) Iterative Methods for Linear and Nonlinear Equations, SIAM
Saad Y (1996) Iterative Methods for Sparse Linear Systems, Boston: PWS Publishing Co
Risk Assessment Statement
There are no out of ordinary risks associated with this unit.
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.MS01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: MATLAB Portfolio, Case Study, Exam - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: MATLAB Portfolio, Case Study, Exam - Demonstrate aptitude in computer programming, and familiarity with industry-leading programming languages and relevant specialised mathematical, statistical and generative artificial intelligence software and tools.
Relates to: MATLAB Portfolio, Case Study - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: MATLAB Portfolio, Case Study, Exam - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Case Study, Exam - Work both independently and collaboratively in diverse teams, including cross-cultural and cross-disciplinary teams.
Relates to: Case Study
MV01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: MATLAB Portfolio, Case Study, Exam - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: MATLAB Portfolio, Case Study, Exam - Demonstrate aptitude in computer programming, and familiarity with industry-leading programming languages and relevant specialised mathematical, statistical and generative artificial intelligence software and tools.
Relates to: MATLAB Portfolio, Case Study - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: MATLAB Portfolio, Case Study, Exam - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Case Study, Exam - Work both independently and collaboratively in diverse teams, including cross-cultural and cross-disciplinary teams.
Relates to: Case Study