MXB201 Advanced Linear Algebra

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:	MXB201
Prerequisite(s):	MXB106 and (MXB102 or Admission to ST20)
Equivalent(s):	MAB312
Assumed Knowledge:	MXB105 is assumed knowledge.
Credit points:	12
Timetable	Details in HiQ, if available
Availabilities	Gardens Point Semester 1 More about teaching periods More about unit attendance modes
CSP student contribution	$555
Domestic tuition unit fee	$3,324
International unit fee	$4,296

Much of the power of linear algebra stems from its widely-applicable collection of analytical tools for applied problem-solving. This unit builds upon your knowledge of linear algebra to explore more advanced techniques and applications of matrices and vectors. Furthermore, you will learn how much of what is familiar about linear algebra in Euclidean space can be abstracted to develop a more generally applicable theory. Hence you will develop an appreciation for the power and versatility of linear algebra across the mathematical sciences.

Unit Outline: Semester 1 2024, Gardens Point, Internal

Unit code:	MXB201
Credit points:	12
Pre-requisite:	MXB106 and (MXB102 or admission to ST20)
Equivalent:	MAB312
Assumed Knowledge:	MXB105 is assumed knowledge.
Coordinator:	Timothy Moroney \| t.moroney@qut.edu.au

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of the teaching period.

Overview

Learning Outcomes

On successful completion of this unit you will be able to:

Formulate and solve abstract and real world problems using advanced techniques of linear algebra.
Use computer software to explore and solve problems in linear algebra including obtaining insight into abstract problems via exploration of concrete realisations.
Present mathematical arguments clearly and logically in both written and oral form.
Demonstrate good teamwork practices through collaborative activities in a group environment.

Content

Matrix analysis, review of key matrix properties, facts about linear systems, four fundamental subspaces of a matrix, rank and nullity, the general solution of a linear system of equations. Orthonormal bases, the Gram-Schmidt process. The eigenvalue problem, matrix diagonalisation, computing matrix functions. QR and singular value decompositions. Abstract vector spaces, axioms, extension of concepts from R^n. Inner product spaces, axioms, examples of such spaces including function spaces, best approximations and least squares solutions. Linear transformations, projections.

Learning Approaches

This unit involves lectures and workshops in which you will engage in collaborative activity with peers and teaching staff. The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios. You will utilise technology to assist with solving and visualising key concepts to aid in your understanding.

The emphasis will be on active learning, that is, enhancing your learning by doing activities, encouraging both individual and collaborative learning, developing your written and oral communication skills and your attitudes to promote your life-long learning.

Particularly for your group-based modelling assessment activity, you will work with peers and with teaching staff to develop effective methods and approaches for communicating, evaluating and presenting information, and you will learn how to work effectively within groups with consideration for in-person and remote interactions.

Feedback on Learning and Assessment

Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece 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 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: Problem Solving Task

This assessment will consist of a number of problem solving tasks to be completed individually. These will consist of problem-solution based exercises to demonstrate your understanding of theoretical concepts and their application.

This assignment is eligible for the 48-hour late submission period and assignment extensions.

Weight: 30

Individual/Group: Individual

Due (indicative): Throughout the semester

Related Unit learning outcomes: 1, 2

Related Standards: EASTG1CMP: 1, 1.2, 2, 2.2

Assessment: Model (Theoretical)

In small groups you will apply your skills and understanding of linear algebra to develop mathematical models to describe and solve a real-world problem. Your group will write a technical report to summarise your model, describe the mathematical techniques employed, outline the key implementation details of any algorithms developed, and present your findings and recommendations. You will also provide a succinct video presentation in a professional manner, as if to experts in government, industry or academia.

This assignment is eligible for the 48-hour late submission period and assignment extensions.

Weight: 30

Individual/Group: Individual and group

Due (indicative): End of semester

Related Unit learning outcomes: 1, 2, 3, 4

Related Standards: EASTG1CMP: 1, 1.2, 2, 2.1, 2.2, 2.4, 3, 3.2, 3.4, 3.6

Assessment: Examination (invigilated)

The final examination will be based on unit material drawn from the full semester, and will allow you to demonstrate the theoretical knowledge and problem solving skills you have developed in this unit.

The examination will require attendance on QUT campus.

Weight: 40

Individual/Group: Individual

Due (indicative): End of semester

Related Unit learning outcomes: 1, 3

Related Standards: EASTG1CMP: 1, 1.2, 2, 2.2, 3, 3.2

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

Resource Materials

Recommended text(s)

Anton H. and Rorres C. Elementary Linear Algebra: Applications Version, Wiley

Risk Assessment Statement

There are no out of the ordinary risks associated with this unit.

Standards/Competencies

This unit is designed to support your development of the following standards\competencies.

Engineers Australia Stage 1 Competency Standard for Professional Engineer

MXB201 Advanced Linear Algebra

Unit Outline: Semester 1 2024, Gardens Point, Internal

Overview

Learning Outcomes

Content

Learning Approaches

Feedback on Learning and Assessment

Assessment

Overview

Unit Grading Scheme

Assessment Tasks

Assessment: Problem Solving Task

Assessment: Model (Theoretical)

Assessment: Examination (invigilated)

Academic Integrity

Resources

Resource Materials

Recommended text(s)

Risk Assessment Statement

Standards/Competencies

Engineers Australia Stage 1 Competency Standard for Professional Engineer

1: Knowledge and Skill Base

2: Engineering Application Ability

3: Professional and Personal Attributes

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