Units

---

Sample subject outline - Semester 1 2013

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

The study of linear algebra and matrix theory is of fundamental importance to a variety of mathematical disciplines including statistics, finance, economics, information technology, operations research, applied and computational mathematics. Facts about matrices, and how to manipulate them, are essential for understanding many areas of the mathematical sciences. A staggering fact is that well over 75% of all problems encountered in scientific or industrial applications involve the solution of a linear system at some point. Matrix analysis is therefore an important topic in any course on linear algebra and of fundamental importance to the basic foundations of mathematics. The subject matter is not only intellectually challenging, but successful completion of this unit will enable you to apply the underlying theory and concepts to many of the advanced mathematics units offered within this School.

Aims

The main aim of this unit, which is intended for students majoring in mathematics and students in other courses who require the foundations of linear algebra, is to develop the basic theory of linear algebra and to provide you with the necessary skills to apply this theory in science, technology, engineering and mathematics. It seeks to foster an appreciation of the historical development and the value of the principles and methods presented.

Objectives

On satisfactory completion of this unit, you should be able to:

1. Show an understanding of set theory, algebraic systems, matrix analysis, vector spaces and inner product spaces.
2. Present mathematical arguments clearly and logically.
3. Use a computer algebra package to solve problems in linear algebra.
4. Apply the knowledge of linear algebra in practical situations.

Content

Topics will be selected from the following three sections:

A brief introduction to set theory and algebraic systems; the Euclidean space R^n; a brief review of key matrix properties, facts about linear systems and the properties of matrix inverses; the notions of vector subspaces, spanning sets, linear independence, basis and dimension in R^n; the four fundamental subspaces of a matrix, rank and nullity, the general solution of a linear system of equations; the eigenvalue problem within the Euclidean space framework; matrix diagonalisation; and computing matrix functions.

Arbitrary Vector Spaces: properties and structure of a general, arbitrary vector space; properties of vector subspaces; a brief introduction to linear transformations and change of basis.

Inner Product Spaces: inner products; orthogonality; orthonormal bases; Gram-Schmidt Process and QR-Decomposition; orthogonal projections; best approximation and least squares solutions; data fitting.

Approaches to Teaching and Learning

The work will draw on a wide variety of examples from different areas of application in science and technology of relevance across all cultures, nationalities and genders. You will analyse real world problems to reinforce the relevance of the lecture material that will provide you with a framework for lifelong learning in this area of knowledge. A combination of discussion, working on small real world problems and presenting solutions will promote creativity in problem solving, critical thinking skills and intellectual debate. To support the theoretical concepts lectured to you throughout the semester, a combination of hands-on computer laboratory sessions and practical classes that illustrate specific concepts in linear algebra will be included within your studies.

You will attend 3 hours of lectures and a 1-hour practical session per week.

Assessment

The assessment items in this unit are designed to determine your level of competency, measured against criteria, in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.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 Blackboard.

Assessment name: Problem Solving Task
Description: Your ability to solve problems in linear algebra will be assessed at a number of points during semester via quizzes, diagnostic tests/assignments and/or progress examinations.
Relates to objectives: 1 to 4.
Weight: 40%
Internal or external: Internal
Group or individual: Group with Individual Component
Due date: Throughout Semester

Assessment name: Examination (Theory)
Description: End of semester examination.
Relates to objectives: 1, 2 and 4.
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: Exam Period

Academic Honesty

QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.

A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.

Resource materials

Texts:
To be confirmed. Please check announcements on Blackboard.

Other References:
1. Leon S (2009) Linear Algebra with Applications, 8th Edition, Pearson Education
2. Leon S (2009) Student Study Guide, Linear Algebra with Applications, 8th Edition, Pearson Prentice Hall
3. Lay D. (2012) Linear Algebra and Its Applications, 4/E, Pearson.
4. Poole D. (2011) Linear Algebra A Modern Introduction, 3/E, Brooks/Cole.
5. Anton H. and Rorres C. (2010) Elementary Linear Algebra: Applications Version, 10th Edition, Wiley
6. Strang G. (2009) Introduction to Linear Algebra, Fourth Edition, Wellesley-Cambridge Press.
7. Larson R. & Falvo D. C. (2009) Elementary Linear Algebra 6/E, Houghton Mifflin

Many other good references pertaining to the topic are available in the Library.

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 labs. Emergency exits and assembly areas will be pointed out in the first few lectures. Students are referred to the University policy on health and safety.

http://www.hrd.qut.edu.au/healthsafely/healthsafe/index.jsp

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

Last modified: 16-Oct-2012