Warning: The information on this page is indicative. The subject outline for a particular session, location and mode of offering is the authoritative source of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.
Subject handbook information prior to 2023 is available in the Archives.UTS: Science: Mathematical and Physical Sciences
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 35101 Introduction to Linear Dynamical Systems OR 37131 Introduction to Linear Dynamical Systems OR 33230 Mathematics 2 OR 33290 Statistics and Mathematics for Science
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 35212 Computational Linear Algebra
Description
In this subject, students develop an understanding of the theory of linear algebra, applications of linear algebra, and some of the main computational techniques used in these applications. Topics include systems of linear equations (LU factorisation and iterative methods); vector spaces; inner product spaces; Gram-Schmidt orthogonalisation, QR decomposition; approximation theory: least squares and orthogonal polynomials; the eigenvalue problem; singular value decomposition and applications.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | apply skills in theoretical and computational techniques of linear algebra to solve substantial problems; |
|---|---|
| 2. | understand, explain and prove the principal ideas and results which underpin the study of linear algebra; |
| 3. | choose the most appropriate technique from those studied to solve a problem in linear algebra; |
| 4. | contribute constructively and effectively to the conduct and outcome of a team project; |
| 5. | implement computational algorithms in linear algebra problems using Mathematica |
| 6. | find and analyse real world applications of linear algebra |
| 7. | describe and apply relevant mathematical aspects of the use of linear algebra in an area of professional practice or social interest, |
| 8. | communicate clearly in the mathematical terminology of linear algebra |
| 9. | describe relevant mathematical aspects of real world applications of linear algebra in language appropriate to a lay audience |
Contribution to the development of graduate attributes
The ideas and techniques introduced in this subject are further developed and applied in a wide range of other subjects in the areas of differential equations, mathematical methods, optimisation and statistics, all of which underpin the professional and research practice of mathematical techniques. The subject is taught with an emphasis on fundamental basics as well as practical approaches, with the workshop classes and computer laboratories serving as an introduction to the routine use of the relevant approaches for solving mathematical problems, and also to develop skills for the use of computational systems in professional mathematical practice.
The subject contributes to strengthening the attributes of graduates in:
1. Disciplinary knowledge
2. Research, inquiry and Critical Thinking
3. Professional, Ethical and Social Responsibility
4. Reflection, Innovation, Creativity
5. Communication
Teaching and learning strategies
One 2-hour lecture per week is delivered online via ZOOM and recorded. One 2-hour workshop per week (“Cmp”), multiple options for enrolment, is delivered on campus. The on-campus workshops will not be recoreded. An online recorded workshop will be provided for students who are not able to attend face-to-face classes. All the relevant teaching materials will be published on Canvas. It is recommended that classes each week should be supported by at least five hours per week of individual or group study. lndividual assignments are intended to provide ongoing training and feedback on the progress in the subject.
Content (topics)
- Systems of linear equations;
- Linear spaces and subspaces; linear dependence/independence;
- Basis, dimensions, coordinate systems;
- Linear transformations, eigenvectors and eigenvalues;
- Orthogonality, projections, orthogonalisation and orthogonal decomposition;
- Least-squares solutions;
- Quadratic forms;
- LU factorisation; iterative methods.
Assessment
Assessment task 1: Individual assignments
| Intent: | This assessment item addresses the following graduate attributes:1. Disciplinary Knowledge. 2. Research, inquiry and critical thinking. 3. Professional, ethical and social responsibility. 4. Reflection, Innovation, Creativity. 5. Communication. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s):1, 2, 3, 7 and 8This assessment task contributes to the development of course intended learning outcome(s):1.1, 2.2, 3.1, 4.3 and 5.3 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 16% |
| Length: | 2 hours on campus |
| Criteria: | Correct application of knowledge and procedures of linear algebra;Correct choice of problem solving strategies and procedures;Appropriate and correct implementation of solutions using standard software;Correct application of linear algebraic techniques to problems arising in a business, industry, commecial or social context;Clear communication using correct mathematical terminology. |
Assessment task 2: Mastery tests
| Intent: | This assessment item addresses the following graduate attributes:1. Disciplinary Knowledge. 2. Research, inquiry and critical thinking. 4. Reflection, Innovation, Creativity. 5. Communication. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s):1, 2, 3 and 8This assessment task contributes to the development of course intended learning outcome(s):1.3, 2.2, 4.3 and 5.1 |
| Type: | Quiz/test |
| Groupwork: | Individual |
| Weight: | 34% |
| Length: | 30 minutes each of the 8 tests |
| Criteria: | Correct application of knowledge and procedures of linear algebra;Quality of explanation of fundamental concepts and proofs of key results;Correct choice of problem solving strategies;Clear communication using correct mathematical terminology. |
Assessment task 3: Final exam
| Intent: | This assessment item addresses the following graduate attributes:1. Disciplinary Knowledge. 2. Research, inquiry and critical thinking. 4. Reflection, Innovation, Creativity. 5. Communication. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s):1, 2, 3 and 8This assessment task contributes to the development of course intended learning outcome(s):1.3, 2.3, 4.3 and 5.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 50% |
| Length: | Two hours, on campus |
| Criteria: | Correct application of knowledge and procedures of linear algebra;Quality of explanation of fundamental concepts and proofs of key results;Correct choice of problem solving strategies;Clear communication using correct mathematical terminology. |
Minimum requirements
In order to pass this subject, a final result (the sum of all the marks with all the assessment tasks) of 50% or more must be achieved.
In addition, the final exam (assessment task 3) requires at least 40% of the exam marks (that is, at least 20% of the total marks in this subject, should be collected at the final exam).
If the 40% threshold is not reached at the final exam, an X grade fail will be awarded for the subject, irrespective of the overall mark.
Recommended texts
Lay, D. C. Linear Algebra and Its Applications, 4th Edition, Pearson, 2012.
Craddock M., and Langtry, T. N. Notes on Computational Techniques in Linear Algebra, UTS, 2008(9).
References
- Anton, H. & Rorres, C. Elementary Linear Algebra (Applications Version), 10th Edition, John Wiley & Sons, 2010.
- Strang, G. Linear Algebra and its Applications, Harcourt Brace Jovanovich.
- Johnson, E. Linear Algebra with Mathematica, Brooks Cole, 1995.
- S.S. Rao. Applied Numerical Methods for Scientists and Engineers, Prentice Hall, 2002. ISBN: 0-13-089480-X
- W. Cheney and D. Kincaid. Numerical Methods and Computing, 7th Edition. Brooks-Cole 2012.
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