University of Technology Sydney

68105 Algebra

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 2024 is available in the Archives.

UTS: Science: Mathematical and Physical Sciences
Credit points: 6 cp
Result type: Grade and marks

Requisite(s): 68102 Mathematics for Secondary Education Foundations
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 37233 Linear Algebra

Description

In this subject, students develop an understanding of the theory and skills in applying algebra and linear algebra.

Topics include solving systems of linear equations, defining and working with matrices, matrix algebra including inverses, determinants, elementary matrices, decomposition methods for matrices including LU factorisation, diagonalisation and singular value decompositions, vector spaces and subspaces, span, dimension and linear independence, applications to solving second order and coupled systems of differential equations, complex numbers.

Subject learning objectives (SLOs)

Upon successful completion of this subject students should be able to:

1. apply fundamental concepts of mathematics to solve problems involving linear algebra
2. apply knowledge of the conceptual development of linear algebra to explain procedures and calculations
3. use mathematical terminology and symbols to define concepts
4. apply mathematical knowledge and skills in a variety of situations, in both familiar and new contexts
5. communicate mathematical knowledge clearly, logically and critically

Contribution to the development of graduate attributes

1.0 Disciplinary knowledge

The online contents and tutorial activities will allow students to develop practical and theoretical skills in Algebra.

2.0 Research, inquiry and critical thinking

The collaborative approach to problem formulations and solutions used in the tutorials helps students develop skills in identifying and evaluating alternative approaches to solving problems.

4.0 Reflection, innovation, creativity

The micro-teaching assessment task requires students to think about how to present material creatively and engagingly, and reflect afterwards on its effectiveness in communicating and teaching the concepts.

5.0 Communication

Presentation of written and oral solutions to problems using appropriate professional language is emphasised in the tutorials and assessment. All assessment tasks require the appropriate presentation of information, reasoning and conclusions and require students to gain meaning from instructions (written or verbal) and problem statements.

Teaching and learning strategies

This subject requires engaging with content (online via Canvas) and actively participating in a 2 hour tutorial once a week. There is also about 2-3 hours of written homework each week. As students engage in the interactive and collaborative tutorial sessions they are provided with formative feedback on the comprehension of concepts, and on skill development from both peers and the tutor.

Through the weekly homework tasks, students will build their problem solving and mathematical skills. Students will also develop a high standard of written communication to explain their solutions and the steps taken to arrive that those solutions.

In the Microteach assessment components (run as part of the weekly tutorials) students will learn the professional skills of presenting mathematical explanations to their peers and tutor, where students will demonstrate their discipline knowledge in the context of professional practice. Oral and written communication to a target audience, as well as mathematical interest and correctness, is key.

Feedback on microteaching will be provided via discussions in the tutorials with peers and the tutor, and some written submissions (uploading a short report, copy of presentation slides, and final written solutions).

Content (topics)

  • Systems of linear equations;
  • Determinant, elementary matrices;
  • LU factorisation;
  • Eigenvectors and eigenvalues;
  • Linear spaces and subspaces; linear dependence/independence;
  • Basis, dimensions;
  • Linear transformations.

Assessment

Assessment task 1: Understanding and skills assessments

Intent:

This assessment task contributes to the development of the following graduate attributes:

1. Disciplinary Knowledge

2. Research, inquiry and critical thinking

4. Reflection, Innovation, Creativity

Objective(s):

This assessment task addresses subject learning objective(s):

1, 3, 4 and 5

This assessment task contributes to the development of course intended learning outcome(s):

1.1, 2.1 and 4.1

Type: Quiz/test
Groupwork: Individual
Weight: 35%
Criteria:
  1. Correct application of knowledge and procedures of linear algebra;
  2. Correct choice of problem solving strategies and procedures;
  3. Appropriate and correct implementation of solutions using standard software;
  4. Correct application of linear algebraic techniques to problems arising in a business, industry, commecial or social context;
  5. Clear communication using correct mathematical terminology.

Assessment task 2: Micro-teaching

Intent:

This assessment task contributes to the development of 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, 4 and 5

This assessment task contributes to the development of course intended learning outcome(s):

1.1, 2.1, 4.1 and 5.1

Type: Demonstration
Groupwork: Group, individually assessed
Weight: 35%
Length:

To be advised on Canvas

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 task contributes to the development of the following graduate attributes:

2. Research, inquiry and critical thinking

4. Reflection, Innovation, Creativity

Objective(s):

This assessment task addresses subject learning objective(s):

1, 2, 3, 4 and 5

This assessment task contributes to the development of course intended learning outcome(s):

2.1 and 4.1

Type: Quiz/test
Groupwork: Individual
Weight: 30%
Criteria:
  1. Correct application of knowledge and procedures of linear algebra;
  2. Quality of explanation of fundamental concepts and proofs of key results;
  3. Correct choice of problem solving strategies;
  4. 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.

Recommended texts

Any textbook with title "Linear Algebra" should be useful for the first half of this subject.

For the second half we will make use of the textbook:

Title: Linear Algebra Done Right
Author: Axler, Sheldon
ISBN: 3319110802
Edition: 3rd ed. 2015

This is available as free PDF via the UTS Library (see Canvas for a link).