Course Title: Applied Linear Algebra

Part A: Course Overview

Course Title: Applied Linear Algebra

Credit Points: 12.00

Terms

Teaching Period(s)

MATH2311

City Campus

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 2 2016

MATH2311

City Campus

171H School of Science

Face-to-Face

Sem 2 2017,
Sem 2 2018,
Sem 2 2019,
Sem 2 2020

Course Coordinator: Dr Graham Clarke

Course Coordinator Phone: +61 3 9925 3225

Course Coordinator Email: g.clarke@rmit.edu.au

Course Coordinator Location: 15.3.14

Pre-requisite Courses and Assumed Knowledge and Capabilities

To successfully complete this course, you are expected to have capabilities consistent with the completion of MATH1150. That is, you are expected to be able to identify and apply basic concepts of set theory, arithmetic, logic, proof techniques, binary relations, graphs and trees; and produce convincing arguments, conceive and/or analyse basic mathematical proofs and discriminate between valid and unreliable arguments. You are also expected to be concurrently developing capabilities consistent with the completion of MATH1144. That is, you are expected to be developing the ability to correctly recognise and apply the concepts of vectors; perform basic vector algebraic operations, including finding sum, scalar multiple, dot product and cross product of vectors; solve simultaneous linear equations; recognise and apply the concepts of matrices; perform basic algebraic operations on matrices, including finding sum, scalar multiple, transpose, matrix product and inverses; set up parametric equations for straight lines and equations for planes in space; and perform elementary row operations on matrices.

Course Description

Applied Linear Algebra introduces and studies operations and methods that are the fundamental tools of mathematicians and applied scientists. The course introduces the structure and properties of Linear Algebra (vector spaces and subspaces, linear independence, basis, kernel, dimension; inner products, linear transformations, eigenvalues, eigenvectors and diagonalisation) and the application of Linear Algebra to areas such as coding theory, network analysis, linear optimisation and Markov chains.

Maple, Mathematica, R and/or Excel will be used in lab sessions to illustrate the concepts and discuss their possible use in real life applications.

Objectives/Learning Outcomes/Capability Development

This course contributes to the following Program Learning Outcomes for BP083 Bachelor of Science (Mathematics), BP245 Bachelor of Science (Statistics) and BH119 Bachelor of Analytics (Hons):

Knowledge and technical competence:

• use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.

Problem-solving:

• synthesise and flexibly apply knowledge to characterise, analyse and solve a wide range of problems
• balance the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution.

Teamwork and project management:

• contribute to professional work settings through effective participation in teams and organisation of project tasks
• constructively engage with other team members and resolve conflict.

Communication:

• communicate both technical and non-technical material in a range of forms (written, electronic, graphic, oral) and tailor the style and means of communication to different audiences. Of particular interest is the ability to explain technical material, without unnecessary jargon, to lay persons such as the general public or line managers.

Information literacy:

• communicate and use data and information and evaluate its quality with respect to its authority and relevance.

On successful completion of this course, you should be able to:

• Describe and manipulate vector spaces, subspaces and their bases.
• Determine the kernel, image space and matrix representation of a linear transformation.
• Construct an orthonormal basis from a given basis and obtaining a basis for the orthogonal complement.
• Apply linear algebra tools to examples in coding theory or network analysis.
• Use linear and Boolean optimisation together with the basic tools for solving the problems that arise in modelling these techniques.
• Construct and apply Markov chains to practical problems.

Overview of Learning Activities

Key concepts will be explained and illustrated in detail in lectures. Supervised tutorials will build your capacity to use and apply the concepts for modelling and solving problems, to encourage you to think critically and analytically and provide feedback on your academic progress. Computer laboratory sessions will illustrate and experiment with key notions using software such as Maple, Mathematica, R or Excel. Working on your group project will provide you with the opportunity to learn, in detail, about a specific application of linear algebra. You are expected to undertake private study where you will work through the course material presented in class in addition to any homework problems.

Total study hours

Students will have 4 hours of formal contact per week, for 12 weeks, comprising 2 hours per week of face-to-face lectures and 2 additional hours per week which will alternate between a tutorial and a computer laboratory session. It is also expected that students undertake, on average, 4 hours per week of independent study of the lecture material, suggested problems and in-class exercises.

Overview of Learning Resources

You will be able to access course information and learning materials through myRMIT Studies (also known as Canvas). On Canvas you will have access to important announcements, staff contact details, the teaching schedule, online notes, assessment timelines, review exercises and past exam papers. You are advised to read your student e-mail account daily for important announcements. You should also visit myRMIT Studies at least once a day, as important announcements regarding the course will be often be made there, and all-important documents related to the course will be available there.

A library guide is available at: http://rmit.libguides.com/mathstats

Overview of Assessment

☒This course has no hurdle requirements.

The assessment will be a combination of hand-written work, computer generated output, group work and end-of-semester hand-written exams.

Two in-class tests (10% each) will assess your ability to apply analytic and problem-solving skills.

Weighting 20%

This assessment task supports CLOs 1, 2, 3 and 4.

Homework assignments will assess your ability to apply computer packages to problems in linear algebra.

Weighting 10%

This assessment task supports CLOs 1, 2, 3 and 4.

The group project will allow you to explore in depth one of the topics and present it to the class. It will assess technical skills as well as soft skills, particularly the ability to work in a team, to communicate and to use external sources of information.

Weighting 20%

This assessment task supports CLOs 1, 2, 3, 4 and 5.