ALGEBRA, LINEAR CODES AND AUTOMATA

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Overview

This subject, delivered in two parallel streams, introduces a range of concepts from number theory, group theory and formal language theory tying the ideas together through some practical applications. The number and group theory stream first considers modular arithmetic and a range of number theoretic results that underpin RSA public key encryption before moving on to a general group theory module with applications to symmetries and error correcting codes. The formal language stream deals with regular expressions, regular languages and their relationship with automata. Context free languages are studied along with their related automa. An introductory discussion of Turing machines leads to model for computation.

Portfolio

Science, Health & Engineering (Pre 2022)

School

Subject coordinator

Michael Payne

Subject type

Undergraduate

Year level

Year Level 2 - UG

AQF level

Level 6 - Advanced Diploma

Available as elective

Yes

Available to study abroad / exchange students

Yes

Capstone subject
Capstones provide students with a way of integrating and applying knowledge and skills gained throughout their course.

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Subject instances

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Career ready

Work based learning (placement):No

Subject intended learning outcomes

On successful completion you will be able to:

Perform transformations and calculations involving various categories of finite automata.

Demonstrate equivalences between particular formal languages and finite automata.

Perform calculations in modular arithmetic and apply number theoretic results in a range of applications.

Demonstrate whether a structure is a group and use structural properties to determine whether or not two structures are isomorphic.

Perform composition of cycles in cyclic groups and find the symmetry group of geometric objects.

Perform mathematical calculations relevant to cryptography.

Communicate an understanding of concepts in algebra and theoretical computer science using both words and mathematical notation in a precise and succinct manner.

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