# ALGEBRA, LINEAR CODES AND AUTOMATA

MAT2ALC

2018

Credit points: 15

## Subject outline

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.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorTomasz Kowalski

Available to Study Abroad StudentsYes

Subject year levelYear Level 2 - UG

Exchange StudentsYes

## Subject particulars

### Subject rules

Prerequisites MAT1DM or MAT1NLA

Co-requisitesN/A

Incompatible subjects MAT2AAL

Equivalent subjectsN/A

Special conditionsN/A

## Graduate capabilities & intended learning outcomes

01. Perform transformations and calculations involving various categories of finite automata.

Activities:
Students practice these techniques in practice classes and assignments.

02. Demonstrate equivalences between particular formal languages and finite automata.

Activities:
Students practice these techniques in practice classes and assignments.

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

Activities:
Students practice these techniques in practice classes and assignments.

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

Activities:
Students practice these techniques in practice classes and assignments.

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

Activities:
Students practice these techniques in practice classes and assignments.

06. Perform mathematical calculations relevant to cryptography.

Activities:
Students practice these techniques in practice classes and assignments.

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

Activities:
Mathematical writing is modelled in lectures and by use of model solutions to practice classes and assignments. Feedback is given on marked assignments on student's progress towards this ILO.

## Subject options

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Start date between: and    Key dates

## Melbourne, 2018, Semester 2, Day

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorTomasz Kowalski

### Class requirements

Lecture
Two 1.0 hours lecture per week on weekdays during the day and delivered via face-to-face.

Practical
Two 1.0 hours practical per week on weekdays during the day and delivered via face-to-face.