# ALGEBRA, LINEAR CODES AND AUTOMATA

MAT2ALC

2021

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.

SchoolEngineering and Mathematical Sciences

Credit points15

Subject Co-ordinatorTomasz Kowalski

Subject year levelYear Level 2 - UG

Available as ElectiveNo

Learning ActivitiesN/A

Capstone subjectNo

## Subject particulars

### Subject rules

PrerequisitesMAT1DM OR MAT1NLA

Co-requisitesN/A

Incompatible subjectsMAT2AAL

Equivalent subjectsN/A

Quota Management StrategyN/A

Quota-conditions or rulesN/A

Special conditionsN/A

Minimum credit point requirementN/A

Assumed knowledgeN/A

Career-focusedNo

Work-based learningNo

Self sourced or Uni sourcedN/A

Entire subject or partial subjectN/A

Total hours/days requiredN/A

Location of WBL activity (region)N/A

## Graduate capabilities & intended learning outcomes

### Intended Learning Outcomes

01. Perform transformations and calculations involving various categories of finite automata.
02. Demonstrate equivalences between particular formal languages and finite automata.
03. Perform calculations in modular arithmetic and apply number theoretic results in a range of applications.
04. Demonstrate whether a structure is a group and use structural properties to determine whether or not two structures are isomorphic.
05. Perform composition of cycles in cyclic groups and find the symmetry group of geometric objects.
06. Perform mathematical calculations relevant to cryptography.
07. Communicate an understanding of concepts in algebra and theoretical computer science using both words and mathematical notation in a precise and succinct manner.

## Subject options

Select to view your study options…

Start date between: and    Key dates

## Melbourne (Bundoora), 2021, Semester 2, Day

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Subject Instance Co-ordinatorTomasz Kowalski

### Class requirements

LectureWeek: 0 - 0
Two 1.00 hour lecture per week on weekdays during the day from week 0 to week 0 and delivered via face-to-face.

PracticalWeek: 0 - 0
Two 1.00 hour practical per week on weekdays during the day from week 0 to week 0 and delivered via face-to-face.

### Assessments

Assessment elementCategoryContributionHurdle% ILO*

One 3-hour examination

Central examIndividualNo70 SILO1, SILO2, SILO3, SILO4, SILO5, SILO6, SILO7

Written Assignments (1500 word equivalent total)

AssignmentIndividualNo30 SILO1, SILO2, SILO3, SILO4, SILO5, SILO6, SILO7