ALGEBRA, LINEAR CODES AND AUTOMATA
MAT2ALC
2015
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.
School: School Engineering&Mathematical Sciences
Credit points: 15
Subject Co-ordinator: Tomasz Kowalski
Available to Study Abroad Students: Yes
Subject year level: Year Level 2 - UG
Exchange Students: Yes
Subject particulars
Subject rules
Prerequisites: MAT1DM or MAT1NLA
Co-requisites: N/A
Incompatible subjects: N/A
Equivalent subjects: N/A
Special conditions: N/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.
- Related graduate capabilities and elements:
- Critical Thinking(Critical Thinking)
- Discipline-specific GCs(Discipline-specific GCs)
02. Demonstrate equivalences between particular formal languages and finite automata.
- Activities:
- Students practice these techniques in practice classes and assignments.
- Related graduate capabilities and elements:
- Critical Thinking(Critical Thinking)
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.
- Related graduate capabilities and elements:
- Creative Problem-solving(Creative Problem-solving)
- Discipline-specific GCs(Discipline-specific GCs)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
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.
- Related graduate capabilities and elements:
- Writing(Writing)
- Critical Thinking(Critical Thinking)
- Creative Problem-solving(Creative Problem-solving)
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.
- Related graduate capabilities and elements:
- Discipline-specific GCs(Discipline-specific GCs)
06. Perform mathematical calculations relevant to cryptography.
- Activities:
- Students practice these techniques in practice classes and assignments.
- Related graduate capabilities and elements:
- Discipline-specific GCs(Discipline-specific GCs)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
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.
- Related graduate capabilities and elements:
- Writing(Writing)
Melbourne, 2015, Semester 2, Day
Overview
Online enrolment: Yes
Maximum enrolment size: N/A
Enrolment information:
Subject Instance Co-ordinator: Tomasz 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.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| One 3-hour examination | 70 | 01, 02, 03, 04, 05, 06, 07 | |
| Written Assignments | 30 | 01, 02, 03, 04, 05, 06, 07 |