ALGEBRA, LINEAR CODES AND AUTOMATA

MAT2ALC

2020

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: Engineering and Mathematical Sciences (Pre 2022)

Credit points: 15

Subject Co-ordinator: Tomasz Kowalski

Available to Study Abroad/Exchange Students: Yes

Subject year level: Year Level 2 - UG

Exchange Students: No

Available as Elective: No

Learning Activities: N/A

Capstone subject: No

Subject particulars

Subject rules

Prerequisites: MAT1NLA OR MAT1DM

Co-requisites: N/A

Incompatible subjects: MAT2AAL

Equivalent subjects: N/A

Quota Management Strategy: N/A

Quota-conditions or rules: N/A

Special conditions: N/A

Minimum credit point requirement: N/A

Assumed knowledge: N/A

Career Ready

Career-focused: No

Work-based learning: No

Self sourced or Uni sourced: N/A

Entire subject or partial subject: N/A

Total hours/days required: N/A

Location of WBL activity (region): N/A

WBL addtional requirements: N/A

Graduate capabilities & intended learning outcomes

Graduate Capabilities

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.

Melbourne (Bundoora), 2020, Semester 2, Day

Overview

Online enrolment: Yes

Maximum enrolment size: N/A

Enrolment information: N/A

Subject Instance Co-ordinator: Tomasz 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 element	Comments	Category	Contribution	Hurdle	%	ILO*
One 3-hour examination	N/A	N/A	N/A	No	70	SILO1, SILO2, SILO3, SILO4, SILO5, SILO6, SILO7
Written Assignments (1500 word equivalent total)	N/A	N/A	N/A	No	30	SILO1, SILO2, SILO3, SILO4, SILO5, SILO6, SILO7