Mathematical Structures G (8938.3)

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Unit Outlines

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• Semester 1, 2018, ON-CAMPUS, BRUCE (182258) - View
• Semester 1, 2017, ON-CAMPUS, BRUCE (165932) - View
• Semester 1, 2016, ON-CAMPUS, BRUCE (154747) - View
• Semester 1, 2015, ON-CAMPUS, BRUCE (145830) - View

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Syllabus

This unit teaches number theory and an introduction to abstract algebra. Topics include modular arithmetic, prime numbers, groups, permutations, rings and fields. These topics have many applications to software engineering, information technology, and physics. The unit provides students with a thorough understanding of the basic techniques, together with an introduction to applications, particularly the RSA algorithm and geometric symmetry. We will cover finite field, the mathematical structures underpinning coding theory and cryptography.

Learning Outcomes

On successful completion of this unit, students will be able to:

1. Demonstrate understanding of the concepts and methods of number theory and abstract algebra;

2. Compute with the RSA algorithm and permutation groups, either manually and with mathematical software;

3. Recognise the range of applications of abstract algebra in modern information technology;

4. Analyse and solve contemporary problems of both theoretical and practical importance; and

5. Interpret and assess the real-life implications of these applications.

Assessment Items

Contact Hours

A 2-hour lecture and a 2-hour tutorial per week.

Prerequisites

6699 Discrete Mathematics G.

Corequisites

None.

Assumed Knowledge

None.

Equivalent Units

None.