Overview

Prime numbers; Euclidean algorithm; congruences; the Euler totient function; the theorems of Fermat, Euler and Wilson; RSA public key cryptosystem; Chinese remainder theorem; quadratic reciprocity; primitive roots; factorisation and primality testing algorithms; secure key exchange; elliptic curve cryptography.

Offerings

S2-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Professor Ian Wanless

Unit Coordinator(s)

Professor Ian Wanless

Notes

This unit shares lectures and applied classes with MTH3137, but has separate assessment.

Learning outcomes

On successful completion of this unit, you should be able to:
1.

Apply the classification of numbers and analyse their relationships, such as divisibility and primality;

2.

Illustrate the power of pure mathematics and appreciate its beauty;

3.

Demonstrate an understanding of the fundamental concepts of number theory;

4.

Explain how thousands of years of pure mathematical developments have enabled secure electronic communication and commerce;

5.

Employ fundamental number theoretic algorithms for a range of tasks including exchanging information securely and testing whether numbers are prime.

Teaching approach

Active learning

Assessment

1 - Continuous assessment
2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions
Seminars

Workload requirements

Workload

Availability in areas of study

Mathematics
Pure mathematics
Applied mathematics
Statistics
Computer science (pending FIT approval).