PMTH338 Number Theory

Updated: 30 January 2017
Credit Points 6
Offering
Responsible Campus Teaching Period Mode of Study
Armidale Trimester 1 Off Campus
Armidale Trimester 1 On Campus
Intensive School(s) None
Supervised Exam There is a UNE Supervised Examination held at the end of the teaching period in which you are enrolled.
Pre-requisites 12cp from PMTH212 or PMTH213 or AMTH250 or MATH260 or STAT261 or candidature in a postgraduate award
Co-requisites None
Restrictions None
Notes None
Combined Units None
Coordinator(s) Jelena Schmalz (jschmalz@une.edu.au)
Unit Description

This unit will emphasise the importance of proof in mathematics. Topics include: prime numbers and factorisation of integers; congruences; application to public key cryptography; primitive roots; primality tests; quadratic residues and reciprocity; some nonlinear Diophantine equations.

Important Information

Where calculators are permitted in examinations, it must be selected from an approved list, which can be accessed from the Further Information link below.

Further information

Recommended Material
Optional

Text(s):

Note: Recommended material is held in the University Library - purchase is optional

Elementary Number Theory and its Applications

ISBN: 9780321500311
Rosen, K.H., Addison-Wesley 6th ed. 2008

Note: The 5th ed. (ISBN 9780321237071) is also acceptable.

Text refers to: Trimester 1, On and Off Campus

Disclaimer Unit information may be subject to change prior to commencement of the teaching period.
Assessment
Must
Complete
Title Exam Length Weight Mode No. Words
Compulsory Assessment 1 5%
Assessment Notes

Problem-based assignment

Relates to Learning Outcomes (LO)

LO: 1, 2, 3, 4

Compulsory Assessment 2 7%
Assessment Notes

Problem-based assignment

Relates to Learning Outcomes (LO)

LO: 1, 2, 3, 4

Compulsory Assessment 3 7%
Assessment Notes

Problem-based assignment

Relates to Learning Outcomes (LO)

LO: 1, 2, 3, 4

Compulsory Assessment 4 7%
Assessment Notes

Problem-based assignment

Relates to Learning Outcomes (LO)

LO: 1, 2, 3, 4

Compulsory Assessment 5 7%
Assessment Notes

Problem-based assignment

Relates to Learning Outcomes (LO)

LO: 1, 2, 3, 4

Compulsory Assessment 6 7%
Assessment Notes

Problem-based assignment

Relates to Learning Outcomes (LO)

LO: 1, 2, 3, 4

Compulsory Final Examination 2 hrs 15 mins 60%
Assessment Notes

It is mandatory to pass this examination in order to pass this unit.

Relates to Learning Outcomes (LO)

LO: 1, 2, 3, 4


Learning Outcomes (LO) Upon completion of this unit, students will be able to:
  1. demonstrate a broad and coherent knowledge of the rigorous concept of integers, including the fundamental theorem of number theory;
  2. demonstrate a broad and coherent knowledge of, and apply the concept of, congruences; this will also demonstrate the ability to analyse, generate and transmit solutions to sometimes complex problems;
  3. demonstrate a broad and coherent knowledge of the principle of RSA cryprography; and
  4. demonstrate a broad and coherent knowledge of the concept of quadratic residues.