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PMTH338 Number Theory

Updated: 15 January 2013
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 BMath/BTeach or candidature in a postgraduate award in the School of Environmental and Rural Science or School of Science and Technology
Co-requisites None
Restrictions None
Notes None
Combined Units None
Coordinator(s) Yihong Du (ydu@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
Title Exam Length Weight Mode No. Words
Assignments 30%
Assessment Notes
6 problem-based assignments
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 2, 3, 4 GA: 1, 2, 6
Final Examination 2 hrs 70%
Relates to Learning Outcomes (LO) and Graduate Attributes (GA)
LO: 1, 2, 3, 4 GA: 1, 2, 6

Learning Outcomes (LO) Upon completion of this unit, students will be able to:
  1. understand the rigorous concept of integers, including the fundamental theorem of number theory;
  2. understand and apply the concept of congruences;
  3. understand the principle of RSA cryprography; and
  4. understand the concept of quadratic residues.

Graduate Attributes (GA)
Attribute Taught Assessed Practised
1 Knowledge of a Discipline
Embedded in problem-solving skills. Demonstrated in lectures, practised and applied in tutorials, assessed in problem-based assignment tasks and exams. 		True True True
2 Communication Skills
The student will be encourgaed to participate actively in discussion during lectures and tutorials. Written communications skills, particularly with regard to construction and presentation of logical expositions and arguments, will be taught and assessed. 		True True True
4 Information Literacy
The student will be guided in the use of online resources, library and internet access to recommended references, particularly in conjunction with assignment tasks. 		True
5 Life-Long Learning
The student will discover the breadth of the discipline through this introductory unit, and will become aware of it's ongoing development as a tool of higher research. 		True
6 Problem Solving
The student will encounter in this unit a field of knowledge that is intensely problem-based, and will acquire skill in connecting ideas within a network of logical relationships. A high emphasis will be placed on the development of analytical and deductive reasoning. 		True True True
   

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