Note: This is an archived Handbook entry from 2010.
|Dates & Locations:|| |
This subject has the following teaching availabilities in 2010:Semester 2, Parkville - Taught on campus.
Lectures and practice classes.
Timetable can be viewed here. For information about these dates, click here.
|Time Commitment:||Contact Hours: 3 x one hour lectures per week, 1 x one hour practice class per week |
Total Time Commitment: Estimated total time commitment of 120 hours
Any second year level subject from the Department of Mathematics and Statistics.
|Recommended Background Knowledge:||None|
|Non Allowed Subjects:||None|
|Core Participation Requirements:||It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their active and safe participation in a subject are encouraged to discuss this with the relevant subject coordinator and the Disability Liaison Unit.|
CoordinatorDr John Groves
Third Year Coordinator
This subject introduces the elementary concepts of divisibility; the basic theory and use of congruences; the properties of powers of elements in congruences, particularly Euler's theorem; the law of quadratic reciprocity; and basic properties of continued fractions and some applications. It develops applications of all of the above to primality testing, factorisation algorithms and cryptanalysis. This subject demonstrates the extent and uses of elementary number theory, its applicability in other parts of mathematics, and its potential for application outside of mathematics.
Topics include factorisation, primes and greatest common divisors; congruences; primitive roots; quadratic reciprocity; continued fractions and Pell's equation; compositeness testing and factorisation; and applications to cryptanalysis.
On completion of this subject, students should:
Two written assignments due early in semester and at the end of semester amounting to a total of up to 25 pages and a 50-minute written test held mid-semester (equally weighted, with a total of either 0% or 20%), and a 3-hour written examination in the examination period (80% or 100%). The relative weighting of the examination and total assignment plus test mark will be chosen so as to maximise the student's final mark.
|Breadth Options:|| |
This subject potentially can be taken as a breadth subject component for the following courses:
You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.
|Fees Information:||Subject EFTSL, Level, Discipline & Census Date|
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.
Bachelor of Science |
Mathematics and Statistics (Discrete Mathematics specialisation) |
Mathematics and Statistics (Pure Mathematics specialisation)
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