Handbook 1996 : Faculty of Science (Volume 4 page 213)
Mathematics subject : Next:618-321 | Prev:618-311 | Search | Help
618-312 "Number Theory" appears differently in several places - choose the one you want:
1. Mathematics, Faculty of Science (v4, p213) : Next:618-321 | Prev:618-311
Credit points: 15.0
Coordinator: Dr W D Neumann
Prerequisite: One of Mathematics 618-111, 618-121, 618-142, 618-200, 618-211; or Mathematics 101 (1995 Handbook).
Contact: 39 lectures (three a week)
Timetable: Second semester
Objectives:
On completion of this subject, students should:Comprehend:
- elementary concepts of divisibility;
- basic theory and use of congruences;
- properties of powers of elements in congruences, particularly Euler's theorem;
- the definition and use of primitive roots;
- the law of quadratic reciprocity;
- basic properties of continued fractions and some applications;
- applications of all of the above to primality testing, factorization algorithms and cryptanalysis.
Have developed:
- an ability to perform the algorithms inherent in the course material;
- the ability to understand and to present proofs related to the course material.
Appreciate:
- the extent and uses of elementary number theory; its applicability in other parts of mathematics; its potential for application outside of mathematics.
Content:
Factorisation, primes, greatest common divisors. Congruences. Primitive roots; quadratic reciprocity; continued fractions, Pell's equation. Compositeness testing and factorisation. Applications to cryptanalysis.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
1. Mathematics, Faculty of Science (v4, p213) : Next:618-321 | Prev:618-311
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-331 | Prev:618-311
Credit points: 15.0
Coordinator: Dr W D Neumann.
Prerequisite: One of Mathematics 618-111, 618-121, 618-142, 618-200, 618-211; or Mathematics 101 (1995 Handbook. )
Contact: 39 lectures (three each week)
Timetable: Second semester.
Objectives:
On completion of this subject, students should:Comprehend:
- elementary concepts of divisibility;
- basic theory and use of congruences;
- properties of powers of elements in congruences, particularly Euler's theorem;
- the definition and use of primitive roots;
- the law of quadratic reciprocity;
- basic properties of continued fractions and some applications;
- applications of all of the above to primality testing, factorization algorithms and cryptanalysis.
Have developed:
- an ability to perform the algorithms inherent in the course material;
- the ability to understand and to present proofs related to the course material.
Appreciate:
- the extent and uses of elementary number theory; its applicability in other parts of mathematics; its potential for application outside of mathematics.
Content:
Factorisation, primes, greatest common divisors. Congruences. Primitive roots; quadratic reciprocity; continued fractions, Pell's equation. Compositeness testing and factorisation. Applications to cryptanalysis.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
* Note that CONTACT, PREREQUISITES differs from the maintainer's version above. A log of variations is available.
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-331 | Prev:618-311
Status: Official 1996 Date created: Oct 9 1995 Last modified: Oct 9 1995 Authorised by: Academic Registrar Email enquiries: Course_Information@registrar.unimelb.edu.au
Maintained by: Dept. of Mathematics, Faculty of Science.
Copyright © University of Melbourne 1995,1996.