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Handbook 1997 : Faculty of Science : Mathematics

618-351 Number Theory

Note:

It is not possible to gain credit for both 618-351 and 618-312 (1996 Handbook).

Credit Points:

15.0

Coordinator:

Dr M Shapiro

Prerequisite/s:

One of Mathematics 618-111, 618-121, 618-142, 618-200, 618-211; or Mathematics 101 (1995 Handbook).

Timetable:

Semester 1

Contact:

39 lectures (three a week)

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 law of quadratic reciprocity;

  • basic properties of continued fractions and some applications;

  • applications of all of the above to primality testing, factorisation 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.
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Handbook 1997 : Faculty of Science : Mathematics 
Status:                   OFFICIAL 1997
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Copyright © University of Melbourne 1997.