620-351 Number Theory

Note

Students may only gain credit for one of 620-351, 618-351 (1997 Handbook), 618-312 (1996 Handbook).

Credit Points

Coordinator

Prerequisites

One of 620-111, 620-121, 620-142, 620-200, 620-211 (1997 Handbook 618-111, 618-121, 618-142, 618-200, 618-211).

Semester

Contact

Subject Description

Students completing this subject 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 the ability to

• perform the algorithms inherent in the subject material;
• understand and present proofs related to the subject material;

and appreciate

• the extent and uses of elementary number theory;
• its applicability in other parts of mathematics;
• its potential for application outside of mathematics.

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 24 pages of written assignments and a three-hour end-of-semester written examination.