MAT3091

Number theory

Not offered in 1999

Coordinator: Dr Paul Cally

4 points - Two 1-hour lectures per week - First semester - Clayton - Prerequisites: MAT2020 - Prohibitions: MAP3051

Objectives On the completion of this subject, students will be able to compute the greatest common divisor of two numbers and establish some of its basic properties; demonstrate the existence of an infinite collection of primes and establish some basic results concerning prime numbers; solve congruences and apply congruence theory to the solution of Diophantine equations; calculate residue systems, establish Euler's Theorem and Wilson's Theorem; solve simultaneous linear congruences and polynomial congruences; establish properties of quadratic residues and develop a familiarity with the Legendre symbol and Jacobi symbol; prove Gauss's Law for quadratic reciprocity, and use algebraic numbers to solve problems about the integers.

Synopsis Primes, unique factorisation and greatest common divisor. Modular arithmetic, quadratic residues and primality testing. Algebraic concepts in number theory. Public key cryptosystems.

Assessment Examination (2 hours): 70% - Assignments: 30%

Recommended texts

Niven I, Zuckerman H S and Montgomery H The theory of numbers Wiley, 1991

Back to the 1999 Science Handbook