Number Theory

Description

Number Theory, which deals with properties of the positive integers, is one of the oldest branches of mathematics. Many of its problems are very easy to understand, but some such as Fermat's famous "Last Theorem" are devilishly hard to solve. In recent years, old ideas have found practical applications.

This course provides an introduction to the important basic topics of number theory: prime numbers, factorisation, congruence and diophantine equations. These topics are treated from a modern point of view, emphasising the underlying algebraic structure. They provide the necessary background for a brief introduction to modern cryptography.

Availability

Callaghan Campus

  • Semester 2 - 2015

Learning Outcomes

1. Hold an in-depth knowledge of a primary branch of mathematics

2. Demonstrate how many of the abstract ideas they have previously studied can be used

3. Develop problem-solving and communication skills

Content

  • Primes and divisibility
  • Congruences and their applications
  • Quadratic residues
  • Diophantine equations
  • Applications to other areas, including cryptography

Assumed Knowledge

MATH2320 or MATH2330

Assessment Items

Formal Examination: Examination

Presentation: Presentation

Written Assignment: Essays/Written Assignments

Contact Hours

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term