The University of Newcastle, Australia
Available in 2020

Course handbook

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.


Availability2020 Course Timetables

Callaghan

  • Semester 1 - 2020

Learning outcomes

On successful completion of the course students will be able to:

1. Explain some of the concepts of number theory, a primary area of mathematics, using examples.

2. Apply mathematical ideas and concepts within the context of number theory.

3. Solve a range of problems in number theory.

4. Communicate number-theoretic techniques to a mathematical audience.


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

Quiz: Quizzes

Written Assignment: Essays/Written Assignments


Contact hours

Callaghan

Lecture

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