Modern Society is built on a foundation of algorithms underpinned by the ubiquity of the computer, a discrete device that depends upon its programmed ability to understand the integers. In this course, we will use a foundation of paradigmatic algorithms to underpin our understanding of the integers, focussing on their properties and representations and how that informs our understanding and intuition of the mathematical world.
This course provides an introduction to the important basic topics of number theory: prime numbers, factorisation, congruence and representation of numbers and Diophantine equations – via the use of fundamental algorithms.
Availability2021 Course Timetables
- Semester 2 - 2021
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.
• Primes and divisibility
• The Division algorithm, congruences and their applications
• The Euclidian algorithm, linear Diophantine equations
• The Chinese remainder theorem
• Representations of numbers: base and continued fraction
• Primitive roots and base expansions of rational numbers
• Theory of linear recurrences and rational functions
• Quadratic reciprocity
Formal Examination: Examination
Written Assignment: Essays/Written Assignments
Face to Face On Campus 3 hour(s) per Week for Full Term
The University of Newcastle acknowledges the traditional custodians of the lands within our footprint areas: Awabakal, Darkinjung, Biripai, Worimi, Wonnarua, and Eora Nations. We also pay respect to the wisdom of our Elders past and present.