MATH3170
10 units
3000 level
Course handbook
Description
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.
Availability2024 Course Timetables
Callaghan
- Semester 2 - 2024
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
• 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
Assumed knowledge
MATH2340 or MATH1220
Assessment items
In Term Test: In Term Test
Quiz: Quiz
Written Assignment: Essays/Written Assignments
Contact hours
Semester 2 - 2024 - Callaghan
Lecture-2
- Face to Face On Campus 3 hour(s) per week(s) for 13 week(s) starting in week 1
Course outline
Course outline not yet available.
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.