Problems and Proofs

Semester Elective Unit

Prerequisites

Year 9 Mathematics, with a B average or higher, or Year 9 Mathematics A

Course Description

This course provides a rich experience of where the key discoveries in mathematics have come from historically and their applications to science, engineering and computing. Students become familiar with the process of generalisation, conjecture and proof, and engage in non-routine problems to explore the skills of a mathematician.

Essential Questions

How does mathematics relate to science, engineering and computing?
How did some of the big ideas in mathematics develop over time?
What are the key problems mathematics is still trying to solve?
How can we systematically generalise solutions to a problem to develop conjectures and form irrefutable proofs?

Areas of Study

Generalisations, Conjectures and Proofs

Investigate the process of generalisation and hypothesis or conjecture when solving problems.
Develop an understanding of the notation, form and uses of a variety of proofs.
Implement mathematical proof in a student led investigation.

Applications of Mathematics in Science, Engineering and Computing

An introduction to complex numbers and their connections to engineering.
An introduction to binary and the connections between mathematics and computing.
Applications of statistics and probability in science.

History of Mathematics

Investigate some historical techniques for arithmetic algorithms.
Investigate the life, work and influence of a notable mathematician.
Develop an understanding of how mathematical ideas have developed over time.
Develop an appreciation for how social, cultural and historical factors have influenced the development of mathematics.
Understand how mathematics contributed to society and human culture.

Assessment