Nature and Beauty of Mathematics

Curriculum Focus

Mathematics is the language of the universe, the language of science and engineering. It allows us to make better decisions about our daily lives and build a better world. At the same time, it is as much art as it is science, full of its own beauty and wonders.

In this unit students will be introduced to exciting and challenging topics outside the usual school curriculum. Examples include (but are not limited to) infinity and its fundamental role in modern mathematics, visualising higher dimensions, the golden ratio and the Fibonacci numbers in nature, the mathematics of optimal design (soap films, shortest networks, travelling salesman problem), 3-dimensional manifolds as the possible shapes of our universe, the nature of numbers (primes, codes and cryptography), fractals, mathematical paradoxes, and the mathematics of card shuffling and magic tricks.

This unit is intended for students in Year 1 at John Monash Science School, but is open to all students at JMSS. Other than Year 9 Mathematics, there are no prerequisites, however a strong understanding and enthusiasm for mathematics is expected.

Learning Outcomes

In this course, students will gain an understanding of what it means to be a mathematician by developing skills in experimentation, visualisation and communication of complex mathematical theories. They will learn to appreciate the nature, power and beauty of mathematics. They will use mathematics as a universal key to making sense of the world, a key that enables them to master any other subject or skill.

Central to mathematics is problem solving. Students will be given a wide variety of problems and, on completion of this course, they will be expected to articulate both their solutions and their processes to answering questions. Specifically, students will be able to use and analyse real data to make informed predictions, calculate the aesthetic properties of nature and social constructs, and describe mathematics in the context of history and culture. Students will work individually and collaboratively on topics of personal interest and develop the skills to effectively communicate and present mathematical understanding. Opportunities will be provided to present to the school community, university academics and the general public.

Assessment

Explorative tasks

Research projects

Semester exam