# ANU Extension

ANU Extension provides an enhanced learning experience for year 11 and 12 students in ACT schools and colleges. ANU Extension students will enrol in an ANU academic award program. Further information is available on the ANU Extension website.

## Mathematics course

The mathematics classes are taught by specially selected teachers. The syllabus and course materials are developed in collaboration with ANU academics who also give special lectures. Students and teachers have full access to ANU library and other facilities. Early admission to ANU and University credit are associated with this program.

Students studying mathematics undertake a Minor at ANU and normally combine this with a Major-Minor from their home college/school to take out a Double Major.

### Overview

The goal is to introduce students to contemporary mainstream 20th and 21st century mathematics. This is not an easy task. Mathematics is a giant scaffolding which normally needs to be constructed in one's mind before one can ascend to appreciate the view. Calculus and algebra learnt in college are essential parts of this scaffolding and are fundamental for further mathematics, but most of this material was discovered in the 18th century.

In the course we will take a few short cuts and only use calculus at a later stage. We will investigate some very exciting and useful modern mathematics and get a feeling for "what mathematics is all about". The mathematics which students will see in this course is usually not covered until higher level courses in second or third year at University. Naturally, it is then studied in much greater depth. The way we will proceed is by studying carefully chosen parts and representative examples from various areas of mathematics which illustrate important and general key concepts. In the process students will have the opportunity to gain a real understanding and feeling for the beauty, utility and breadth of mathematics.

### Texts

The background text is *The Heart of Mathematics* by Burger and Starbird. It is one of a small number of texts intended to convey a feeling for the theory and applications of contemporary mathematics at an early stage in one's studies. However, it is directed at a different group of students - undergraduate students in the United States with little mathematics background (eg no calculus) who might take no other mathematics courses in their studies. Despite its apparently informal style, *The Heart of Mathematics* introduces a significant amount of interesting contemporary mathematics. The arguments are usually complete (and if not, this is indicated), correct and well motivated. They are often done by means of studying particular but important examples which bring out the main ideas of the general setting.

The self contained notes An Introduction to Contemporary Mathematics (PDF, 7.3MB) parallel and extend the development in the background text and provide a higher level and more extensive treatement of the material there. They are the text for the course and are also intended as a resource for teachers. The best approach would be for students to read both texts, as suggested by the teachers involved.