Macquarie University

For convenience these notes have been classified according to their level. The Elementary notes require very little prerequiste knowledge and therefore are suitable for adults who have largely forgotten the mathematics they learnt at school.

However their main use is for university students whose high school mathematics is insufficient for regular first year university mathematics courses.

They are not really suitable as school texts as they require a certain level of maturity. That is not to say that a bright school pupil couldn't effectively make use of them.

These notes have been used over many years for various courses at Macquarie University. We have been quite innovative with course content here and, while we mostly teach fairly standard material we also include an elementary account of some material that's usually only taught in advanced postgraduate courses.

In addition some of the content, although closely related to standard material, does not appear elsewhere. For example, some of the techniques presented here are simpler or more powerful than the ones you normally find in textbooks.

Though mathematically rigorous, the style in these notes is informal and there are numerous "stories" to illustrate the concepts. There are also many exercises with solutions.

While most of the sets of notes have undergone many revisions, a few are under construction and contain only a couple of chapters at this stage.

These notes were written by Christopher Cooper. Feel free to give feedback, particularly if you can point out errors, obscurities, or poor layout.

These notes are freely available to anybody, not just Macquarie students. But it would be appreciated if you make use of these notes and you are not a Macquarie student that you send me an email mentioning the fact that you are using them. Also it would be nice, if you live outside of Australia, that you send me a postcard of where you live!

You may also be interested in the Lecture Notes of William Chen. And you may wish to visit the website of Macquarie University Department of Mathematics.