MATHEMATICS NOTES For convenience these notes have been classified according to their level.
ELEMENTARY 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.
One of these sets of notes, however, is designed as an adult education type course. It is MATHEMATICS AT THE EDGE OF THE RATIONAL UNIVERSE. It presents a wide range of Mathematics with a minimum of technical detail and highlights how some parts of the subject are really wierd. Chapters include THE INFINITE, THE IMPOSSIBLE, THE UNCOMPUTABLE, THE UNDECIDABLE
HIGHER LEVELS Some of 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.
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. It would be appreciated if you make use of these notes, and find them useful, that you send me an email mentioning the fact that you are using them.
Send feedback to christopherdonaldcooper@gmail.com