David Angell's Home Page

Irrationality and Transcendence in Number Theory


My text book Irrationality and Transcendence in Number Theory has been published by Taylor and Francis/CRC Press and is now available. It tells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century. It focuses on themes of irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, and relations between automata and transcendence. This book serves as a guide and introduction to number theory for advanced undergraduates and early postgraduates. Readers are led through the developments in number theory from ancient to modern times. The book includes a wide range of exercises, from routine problems to surprising and thought-provoking extension material.

Irrationality and Transcendence in Number Theory is now available from the publishers, or from the UNSW bookshop, or through any of the usual online retailers, for example, Book Depository and Amazon.

I am delighted to thank Helena Brusic of The Imagination Agency for her wonderful cover image!

an exponential sum I have been teaching in the School of Mathematics and Statistics at the University of New South Wales since 1989. In recent years I have attempted to provide printed notes for all of my higher year lecture courses, and have made them accessible on the web where possible. This page serves as the top level of an archive which I hope will ultimately make all of these notes available to users of the Internet.

As everyone knows, stealing documents by means of the Internet is perfectly simple. Please don't do it!!! These notes are copyright, which means that you are very welcome to view them online, and even to download them for your own personal use, but not to distribute them to other people without my permission. If you contact me by email I will be very glad to give this permission unless I see some good reason why I should not.

Please be aware that my lecture notes are intended to be used as a basis, not as a substitute, for lectures. There may be various spots at which the reader feels some extra explanation is needed: such additional material would have been given verbally in lectures. Nevertheless, enquiries and comments about the lecture notes are welcome, and may be emailed to me here.

For course enquiries, consult the School of Mathematics and Statistics website. Follow the link for current students or for future students.

The Bourbaki Ensemble

Read about The Bourbaki Ensemble, possibly the only orchestra in the world to be named after a polycephalic French mathematician!

The Bourbaki Ensemble

Orchestra 143

Also Orchestra 143, a classical chamber orchestra whose name involves a fundamental error in combinatorics.

Mathematics Lecture Notes

All of my lecture notes are available in PostScript and may be read using Ghostview or Gview or GV. If you are a student at UNSW and are reading this through your account at the School of Mathematics and Statistics then one of these should be available and the lecture notes should open automatically. If you cannot read the notes you want, try downloading the appropriate software from here. Some of my lecture notes are also available in PDF, but I recommend using the PostScript version.

Extension articles

Besides teaching university courses I have given talks on various topics at the Mathematical Association of NSW annual Talented Students' Day, and have published articles in Parabola, a mathematics journal for secondary students and teachers published by the Australian Mathematics Trust in association with the School of Mathematics. Here is a list of some talks and articles - more links will be added soon.

Last modified 17 January 2022
David Angell, david.angell@unsw.edu.au, [61] (2) 9385 7061
School of Mathematics and Statistics, University of New South Wales
UNSW Sydney NSW 2052, Australia