Irrationality and Transcendence in Number Theory 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.

Features

• Uses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation
• Suitable as a primary textbook for advanced undergraduate courses in number theory, or as supplementary reading for interested postgraduates
• Each chapter concludes with an appendix setting out the basic facts needed from each topic, so that the book is accessible to readers without any specific specialist background

About the Author

David Angell studied mathematics at Monash University and the University of New South Wales, Australia, earning a Ph.D. from the latter institution with a thesis on Mahler's method in transcendence theory. He has been a member of the academic staff in the School of Mathematics at UNSW since 1989, and has consistently received glowing evaluations of his teaching both from colleagues and from students. David has taught a wide variety of mathematics subjects, but his favourites have always been number theory and discrete mathematics. He is particularly interested in teaching students to produce proofs and other mathematical writing which are clearly expressed, logically impeccable and engaging for the reader. David is strongly committed to extension activities for secondary school students. He has for many years been the problems editor for Parabola, the online mathematics magazine produced by UNSW, as well as contributing a number of articles to the magazine. He has also given talks on a wide variety of topics to final-year secondary students.

Beyond mathematics, David is an enthusiast for wilderness activities and has undertaken expeditions in Australia, Greenland, Nepal, Morocco and many other areas. He is a keen amateur musician, and is the founding conductor of the Bourbaki Ensemble, a chamber string orchestra based in Sydney, Australia.

Reviews

"Exceptionally informative, impressively organized and presented, Irrationality and Transcendence in Number Theory is an ideal selection as a curriculum textbook."
- Midwest Books Review
"This excellent book not only helps fill a substantial gap in the undergraduate mathematics literature, but it does so in a way that most students will, I think, find interesting, inviting and accessible.
[. . .] This material is, of course, very nontrivial, but Angell goes to great lengths to make it accessible. He writes slowly and clearly and spends a lot of time motivating results. As previously noted, he also includes background Appendices in each chapter.
There are other useful pedagogical features. Each chapter ends with an extensive collection of exercises, most of them non-routine; a 20-page section at the end of the book offers hints to these. The book also contains a five-page bibliography (one that, surprisingly, omits the Burger/Tubbs book mentioned earlier) that directs a reader to useful sources.
The subject matter of this book is interesting and beautiful and deserves to be made accessible to well-prepared senior undergraduates. Angell has done an excellent job in helping to do so."
- MAA Reviews

"The thoughtfully organised book is very well written-meticulous care has been taken to make the material accessible to students new to the topics. The delightfully written text is sprinkled with relevant examples and useful comments, and the required background materials in number theory, mathematical analysis or algebra are set out in appendices at the end of each chapter. There are also plenty of well constructed exercises, with generous hints to most of them at the end of the book."
- The Mathematical Gazette

Book Information
ISBN 9780367628376
Author David Angell
Format Hardback
Page Count 224
Imprint Chapman & Hall/CRC
Publisher Taylor & Francis Ltd
Weight(grams) 467g