Irrationality and Transcendence in Number Theory

By: David Angell

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Paperback | 29 January 2024

At a Glance

Paperback
244 Pages

Dimensions(cm)
23.39 x 15.6 x 1.3

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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

Industry 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

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