Irrationality and Transcendence in Number Theory

Irrationality and Transcendence in Number Theory is a book that explores the themes of irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, and relations between automata and transcendence. It is a guide and introduction to number theory for advanced undergraduates and early postgraduates, with a wide range of exercises and appendixes.

Format: Hardback
Length: 224 pages
Publication date: 31 December 2021
Publisher: Taylor & Francis Ltd

Irrationality and Transcendence in Number Theory is a comprehensive exploration of the fascinating world of irrational numbers, from their ancient origins in the days of Pythagoras to the groundbreaking insights of Baker and Mahler in the 20th century. This book delves into themes such as irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, and the intricate connections between automata and transcendence. Serving as a valuable guide and introduction to number theory for advanced undergraduates and early postgraduates, it takes readers on a journey through the developments in number theory, spanning from ancient civilizations to modern times.

The book employs a diverse range of mathematical techniques, drawing from number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation. This interdisciplinary approach ensures a thorough understanding of the subject matter. Designed as a primary textbook for advanced undergraduate courses in number theory or as supplementary reading for interested postgraduates, each chapter concludes with an appendix that provides essential facts and background information, making the book accessible to readers with no prior specialist knowledge.

Throughout its pages, Irrationality and Transcendence in Number Theory offers a wealth of exercises, ranging from routine problems to surprising and thought-provoking extension material. These exercises not only reinforce the concepts discussed but also encourage critical thinking and problem-solving skills. Whether you are a mathematics enthusiast or seeking to expand your knowledge in number theory, this book is an invaluable resource that will deepen your understanding of this fascinating field.

Weight: 608g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367628376