-PDF Download- Irrationality And Transcendence In Number Theory EBOOK

Irrationality and Transcendence in Number Theory

Author: David Angell

Publisher: CRC Press

Published: 2021-12-30

Total Pages: 201

ISBN-13: 1000523780

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.

Transcendental Number Theory

Author: Alan Baker

Publisher: Cambridge University Press

Published: 2022-06-09

Total Pages: 185

ISBN-13: 100922994X

DOWNLOAD EBOOK →

Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

Irrational Numbers

Author: Ivan Niven

Publisher: American Mathematical Soc.

Published: 1985-12-31

Total Pages: 164

ISBN-13: 1614440115

DOWNLOAD EBOOK →

In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary techniques. The last third of the monograph treats normal and transcendental numbers, including the transcendence of p and its generalization in the Lindermann theorem, and the Gelfond-Schneider theorem. Most of the material in the first two thirds of the book presupposes only calculus and beginning number theory. The book is almost wholly self-contained. The results needed from analysis and algebra are central and well-known theorems, and complete references to standard works are given to help the beginner. The chapters are, for the most part, independent. There is a set of notes at the end of each chapter citing the main sources used by the author and suggesting further reading.

Number Theory IV

Author: A.N. Parshin

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 351

ISBN-13: 3662036444

DOWNLOAD EBOOK →

This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.

Number Theory IV

Author: A.N. Parshin

Publisher: Springer

Published: 1997-10-06

Total Pages: 345

ISBN-13: 9783540614678

DOWNLOAD EBOOK →

Number Theory

Author: Daniel Duverney

Publisher: World Scientific

Published: 2010

Total Pages: 348

ISBN-13: 9814307467

DOWNLOAD EBOOK →

This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory. Clear, concise, and self-contained, the topics are covered in 12 chapters with more than 200 solved exercises. The textbook may be used by undergraduates and graduate students, as well as high school mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, the fascinating branch of mathematics.

Transcendental Numbers

Author: M. Ram Murty

Publisher: Springer

Published: 2014-06-24

Total Pages: 219

ISBN-13: 1493908324

DOWNLOAD EBOOK →

This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.

Contributions to the Theory of Transcendental Numbers

Author: Gregory Chudnovsky

Publisher: American Mathematical Soc.

Published: 1984

Total Pages: 464

ISBN-13: 0821815008

DOWNLOAD EBOOK →

Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.

Number Theory IV

Author: A.N. Parshin

Publisher: Springer

Published: 2012-12-22

Total Pages: 345

ISBN-13: 9783662036457

DOWNLOAD EBOOK →

Making Transcendence Transparent

Author: Edward B. Burger

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 266

ISBN-13: 1475741146

DOWNLOAD EBOOK →

This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.