The Enchantment of Numbers

2025
ISBN: 978-3-031-76567-4
Verlag: Springer Nature Switzerland

Buch, Englisch, 324 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 680 g

Reihe: CMS/CAIMS Books in Mathematics

Inspired by the classic by Albert H. Beiler, this book brings the excitement of recreational number theory into the 21st century through the lens of computational techniques. While Beiler’s work, originally published in 1964, captivated readers with its breadth and charm, some sections have become dated. Here, we re-examine most of the key topics Beiler covered, while introducing fresh updates and insights rooted in computational number theory.

The authors aim to present efficient computer algorithms to tackle various problems that arise in the theory of numbers, providing a deeper and more modern perspective on these timeless puzzles. Though we cannot rival Beiler’s exuberant prose, we hope our enduring fascination with these topics — cultivated over decades of study and teaching — will shine through and resonate with readers.

The book is structured into 21 chapters, each focusing on different facets of number theory with which the authors have extensive expertise. From ancient problems to contemporary computational challenges, this volume will reignite the joy and wonder found in numbers while incorporating the power of modern computation. Whether you're a seasoned mathematician or a curious learner, this book promises a journey through the rich and playful landscape of number theory, making both historical and new discoveries accessible to all.

Zielgruppe

Popular/general

Autoren/Hrsg.

Williams, Hugh C.

Roettger, Eric L. F.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

Introduction.- Division, factors, primes, congruences, gcd, etc.- Representations of Integers.- Integer Powers.- The Binomial Congruence.- The Binomial Coe?cients.- Public-Key Cryptography.- Fibonacci and Lucas Numbers.- Sociable Numbers.- Lucas and Lehmer Sequences.- Primality.- Prime Curios.- Linear Recurrence Sequences.- Simple Continued Fractions.- Integer Factorization.- Sieve Devices.- Simple Continued Fraction of v.- Formulas for Primes.- The Pell Equation.- Some Diophantine Equations.- Conclusion.

Über Autor(innen)

Eric completed his undergraduate work in 2002 from the University of Regina receiving bachelor degrees in both mathematics and computer science. He remained in Regina for his masters work, doing research on Lucas functions under the supervision of Dr. Richard McIntosh. He went on to complete his doctorate at the University of Calgary, with a dissertation titled, A Cubic Extension of the Lucas Functions, under the supervision of Dr. Hugh Williams and Dr. Siguna Muller.

Eric is an Associate Professor cross appointed between the departments of General Education and Mathematics and Computing. Eric works in the area of elementary number theory, in particular with Lucas functions and other divisibility sequences.

 Dr. Hugh Williams is internationally recognized as an expert in computational number theory and its applications to cryptography.  He has authored over 150 refereed journal papers, 30 refereed conference papers and 20 books or book chapters.  After a university career of 46 years, he was appointed Professor Emeritus in Mathematics and Statistics at the University of Calgary.