Exploring the perfect number problem, this book delves into the origins of Mersenne primes and the Fibonacci sequence, incorporating original research findings. It introduces square sum perfect numbers and reveals their connections to the Fibonacci and Lucas sequences, the twin prime conjecture, and Fermat primes. The author raises intriguing questions and conjectures, inviting readers to consider the deeper relationships between these mathematical concepts.
Exploring the essence and evolution of natural numbers, this book comprises seven chapters that blend foundational elements of elementary number theory with contemporary research findings. Notably, it honors Qin Jiushao by renaming the Chinese Remainder Theorem. The sixth chapter delves into intriguing congruences modulo integer powers, while the seventh presents a novel problem that merges additive and multiplicative number theory. This work serves both as an educational resource and a contribution to ongoing mathematical discourse.
A Promenade through the Civilizations of Our World
This volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resulting applications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.
