Mark Burgin 
TRILOGY NUMBERS & ARITHME (BK1) [EPUB ebook] 
Book 1: History of Numbers and Arithmetic: An Information Perspective

The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.

The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.

This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.

Contents:

• Preface


• About the Author


• Acknowledgments


• Introduction


• The Story of Numbers and Arithmetic from Ancient Times to the Beginning of the Second Millennium


• The Chronicle of Numbers and Arithmetic from the Beginning of the Second Millennium to the Beginning of the 20th Century


• Acceleration of the Development in Arithmetic and Numerical Systems in the 20th and 21st Centuries


• Discovery of Non-Diophantine Arithmetics and Their Applications


• Non-Diophantine Operations with Numbers and Related Constructions in the History of Mathematics and Science


• Appendix: List of Arithmetics Used in Mathematics and Beyond


• Bibliography


• Index

Readership: Researchers and graduate students in mathematics, history, and philosophy.

Key Features:

• Includes the developments in these areas in the 20th century and later. Besides whole numbers and real numbers, a diversity of new classes of numbers and arithmetics are introduced


• A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic


• Another unique aspect of this book is the demonstration that numbers don’t define arithmetics but serve as building elements of arithmetics. This means that from the same numbers, it is possible to build different arithmetics in the same way as from the same bricks it is possible to build a variety of buildings