GENERAL PURE AND APPLIED MATHEMATICS World Scientific Series in Information Studies
Textbook
TRILOGY OF NUMBERS AND ARITHMETIC
AN INTRODUCTION TO ABSTRACT ALGEBRA
Book 1: History of Numbers and Arithmetic: An Information Perspective
Sets, Groups, Rings, and Fields by Steven H Weintraub (Lehigh University, USA)
by Mark Burgin (University of California, Los Angeles, USA)
This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.
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.
It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.
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.
Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students’ knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.
Contents: Introduction; The Story About 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; The 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: Arithmetics Used by People; Bibliography; Index.
Contents: Set Theory; Group Theory; Ring Theory; Field Theory; Rings of Algebraic Integers and Dedekind Rings. Readership: Advanced undergraduate and beginning graduate students. 250pp 978-981-124-666-1 978-981-124-755-2(pbk)
Mar 2022 US$98 £85 US$48 £40
Readership: Researchers and graduate students in mathematics, history, and philosophy.
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350pp 978-981-123-683-9 17
Advance Book Information • January – February 2022
Mar 2022 US$118 £105
BOOKS
In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.
