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GENERAL PURE & APPLIED MATHEMATICS
Textbook AN INTRODUCTION TO ABSTRACT ALGEBRA
Sets, Groups, Rings, and Fields
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by Steven H Weintraub (Lehigh University, 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.
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.
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.
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: Set Theory; Group Theory; Ring Theory; Field Theory; Rings of Algebraic Integers and Dedekind Rings.
Readership: Advanced undergraduate and beginning graduate students.
250pp Mar 2022 978-981-124-666-1 US$98 £85 978-981-124-755-2(pbk) US$48 £40
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TRILOGY OF NUMBERS AND ARITHMETIC
Book 1: History of Numbers and Arithmetic: An Information Perspective
by Mark Burgin (University of California, Los Angeles, USA) 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. 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: 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. Readership: Researchers and graduate students in mathematics, history, and philosophy.
