General Pure Mathematics & General Applied Mathematics

Structure and Randomness in Computability and Set Theory

edited by Douglas Cenzer (University of Florida, USA), Christopher Porter (Drake University, USA) & Jindrich Zapletal (University of Florida, USA) This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSFsupported annual Southeastern Logic Symposium.

Key Features:

• Prominent contributors and institutions: such as George Barmpalias (Chinese Acad. Sci. and U. Wellington, NZ), Andreas Blass (Fellow of AMS, U. Michigan), Andy LewisPye (London School of Economics) Readership: Graduate students and researchers interested in the interface between set theory and computability.

388pp 978-981-3228-22-1 Oct 2020 US$12 £115

Relations: Concrete, Abstract, and Applied

An Introduction

by Herbert Toth The book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples. Readership: Students and researchers in mathematics and computer science.

572pp 978-981-122-034-0 Jul 2020 US$168 £150

Bestseller How to Measure the Infinite

Mathematics with Infinite and Infinitesimal Numbers

by Vieri Benci & Mauro Di Nasso (Università di Pisa, Italy) “This text shows that the study of the almostforgotten, non-Archimedean mathematics deserves to be utilized more intently in a variety of fields within the larger domain of applied mathematics.” CHOICE This book contains an original introduction to the use of infinitesimal and infinite numbers, namely, the Alpha-Theory, which can be considered as an alternative approach to nonstandard analysis. The basic principles are presented in an elementary way by using the ordinary language of mathematics; this is to be contrasted with other presentations of nonstandard analysis where technical notions from logic are required since the beginning. Some applications are included and aimed at showing the power of the theory. Readership: Advanced undergraduate and graduate students in mathematics and philosophy.

GENERAL PURE MATHEMATICS & GENERAL APPLIED MATHEMATICS

World Scientific Series in Information Studies

Trilogy of Numbers and Arithmetic

Book 1: History of Numbers and Arithmetic: An Information Perspective

by Mark Burgin (University of California, Los Angeles, USA) This book 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 such a way 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. 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. At the same time, a diversity of new classes of numbers and arithmetics were introduced in the 20th century. Readership: Researchers and graduate students in mathematics, history, and philosophy.

350pp Feb 2022 978-981-123-683-9 US$118 £105

Exclusive Publisher!

World Scientific Series in 21st Century Mathematics - Volume 1

Fields Medallists’ Lectures

(3rd Edition)

edited by Sir Michael Atiyah (University of Edinburgh, UK), Daniel Iagolnitzer (CEA-Saclay, France) & Chitat Chong (NUS, Singapore) Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field — that of mathematics. The medal is awarded to the best mathematicians who are 40 or younger, every four years. A list of Fields Medallists and their contributions provides a bird’s-eye view of the major developments in mathematics over the past 80 years. It highlights the areas in which, at various times, the greatest progress has been made.

Readership: Mathematicians and mathematical physicists.

1116pp Aug 2015 978-981-4696-18-0(pbk) US$58 £48 978-981-4696-17-3 US$96 £80

Problems and Solutions in Mathematics

(2nd Edition)

edited by Ta-Tsien Li (Fudan University, China) This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The mathematical problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference. Readership: PhD mathematics students and lecturers.