Now available on WorldSciNet New and Notable Titles in Geometry & Topology Analysis and Beyond Manifolds and Local Structures An Introduction with Examples and Exercises A General Theory by Shigeru Kanemitsu (Kyushu Institute of by Marco Grandis (Università di Genova, Italy) Technology, Japan), Takako Kuzumaki (Gifu University, Japan) & Jianya Liu Key Features: (Shandong University, China) • This textbook presents a unified approach to local structures, a wide This volume aims to bridge between elementary textbooks on calculus and established books on class of mathematical structures advanced analysis. It provides elucidation of the ranging from differentiable manifolds reversible process of differentiation and integration to fibre bundles and simplicial through two featured principles: the chain rule and complexes its inverse — the change of variable — as well as • Notions are presented in a concrete the Leibniz rule and its inverse — the integration way, starting from elementary by parts. Readers will find numerous worked-out examples. There are some 250 examples and exercises in this volume. Detailed exercises; the solution is generally solutions are provided for most of the common exercises so that readers remain enthusiastically motivated in solving and understanding the concepts deferred to the last chapter better. • Many references for further reading or study are given Readership: University students who want to know what analysis is, and Readership: Graduate students, PhD students and researchers in researchers in various disciplines who want to have a glimpse of analysis mathematics, physics & computer science. for possible applications to their own fields. 376pp Feb 2021 328pp Jan 2021 978-981-123-399-9 US$128 £115 978-981-122-448-5 US$88 £75 Geometric Foundations of Metacyclic Groups and the Design D(2) Problem Old and New by Francis E A Johnson by Jay Kappraff (New Jersey Institute of (University College London, UK) Technology, USA) The D(2) problem is a fundamental problem in low dimensional topology. In broad terms, it This book is meant to serve either as a textbook asks when a three-dimensional space can be for an interdisciplinary course in Mathematics continuously deformed into a two-dimensional of Design, or as a trade book for designers. It space without changing the essential algebraic will also be of interest for people interested in properties of the spaces involved. This recreational mathematics showing the connection book solves the D(2) problem for a large, between mathematics and design. Topics from the possibly infinite, number of finite metacyclic book can also be adapted for use in pre-college groups G(p, q). Prior to this the author had mathematics. Each chapter will provide the user solved the D(2) problem for the groups G(p, 2). with ideas that can be incorporated in a design. However, for q > 2, the only previously known Background materials will be provided to show the solutions were for the groups G(7, 3), G(5, 4) and G(7, 6), all done by difficult direct calculation by two of the author’s reader the mathematical principles that lie behind the designs. students, Jonathan Remez (2011) and Jason Vittis (2019). Key Features: Readership: Academic mathematicians; postgraduate and higher. ○ The book is highly graphic oriented with many examples of incorporating mathematics in design 372pp Jan 2021 978-981-122-275-7 US$118 £105 ○ Additional designs will be offered to the purchaser in a website ○ Many topics are novel and have not been presented elsewhere Subscribe or Recommend Readership: General Public, undergraduates and designers who are these Journals to your Librarian! interested in seeing the connection between mathematics and design. www.worldscientific.com/jktr 368pp Mar 2021 www.worldscientific.com/ijgmmp 978-981-121-970-2 US$118 £105 FREE access to the selected articles. *Please log in to your existing account or register for a FREE account to enjoy this. New and Notable Titles in GEOMETRY & TOPOLOGY Fiber Bundles and Homotopy Lecture Notes on General by Dai Tamaki (Shinshu University, Japan) Topology This book is an introduction to fiber bundles and by Guoliang Wang fibrations. But the ultimate goal is to make the reader (Beijing Institute of Technology, China) feel comfortable with basic ideas in homotopy theory. This book is intended as a one-semester course The author found that the classification of principal in general topology, a.k.a. point-set topology, for fiber bundles is an ideal motivation for this purpose. undergraduate students as well as first-year graduate The book begins with elementary examples and students. Such a course is considered a prerequisite then gradually introduces abstract definitions when for further studying analysis, geometry, manifolds, necessary. The reader is assumed to be familiar with and certainly, for a career of mathematical research. point-set topology, but it is the only requirement for this book. Researchers may find it helpful especially from the comprehensive indices. 350pp May 2021 Readership: Advanced undergraduate and graduate students, researchers 978-981-123-799-7 US$118 £105 and practitioners in the fields of topology. 152pp Dec 2020 Series in Algebraic and Differential Geometry - 978-981-122-741-7 US$58 £50 Volume 1 Differential Geometry of Curves Lectures on the Geometry of and Surfaces with Singularities Manifolds (3rd Edition) by Masaaki Umehara (Tokyo Institute of by Technology, Japan), Kentaro Saji (Kobe University, Liviu I Nicolaescu (University of Notre Dame, USA) Japan) & Kotaro Yamada (Tokyo Institute of Technology, Japan) The goal of this book is to introduce the reader to Translated by Wayne Rossman some of the main techniques, ideas and concepts (Kobe University, Japan) frequently used in modern geometry. It starts This book provides a unique and highly accessible approach to singularity from scratch and it covers basic topics such as theory from the perspective of differential geometry of curves and surfaces. differential and integral calculus on manifolds, It is written by three leading experts on the interplay between two important connections on vector bundles and their curvatures, fields — singularity theory and differential geometry. The book introduces basic Riemannian geometry, calculus of variations, DeRham cohomology, singularities and their recognition theorems, and describes their applications integral geometry (tube and Crofton formulas), characteristic classes, elliptic to geometry and topology, restricting the objects of attention to singularities equations on manifolds and Dirac operators. The new edition contains a of plane curves and surfaces in the Euclidean 3-space. In particular, by new chapter on spectral geometry presenting recent results which appear presenting the singular curvature, which originated through research by the here for the first time in printed form. authors, the Gauss–Bonnet theorem for surfaces is generalized to those Readership: Graduate students and researchers in global analysis, with singularities. differential geometry. Readership: Advanced undergraduate and graduate students, and 700pp Oct 2020 researchers interested in the singularity theory from the perspective of 978-981-121-481-3 US$198 £175 differential geometry of curves and surfaces. 978-981-121-595-7(pbk) US$98 £85 380pp Aug 2021 978-981-123-713-3 US$128 £115 Algebraic Surfaces in Positive Characteristics Lectures on Algebraic Topology Purely Inseparable Phenomena in Curves and by Haynes Miller (Massachusetts Institute of Technology, USA) Surfaces by Masayoshi Miyanishi (Osaka University, Japan) Algebraic Topology and basic homotopy theory form a fundamental building & Hiroyuki Ito (Tokyo University of Science, Japan) block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject In the present book, we consider first the forms of the at MIT. The style is engaging and student-friendly, but precise. Every lecture affine line or the additive group, classification of such is accompanied by exercises. It begins slowly in order to gather up students forms and detailed analysis. The forms of the affine with a variety of backgrounds, but gains pace as the course progresses, line considered over the function field of an algebraic and by the end the student has a command of all the basic techniques of curve define the algebraic surfaces with fibrations by curves with moving classical homotopy theory. singularities. These fibrations are investigated via the Mordell – Weil groups, which are originally introduced for elliptic fibrations. This is the first book Readership: Students familiar with general topology and basic modern which explains the phenomena arising from purely inseparable coverings algebra; researchers who need to use the methods of algebraic topology, in and Artin – Schreier coverings. There exists a vast, unexplored world of mathematics at large and in theoretical physics. unirational surfaces. In this book, we explain the Frobenius sandwiches as 300pp Sep 2021 examples of unirational surfaces. 978-981-123-124-7 US$98 £85 Readership: Graduate students and researchers in the fields of Algebraic 978-981-123-285-5(pbk) US$48 £40 Geometry, Fields and Rings, and Commutative Algebra. 456pp Jun 2020 Journal of Knot Theory 978-981-121-520-9 US$138 £120 and Its Ramifications FREE access to featured articles at https://www.worldscientific.com/jktr 2 Prefer Digital? View this flyer online at https://www.worldscientific.com WORLD SCIENTIFIC