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Geometry & Topology
Bestseller Analysis and Beyond
An Introduction with Examples and Exercises
by Shigeru Kanemitsu (Kyushu Institute of Technology, Japan), Takako Kuzumaki (Gifu University, Japan) & Jianya Liu (Shandong University, China) This volume aims to bridge between elementary textbooks on calculus and established books on advanced analysis. It provides elucidation of the reversible process of differentiation and integration through two featured principles: the chain rule and its inverse — the change of variable — as well as the Leibniz rule and its inverse — the integration by parts. The chain rule or differentiation of composite functions is ubiquitous since almost all (a.a.) functions are composite functions of (elementary) functions and with the change of variable method as its reverse process. The Leibniz rule or differentiation of the product of two functions is essential since it makes differentiation nonlinear and with the method of integration by parts as its reverse process. Readership:University students who want to know what analysis is, and researchers in various disciplines who want to have a glimpse of analysis for possible applications to their own fields.
328pp 978-981-122-448-5 Mar 2021 US$88 £75
Basic Lessons on Isometries, Similarities and Inversions in the Euclidean Plane
A Synthetic Approach
by Ioannis Markos Roussos (Hamline University, USA) The aim of this book is to provide a complete synthetic exposition of plane isometries, similarities and inversions to readers who are interested in studying, teaching, and using this material.
The topics developed in this book can provide new proofs and solutions to many results and problems of classical geometry, which are presented with different proofs in the literature. Their applications are numerous and some, such as the Steiner Chains and Point, are useful to engineers. Readership: College and high school students in mathematics, computational geometry, computational sciences.
500pp Sep 2021 978-981-124-037-9(pbk) US$78 £70 978-981-123-985-4 US$148 £130
Series in Algebraic and Differential Geometry - Vol 1
by MasaakiUmehara (Tokyo Institute of Technology, Japan), Kentaro Saji (Kobe University, Japan) & Kotaro Yamada (Tokyo Institute of Technology, Japan) Translated by: Wayne Rossman (Kobe University, Japan) This book provides a unique and highly accessible approach to singularity theory from the perspective of differential geometry of curves and surfaces. It is written by three leading experts on the interplay between two important fields — singularity theory and differential geometry. The book introduces singularities and their recognition theorems, and describes their applications to geometry and topology, restricting the objects of attention to singularities of plane curves and surfaces in the Euclidean 3-space
Key Features
• The book covers a spectrum of material from the most basic facts to advanced research topics, in a way that naturally brings the reader through the different levels Readership: Advanced undergraduate and graduate students, and researchers interested in the singularity theory from the perspective of differential geometry of curves and surfaces.
Metacyclic Groups and the D(2) Problem
by Francis E A Johnson (University College London, UK)
The D(2) problem is a fundamental problem in low dimensional topology. In broad terms, it asks when a three-dimensional space can be continuously deformed into a twodimensional space without changing the essential algebraic properties of the spaces involved.
This book solves the D(2) problem for a large, possibly infinite, number of finite metacyclic groups G(p, q). Prior to this the author had solved the D(2) problem for the groups G(p, 2). However, for q > 2, the only previously known 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 students, Jonathan Remez (2011) and Jason Vittis (2019).
Readership: Academic mathematicians; postgraduate and higher.
372pp 978-981-122-275-7 Jan 2021 US$118 £105
Fiber Bundles and Homotopy
by Dai Tamaki (Shinshu University, Japan)
This book is an introduction to fiber bundles and fibrations. But the ultimate goal is to make the reader feel comfortable with basic ideas in homotopy theory. The author found that the classification of principal fiber bundles is an ideal motivation for this purpose. The notion of homotopy appears naturally in the classification. Basic tools in homotopy theory such as homotopy groups and their long exact sequence need to be introduced. The book begins with elementary examples and then gradually introduces abstract definitions when necessary. The reader is assumed to be familiar with point-set topology, but it is the only requirement for this book.
Readership: Graduate students and researchers in algebraic topology.
336pp 978-981-123-799-7 May 2021 US$118 £105
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Essential Textbook A Royal Road to Topology
Convergence of Filters
by Szymon Dolecki (Mathematical Institute of Burgundy, France)
Convergence theory completes topology in an analogous way as the field of complex numbers algebraically completes the field of real numbers. The class of convergences is closed under several natural, essential operations, under which the class of topologies is not!
The title of this book alludes to the mentioned advantages of the present approach, which I believe to be more gratifying than many traditional ones. Principal classical topics of typical topology courses are included.
Key Features
• The framework of convergence theory is easier, more powerful and far-reaching than that of general topology, thanks to an appropriate level of abstraction, enabling us to see the things with inhanced clarity
Readership: Graduate students of mathematics, Academia (topology, analysis).
500pp 978-981-123-210-7 Apr 2022 US$158 £140
Elementary Topology and Applications
(2nd Edition)
by Carlos R Borges (University of California, Davis, USA)
The textbook is a very good start into the mathematical field of topology. A variety of topological concepts with some elementary applications are introduced. It is organized in such a way that the reader gets to significant applications quickly.
This revised version corrects the many discrepancies in the earlier edition. The emphasis is on the geometric understanding and the use of new concepts, indicating that topology is really the language of modern mathematics.
Readership: Advanced undergraduates and graduates in differential geometry and topology.
220pp 978-981-123-742-3 Aug 2021 US$58 £50
Manifolds and Local Structures
A General Theory
by Marco Grandis (Università di Genova, Italy)
Local structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable ‘elementary spaces’, by means of partial homeomorphisms that fix the gluing conditions and form a sort of ‘intrinsic atlas’.
This uniform approach allows us to move from one basis to another: for instance, the elementary tangent bundle of an open Euclidean space is automatically extended to the tangent bundle of any differentiable manifold. The same holds for tensor calculus.
Technically, the goal of this book is to treat these structures as ‘symmetric enriched categories’ over a suitable basis, generally an ordered category of partial mappings.
Readership: Graduate students, PhD students and researchers in mathematics, physics & computer science. Old and New
by Jay Kappraff (New Jersey Institute of Technology, USA) This book is meant to serve either as a textbook for an interdisciplinary course in Mathematics of Design, or as a trade book for designers. It will also be of interest for people interested in recreational mathematics showing the connection between mathematics and design. Topics from the book can also be adapted for use in pre-college mathematics. Each chapter will provide the user with ideas that can be incorporated in a design. Background materials will be provided to show the reader the mathematical principles that lie behind the designs.
Key Features:
• The book is highly graphic oriented with many examples of incorporating mathematics in design • Additional designs will be offered to the purchaser in a website • Many topics are novel and have not been presented elsewhere • Every effort has been made to make the topics accessible to non-mathematicians while at the same time being of interest to experienced mathematicians Readership: General Public, undergraduates and designers who are interested in seeing the connection between mathematics and design.
368pp 978-981-121-970-2 Mar 2021 US$118 £105
Lecture Notes on General Topology
by Guoliang Wang (Beijing Institute of Technology, China) This book is intended as a one-semester course in general topology, a.k.a. point-set topology, for undergraduate students as well as first-year graduate students. Such a course is considered a prerequisite for further studying analysis, geometry, manifolds, and certainly, for a career of mathematical research. Researchers may find it helpful especially from the comprehensive indices. This book also contains exercises for each chapter with selected solutions. Readership: Advanced undergraduate and graduate students, researchers and practitioners in the fields of topology.
152pp 978-981-122-741-7 Feb 2021 US$58 £50
An Elementary Overview of Mathematical Structures
Algebra, Topology and Categories
by Marco Grandis (Università di Genova, Italy) “The presentation is modeled on the discursive style of the Bourbaki collective, and the coverage of topics is rich and varied. Grandis has provided a large selection of exercises and has sprinkled orienting comments throughout. For an undergraduate library where strong students seek an overview of a significant portion of mathematics, this would be an excellent acquisition. Summing up: Recommended.” CHOICE Since the last century, a large part of Mathematics is concerned with the study of mathematical structures, from groups to fields and vector spaces, from lattices to Boolean algebras, from metric spaces to topological spaces, from topological groups to Banach spaces. The book intends to give a structural overview of these topics, where the basic facts of the different theories are unified through the ‘universal properties’ that they satisfy, and their particularities stand out, perhaps even more. Readership: Undergraduate and graduate students in Mathematics, Physics, Computer Sciences, Chemistry, Statistics, Engineering.
