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World Scientific
Connecting Great Minds
MATHEMATICS
2021
AVA I L A B L E I N P R I N T A N D D I G I TA L
M O R E D I G I TA L P R O D U C T S O N W O R L D S C I N E T
Highlights Mathematics Catalogue 2021
7
page 5 page 5 page page 11
by Tzuong-Tsieng Moh by James S Milne by Harold Cohen (California State University, by Wenxiong Chen (Yeshiva Univ., USA),
(Purdue University, USA) (University of Michigan, USA) Los Angeles, USA) & Daniel Gallup (Pasadena Yan Li (Yeshiva Univ., USA) & Pei Ma
City College, USA) (Nanjing Forestry Univ., China)
page 16 page 16 page 17 page 17
by Cuihong Cai edited by Marc Hallin (Université libre de Bruxelles, edited by Douglas Cenzer (Univ. of by Gary Mar
(Fudan University, China) Belgium), Marco Lippi (Einaudi Institute for Economics Florida, USA), Christopher Porter (Stony Brook University, USA)
and Finance, Italy), Matteo Barigozzi (London School (Drake Univ., USA) & Jindrich Zapletal
of Economics and Political Science, UK), (Univ. of Florida, USA)
Mario Forni (Univ. of Modena and Reggio Emilia, Italy)
& Paolo Zaffaroni (Imperial College London, UK)
page 19 page 20 page 22 page 24
by Alexei A Kornyshev & by Alexey P Isaev (Joint Institute for Nuclear edited by Bruce R Vogeli by William Layton &
Dominic O’Lee Research, Dubna, Russia & M V Lomonosov (Columbia University, USA) & Myron Sussman
(Imperial College London, UK) Moscow State University, Russia) & Valery Mohamed E A El Tom (University of Pittsburgh, USA)
A Rubakov (Russian Academy of Sciences, (Ministry of Education, Sudan)
Moscow, Russia & M V Lomonosov Moscow
State University, Russia)
page 25 page 25 page 28 page 28
by Didier Henrion, Milan Korda (LAAS-CNRS, by Jozsef Beck by Ricardo V Teixeira & by Alfred S Posamentier
France & Univ. of Toulouse, France & Czech (Rutgers University, USA) Jang-Woo Park (University of (City University of New York, USA)
Technical Univ. in Prague, Czech Republic) & Jean Houston-Victoria, USA)
Bernard Lasserre (LAAS-CNRS, France & Inst. of
Mathematics, Univ. of Toulouse, France)
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Mathematics Catalogue 2021
ALGEBRA & RELATED TOPICS
Gröbner – Shirshov Bases Non-Diophantine Arithmetics in
Normal Forms, Combinatorial and Mathematics, Physics and Psychology
Decision Problems in Algebra by Mark Burgin (University of California,
by Leonid Bokut (Sobolev Institute of Los Angeles, USA) & Marek Czachor
Mathematics, Russia), Yuqun Chen (South (Politechnika Gdańska, Poland)
China Normal University, China), Kyriakos
Kalorkoti (University of Edinburgh, United This book provides a detailed exposition of
the theory of non-Diophantine arithmetics and
Kingdom), Pavel Kolesnikov (Sobolev Institute
its various applications. Reading this book,
of Mathematics, Russia) & Viktor Lopatkin
the reader will see that on the one hand, non-
(Saint-Petersburg State University, Russia)
Diophantine arithmetics continue the ancient
The book is about (associative, Lie and other) algebras, groups, tradition of operating with numbers while on the other hand, they
semigroups presented by generators and defining relations. They play a introduce extremely original and innovative ideas.
great role in modern mathematics. It is enough to mention the quantum
Key Features:
groups and Hopf algebra theory, the Kac – Moody and Borcherds algebra
○ It is a unique book on this ground-breaking topic, which
theory, the braid groups and Hecke algebra theory, the Coxeter groups
not only changes people’s understanding of numbers and
and semisimple Lie algebra theory, the plactic monoid theory. One of the
operations with them but also provides diverse applications
main problems for such presentations is the problem of normal forms of
in different areas, which change not only mathematics
their elements. The first book that describes Gröbner – Shirshov bases
and science but also some essential aspects of social
method for Lie algebra in full details
functioning
Readership: Researchers in algebra and combinatorics.
Readership: Researchers and graduate students in mathematics,
308pp Jul 2020 physics, psycholody, and philosophy.
978-981-4619-48-6 US$138 £120 800pp Nov 2020
978-981-121-430-1 US$188 £165
Series on Knots and Everything - Vol 65
Mathematics of Harmony as a P-adic Analytic Functions
New Interdisciplinary Direction and by Alain Escassut (Blaise Pascal University, France)
“Golden” Paradigm of Modern Science P-adic Analytic Functions describes the definition and properties of p-adic
Volume 1: The Golden Section, Fibonacci analytic and meromorphic functions in a complete algebraically closed
Numbers, Pascal Triangle, and Platonic Solids ultrametric field. Various properties of p-adic exponential-polynomials
by Alexey Stakhov (International Club of are examined, such as the Hermite Lindemann theorem in a p-adic field,
the Golden Section, Canada & Academy of with a new proof. The order and type of growth for analytic functions are
Trinitarism, Russia) studied, in the whole field and inside an open disk. P-adic meromorphic
functions are studied, not only on the whole field but also in an open disk
Volume I is the first part of the 3-volume book Mathematics of Harmony
and on the complemental of a closed disk, using Motzkin meromorphic
as a New Interdisciplinary Direction and “Golden” Paradigm of Modern
products. Finally, the p-adic Nevanlinna theory is widely explained,
Science. “Mathematics of Harmony” rises in its origin to the “harmonic
with various applications. Small functions are introduced with results of
ideas” of Pythagoras, Plato and Euclid, this 3-volume book aims
uniqueness for meromorphic functions. The question of whether the ring
to promote more deep understanding of ancient conception of the
of analytic functions — in the whole field or inside an open disk — is a
“Universe Harmony, “ the main conception of ancient Greek science,
Bezout ring is also examined.
and implementation of this conception to modern science and education.
Readership: The target audience consists of researchers and post-
Readership: High school, college and university students and
graduate students in ultrametric analysis and number theory. Also
teachers, professionals, scientists and investors interested in history
appropriate for researchers in Levi-Civita fields in p-adic physics.
of mathematics, Fibonacci numbers, golden section and their
generalization. 350pp Jan 2021
248pp May 2020 978-981-122-621-3 US$128 £115
978-981-120-710-5 US$88 £75
Essential Textbooks
Invitation to Algebra Elements of Linear and Multilinear
A Resource Compendium for Teachers,
Advanced Undergraduate Students and
Algebra
by John M Erdman (Portland State Univ., USA)
Graduate Students in Mathematics
by Vlastimil Dlab & Kenneth S Williams This set of notes is an activity-oriented introduction
4 (Carleton University, Canada) to linear and multilinear algebra. The great
majority of the most elementary results in these
This book presents a compendium style account
subjects are straightforward and can be verified
of a comprehensive mathematical journey from
by the thoughtful student. Indeed, that is the
Arithmetic to Algebra. A number of topics that are
main point of these notes — to convince the beginner that the subject is
missing in present-day textbooks, and which may be attractive to students
accessible. In the material that follows there are numerous indicators that
at the graduate or advanced undergraduate level in mathematics,
suggest activity on the part of the reader: words such as “proposition”,
for example, continued fractions, arithmetic progressions of higher
“example”, “theorem”, “exercise”, and “corollary”, if not followed by a proof
order, complex numbers in plane geometry, differential schemes, path
(and proofs here are very rare) or a reference to a proof, are invitations
semigroups and path algebras, have been carefully presented.
to verify the assertions made.
Readership: Graduates, advanced undergraduates in mathematics and
Readership: Upper division undergraduates, beginning graduate
professors, teachers of mathematics.
students, instructors of linear and multilinear algebra.
452pp Jul 2020
160pp Jan 2021
978-981-121-997-9 US$138 £120
978-981-122-272-6 US$68 £60For more information, visit: www.worldscientific.com WORLD SCIENTIFIC
Written by MOH TZUONG-TSIENG Exercises and Problems in Linear Algebra
by John M Erdman (Portland State University, USA)
Series on University Mathematics - Vol 10
Linear Algebra and its This book contains an extensive collection of exercises
and problems that address relevant topics in linear
Applications algebra. Topics that the author finds missing or
by Tzuong-Tsieng Moh inadequately covered in most existing books are also
(Purdue University, USA) included. The exercises will be both interesting and
From Tzuong-Tsieng Moh, a long-time helpful to an average student. Some are fairly routine
expert in algebra, comes a new book calculations, while others require serious thought.
for students to better understand linear The format of the questions makes them suitable for teachers to use in quizzes
algebra. Writing from an experienced standpoint, Moh touches and assigned homework. Some of the problems may provide excellent topics
on the many facets surrounding linear algebra, including for presentation and discussions. Furthermore, answers are given for all odd-
but not limited to, echelon forms, matrix algebra, linear numbered exercises which will be extremely useful for self-directed learners.
transformations, determinants, dual space, inner products, the
Gram – Schmidt Theorem, Hilbert space, and more. It is ideal Readership: Students and teachers of linear algebra.
for both newcomers and seasoned readers who want to attain a
200pp Nov 2020
deeper understanding on both the basics and advanced topics of
978-981-122-040-1 US$78 £70
linear algebra and its vast applications. The wide range of topics
combined with the depth of each discussion make it essential to 978-981-122-107-1(pbk) US$38 £35
be on the shelf of every mathematical beginner and enthusiast.
Series on Knots and Everything
Readership: Graduate students and researchers interested
in the basic and advanced topics of linear algebra and its Mathematics of Harmony as a
applications. New Interdisciplinary Direction and
316pp Nov 2020 “Golden” Paradigm of Modern Science
978-981-3235-42-7 US$98 £86 Volume 2: Algorithmic Measurement Theory,
Fibonacci and Golden Arithmetic’s and Ternary
Mirror-Symmetrical Arithmetic
Elliptic Curves by Alexey Stakhov (International Club of the Golden
2nd Edition Section, Canada & Academy of Trinitarism, Russia)
by James S Milne
(University of Michigan, USA) Volume II is the second part of the 3-volume book Mathematics of Harmony as
a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science.
This book uses the beautiful theory of “Mathematics of Harmony” rises in its origin to the “harmonic ideas” of
elliptic curves to introduce the reader to Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep
some of the deeper aspects of number understanding of ancient conception of the “Universe Harmony, “ the main
theory. It assumes only a knowledge of
conception of ancient Greek science, and implementation of this conception to
the basic algebra, complex analysis,
modern science and education.
and topology usually taught in first-year
graduate courses. The first three chapters develop the basic (Refer to Page 4 for more information on Volume I)
theory of elliptic curves.
Readership: High school, college and university students, teachers,
For this edition, the text has been completely revised and professionals, scientists and investors interested in history of mathematics,
updated. Fibonacci numbers, golden section and their generalization.
Readership: Graduate students and lecturers in mathematics, 300pp Sep 2020
specifically number theory courses.
978-981-121-346-5 US$98 £85
316pp Sep 2020
978-981-122-183-5 US$98 £85 Series on Knots and Everything
Mathematics of Harmony as a New
Classical and Dynamical Interdisciplinary Direction and “Golden”
Markov and Lagrange Spectra Paradigm of Modern Science
Dynamical, Fractal and Arithmetic Volume 3: The “Golden” Paradigm of Modern
Aspects Science: Prerequisite for the “Golden” Revolution
by Davi Lima (Universidade Federal in Mathematics, Computer Science, and
de Alagoas, Brazil), Carlos Matheus Theoretical Natural Sciences
(CNRS, France), Carlos G Moreira by Alexey Stakhov (International Club of the Golden
(IMPA, Brazil) & Sergio Romaña Section, Canada & Academy of Trinitarism, Russia)
(Universidade Federal do Rio de
Janeiro, Brazil) Volume III is the third part of the 3-volume book Mathematics of Harmony as 5
a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science.
The book intends to give a modern presentation of the classical “Mathematics of Harmony” rises in its origin to the “harmonic ideas” of
Markov and Lagrange spectrum, which are fundamental Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep
objects from the theory of Diophantine approximations and understanding of ancient conception of the “Universe Harmony, “ the main
of their several generalizations related to Dynamical Systems conception of ancient Greek science, and implementation of this conception to
and Differential Geometry. Besides presenting many classical modern science and education.
results, the book includes several topics of recent research on
the subject, connecting several fields of Mathematics — Number (Refer to Page 4 for more information on Volume I)
Theory, Dynamical Systems and Fractal Geometry.
Readership: High school, college and university students, teachers,
Readership: Graduate students and researchers in Number professionals, scientists and investors interested in history of mathematics,
Theory and Dynamical Systems. Fibonacci numbers, golden section and their generalization.
224pp Nov 2020 196pp Sep 2020
978-981-122-528-4 US$88 £75 978-981-121-349-6 US$78 £70Mathematics Catalogue 2021
Notable Titles in Algebra and Principles and Techniques in
Related Topics (2018-2019) Combinatorics
Solutions Manual
by Kean Pew Foo, Mingyan & Simon Lin
Higher Dimensional Categories (University of Illinois at Urbana-Champaign, USA)
From Double to Multiple Categories The solutions to each problem are written from
by Marco Grandis (Università di Genova, Italy) a first principles approach, which would further
The study of higher dimensional categories augment the understanding of the important and
has mostly been developed in the globular recurring concepts in each chapter. Moreover, the
form of 2-categories, n-categories, omega- solutions are written in a relatively self-contained
categories and their weak versions. Here we manner, with very little knowledge of undergraduate mathematics
study a different form: double categories, n-tuple assumed. In that regard, the solutions manual appeals to a wide
categories and multiple categories, with their range of readers, from secondary school and junior college students,
weak and lax versions. This book wants to show undergraduates, to teachers and professors.
the advantages of this form for the theory of adjunctions and limits. Readership: Students doing combinatorics.
Furthermore, this form is much simpler in higher dimension, starting with
dimension three where weak 3-categories (also called tricategories) are 440pp Oct 2018
already quite complicated, much more than weak or lax triple categories. 978-981-3238-84-8(Set)(pbk) US$45 £40
Readership: Graduate and postgraduate students, researchers. See Pg34 for Principles and Techniques in Combinatorics
536pp Oct 2019
978-981-120-510-1 US$168 £150 COMPUTER MATHEMATICS & SCIENCE
2019 Bestseller Linear Algebra and Optimization
Series on Knots and Everything - Vol 63
with Applications to Machine
Board Games Learning
Throughout the History and
Volume I: Linear Algebra for Computer
Multidimensional Spaces
Vision, Robotics, and Machine Learning
by Jorma Kyppö (University of Jyväskylä, Finland)
by Jean Gallier & Jocelyn Quaintance
In this richly illustrated book, Dr Jorma Kyppö (University of Pennsylvania, USA)
explores the history of board games dating back
to Ancient Egypt, Mesopotamia, India and China. This book provides the mathematical
He provides a description of the evolution and various interpretations of fundamentals of linear algebra to practicers in
chess. Furthermore, the book offers the study of the old Celtic and Viking computer vision, machine learning, robotics, applied mathematics,
board games and the old Hawaiian board game Konane, as well as a and electrical engineering. By only assuming a knowledge of calculus,
new hypothesis about the interpretation of the famous Cretan Phaistos the authors develop, in a rigorous yet down to earth manner, the
Disk. Descriptions of several chess variations, including some highlights mathematical theory behind concepts such as: vectors spaces, bases,
of the game theory and tiling in different dimensions, are followed by a linear maps, duality, Hermitian spaces, the spectral theorems, SVD,
multidimensional symmetrical n-person strategy game model, based on and the primary decomposition theorem. At all times, pertinent real-
chess. Final chapter (Concluding remarks) offers the new generalizations world applications are provided. This book includes the mathematical
of the Euler-Poincare’s Characteristic, Pi and Fibonacci sequence. explanations for the tools used which we believe that is adequate for
computer scientists, engineers and mathematicians who really want
Readership: Researchers in combinatorics, complex manifolds and to do serious research and make significant contributions in their
topology, game theory. respective fields.
344pp Jul 2019 Readership: Undergraduate and graduate students.
978-981-3233-52-2 US$118 £105
824pp Feb 2020
978-981-120-639-9 US$198 £175
Essential Textbooks 978-981-120-771-6(pbk) US$98 £85
A Bridge to Linear Algebra
by Dragu Atanasiu (University of Borås, From Fractals and Cellular
Sweden) & Piotr Mikusiński (University of
Central Florida, USA)
Automata to Biology
Information as Order Hidden Within Chance
The book makes a first course in linear algebra by Alberto Strumia (Istituto Nazionale di Alta
more accessible to the majority of students and Matematica “Francesco Severi”, Italy)
it assumes no prior knowledge of the subject.
The didactical level of exposition, together
6 It provides a careful presentation of particular
with many astonishing images and animations,
cases of all core topics. Students will find that the explanations are
accompanied by the related simple computer
clear and detailed in manner. It is considered as a bridge over the
programming codes (in Python and POV-Ray
obstacles in linear algebra and can be used with or without the help of
languages) make this book an extremely and
an instructor. While many linear algebra texts neglect geometry, this
unique useful tool to test the power of algorithmic information in
book includes numerous geometrical applications. For example, the
generating ordered structure models (2D and 3D) like regular geometric
book presents classical analytic geometry using concepts and methods
shapes, complex shapes like fractals and cellular automata, and
from linear algebra, discusses rotations from a geometric viewpoint,
biological systems as the organs of a living body. Informational biologists
gives a rigorous interpretation of the right-hand rule for the cross product
besides mathematicians and physicists of complexity may learn to test
using rotations and applies linear algebra to solve some nontrivial plane
their own capabilities in programming and modelling ordered structures
geometry problems.
starting from random initial conditions at different scale of each system.
Readership: Undergraduate students taking a first course in linear
algebra. Readership: Mathematicians, Physicists, Biologists, Bioengineers,
Computer Programmers, Science philosophers (of all graduate level).
508pp Jun 2019
978-981-120-022-9 US$148 £130 328pp Aug 2020
978-981-120-146-2(pbk) US$78 £70 978-981-121-715-9 US$138 £120For more information, visit: www.worldscientific.com WORLD SCIENTIFIC
World Scientific Series in Information Studies - Vol 11 World Scientific Series in Information Studies - Vol 10
Theoretical Information Studies Philosophy and Methodology of
Information in the World Information
edited by Mark Burgin (University of California, The Study of Information in the Transdisciplinary
Los Angeles, USA) & Gordana Dodig-Crnkovic Perspective
(Chalmers University of Technology, Sweden & edited by Gordana Dodig-Crnkovic (Chalmers
Mälardalen University, Sweden) University of Technology, Sweden & Mälardalen
The book presents results of collaboration across University, Sweden) & Mark Burgin (University
research fields within info-computational and of California, Los Angeles, USA)
info-structural frameworks, in attempt to better The book gives up-to-date, multi-aspect
theoretically and conceptually capture the phenomenon of information exposition of the philosophy and methodology of information, and related
and its dynamics (such as computation and communication), as they areas within the nascent field of the study of information. It presents the
appear on different levels of organization, on different scales and in most recent achievements, ideas and opinions of leading researchers in
different contexts. It covers the broadest range of phenomena related this domain, as well as from physicists, biologists and social scientists.
to information, with their structures and processes, as well as meta-level Collaboration of researchers from different areas and fields opens
investigation of the nature of the study of information including its logic, new perspectives for the understanding of information essential in the
metatheory and methodologies innovative development of science, technology and society.
Readership: Graduate students and researchers in Information Theory. The ideas presented give new insights for those who develop or
536pp Apr 2020 implement scientific, technological or social applications. They are
978-981-3277-48-9 US$158 £140 especially for those who are participating in setting the goals for science
in general and sciences of information in particular.
Readership: Graduate students and researchers in Information Theory.
Codes and Modular Forms
A Dictionary 576pp May 2019
by Minjia Shi (Anhui University, China), 978-981-3277-51-9 US$158 £140
YoungJu Choie (Pohang University of Science
and Technology (POSTECH), South Korea),
Anuradha Sharma (Indraprastha Institute of DIFFERENTIAL & INTEGRAL EQUATIONS
Information Technology Delhi, India) &
Patrick Solé (University of Aix Marseille, France)
Essential Textbooks
There are connections between invariant theory
and modular forms since the times of Felix Klein,
An Introduction to Differential
in the 19th century, connections between codes and lattices since the Equations with Applications
1960’s. The aim of the book is to explore the interplay between codes by Harold Cohen (California State University,
and modular forms. Here modular form is understood in a wide sense Los Angeles, USA) & Daniel Gallup
(Jacobi forms, Siegel forms, Hilbert forms). Codes comprises not only (Pasadena City College, USA)
linear spaces over finite fields but modules over some commutative
This book is for students in a first course in
rings. The connection between codes over finite fields and lattices has
ordinary differential equations. The material is
been well documented since the 1970s. Due to an avalanche of results
organized so that the presentations begin at a
on codes over rings since the 1990’s there is a need for an update at
reasonably introductory level. Subsequent material is developed from
book level.
this beginning. The book contains methods of approximation to solutions
Readership: Graduate students and researchers. of various types of differential equations with practical applications,
which will serve as a guide to programming so that such differential
232pp Nov 2019 equations can be solved numerically with the use of a computer. Students
978-981-121-291-8 US$88 £75 who intend to pursue a major in engineering, physical sciences, or
mathematics will find this book useful.
The Power of Computational Readership: Undergraduate students studying mathematics, physics,
Thinking engineering, business, economics and banking.
Games, Magic and Puzzles to Help You
816pp Sep 2020
Become a Computational Thinker
978-981-3276-65-9 US$168 £150
by Paul Curzon & Peter W McOwan
(Queen Mary University of London, UK)
Solving Linear Partial Differential
“A wonderful book full of ideas with which to
inspire and engage in computational thinking.
Equations
Core concepts and principles are brought to life Spectra
in fun and engaging ways through puzzles, magic by Martin Schechter (University of California,
tricks and games. This is a must-have book for Computing teachers.” Irvine, USA)
7
Dr Kevin R Bond, Managing Director, Educational Computing This book examines the general linear partial
Services Ltd differential equation of arbitrary order m. Even
this involves more methods than are known. We
The book has a unique and enjoyable introduction. The authors describe
ask a simple question: when can an equation be
the elements of computational thinking — such as algorithmic thinking,
solved and how many solutions does it have? The answer is surprising
decomposition, abstraction and pattern matching — in an entertaining
even for equations with constant coefficients. We begin with these
and accessible way, using magic tricks, games and puzzles, as well as
equations, first finding conditions which allow one to solve and obtain a
through real and challenging problems that computer scientists work on.
finite number of solutions. It is then shown how to obtain those solutions
Readership: Suitable as a general book for all those interested in lay by analyzing the structure of the equation very carefully.
science or recreational maths, or just interested in learning more about
Readership: Graduate students, researchers and specialists who come
computational thinking;
across linear partial equations in their work in the fields of mathemetics
232pp Mar 2017 and the physical sciences.
978-1-78634-183-9 US$58 £48
408pp Jul 2020
978-1-78634-184-6(pbk) US$24 £20
978-981-121-630-5 US$148 £130Mathematics Catalogue 2021
Trends in Abstract and Applied Analysis - Vol 9
Essential Textbooks
Boundary Value Problems for
Fractional Differential Equations Difference Equations for Scientists
and Systems and Engineering
by Bashir Ahmad (King Abdulaziz University, Interdisciplinary Difference Equations
Saudi Arabia), Johnny Henderson (Baylor by Michael A Radin (Rochester Institute of
University, USA) & Rodica Luca (“Gheorghe Technology, USA)
Asachi” Technical University of Iasi, Romania) “Radlin has done a nice job in producing a
textbook which provides a learner friendly
This book is devoted to the study of existence of
introduction to difference equations. It would
solutions or positive solutions for various classes suit as a core text for a first year course in the topic, aimed, as the
of Riemann – Liouville and Caputo fractional differential equations, and title suggests, at physical science or engineering undergraduates.
systems of fractional differential equations subject to nonlocal boundary The student who is prepared to work through the book will get a good
conditions. The monograph draws together many of the authors’ results, grounding in basic techniques and gain a feel for the possible behaviours
that have been obtained and highly cited in the literature in the last of standard equations. He will also be given some indication of the
four years. usefulness and potential complexity of discrete systems in modern
science and engineering.” London Mathematical Society
Readership: Mathematical and scientific researchers, and graduate
students in mathematics and science interested in the existence of We introduce interdisciplinary research and get students and the
solutions for fractional differential equations and systems. audience familiarized with the difference equations; solving them
explicitly, determining the long-term behavior of solutions (convergence,
328pp Feb 2021 boundedness and periodicity). We help to develop intuition in analyzing
978-981-122-445-4 US$118 £105 convergence of solutions in terms of subsequences and analyzing
patterns of periodic cycles. Our book helps you learn applications in
Series in Contemporary Applied Mathematics - Vol 22 biology, economics and business, computer science and engineering.
Control and Inverse Problems for Readership: Students and researchers in mathematics, physics, science
Partial Differential Equations and engineering.
edited by Gang Bao (Zhejiang University, China), 332pp Oct 2019
Jean-Michel Coron (Université Pierre et
978-981-120-385-5 US$118 £105
Marie Curie, France) & Tatsien Li (Fudan
978-981-120-296-4(pbk) US$58 £50
University, China)
This book is a collection of lecture notes for the Series on Analysis, Applications and Computation - Vol 9
LIASFMA Hangzhou Autumn School on “Control Nonlinear Waves
and Inverse Problems for Partial Differential A Geometrical Approach
Equations” which was held during October 17 – 22, 2016 at Zhejiang by Petar Popivanov & Angela Slavova
University, Hangzhou, China. This autumn school is one of the activities (Bulgarian Academy of Sciences, Bulgaria)
organized by Sino – French International Associate Laboratory in Applied
Mathematics (LIASFMA). Established jointly by eight institutions in This volume provides an in-depth treatment of
China and France in 2014, LIASFMA aims at providing a platform for several equations and systems of mathematical
many leading French and Chinese mathematicians to conduct in-depth physics, describing the propagation and
researches, extensive exchanges, and student training in broad areas interaction of nonlinear waves as different
of applied mathematics. modifications of these: the KdV equation,
Fornberg – Whitham equation, Vakhnenko equation, Camassa – Holm
Readership: Undergraduate and graduate students and researchers equation, several versions of the NLS equation, Kaup – Kupershmidt
in partial differential equations. equation, Boussinesq paradigm, and Manakov system, amongst others,
264pp Jun 2019 as well as symmetrizable quasilinear hyperbolic systems arising in fluid
978-981-3276-14-7 US$108 £95 dynamics.
Readers not familiar with the complicated methods used in the theory
of the equations of mathematical physics (functional analysis, harmonic
Essential Textbooks
analysis, spectral theory, topological methods, a priori estimates,
Partial Differential Equations conservation laws) can easily be acquainted here with different solutions
Methods, Applications and Theories of some nonlinear PDEs written in a sharp form (waves), with their
2nd Edition geometrical visualization and their interpretation. This volume is self-
by Harumi Hattori (West Virginia University, USA) contained and equipped with simple proofs. It contains many exercises
and examples arising from the applications in mechanics, physics, optics
This is an introductory level textbook for partial
and, quantum mechanics.
differential equations (PDEs). It is suitable for
a one-semester undergraduate level or two- Readership: University and graduate students, mathematicians,
8 semester graduate level course in PDEs or physicists, engineers and specialists in the fields of evolution PDEs
applied mathematics. This volume is application-oriented and rich in and their applications.
examples. Going through these examples, the reader is able to easily
grasp the basics of PDEs. Partial differential equations are becoming a 208pp Jan 2019
core subject in Engineering and the Sciences. This textbook will greatly 978-981-3271-60-9 US$88 £75
benefit those studying in these subjects by covering basic and advanced
topics in PDEs based on applications. Textbook: Request Inspection
Readership: Undergraduate students in mathematics, science, and Copy at sales@wspc.com
engineering. or scan the QR code
428pp Jul 2019
978-981-120-223-0
978-981-122-144-6(pbk)
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for your students at a lower cost.For more information, visit: www.worldscientific.com WORLD SCIENTIFIC
GEOMETRY & TOPOLOGY
Essential Textbooks Biharmonic Submanifolds and Biharmonic
An Elementary Overview of Maps in Riemannian Geometry
by Ye-Lin Ou (Texas A&M University-Commerce, USA)
Mathematical Structures & Bang-Yen Chen (Michigan State University, USA)
Algebra, Topology and Categories
by Marco Grandis Written by 2 experts in the subject, the book aims
(Università di Genova, Italy) to present a comprehensive survey on biharmonic
submanifolds and maps from the viewpoint of Riemannian
This book can be used as a textbook for geometry. It provides some basic knowledge and tools
undergraduate studies and for self-study. used in the study of the subject as well as an overall
It can provide students of Mathematics picture of the development of the subject with most up-
with a unified perspective of subjects which are often kept apart. to-date important results. Since 2000, biharmonic submanifolds and maps have
It is also addressed to students and researchers of disciplines become a vibrant research field with a growing number of researchers around
having strong interactions with Mathematics, like Physics and the world, with many interesting results have been obtained.
Chemistry, Statistics, Computer Science, Engineering.
This book containing basic knowledge, tools for some fundamental problems
Readership: Undergraduate and graduate students in and a comprehensive survey on the study of biharmonic submanifolds and
Mathematics, Physics, Computer Sciences, Chemistry, maps will be greatly beneficial for graduate students and beginning researchers
Statistics, Engineering. who want to study the subject, as well as researchers who have already been
working in the field.
385pp Sep 2020
978-981-122-031-9 US$118 £105 Readership: Graduate students and researchers from the fields of geometry
and analysis.
Algebraic Surfaces in 540pp Apr 2020
Positive Characteristics 978-981-121-237-6 US$178 £155
Purely Inseparable Phenomena
in Curves and Surfaces Fractals and Dynamics in Mathematics, Science, and the
by Masayoshi Miyanishi (Osaka Arts: Theory and Applications - Vol 5
University, Japan) & Hiroyuki Ito Analysis, Probability and Mathematical
(Tokyo University of Science, Japan) Physics on Fractals
This is the first book which explains edited by Patricia Alonso Ruiz (Texas A&M University,
the phenomena arising from purely USA), Joe P Chen (Colgate University, USA),
inseparable coverings and Artin – Schreier coverings. In most Luke G Rogers (University of Connecticut, USA),
cases, the base surfaces are rational, hence the covering Robert S Strichartz (Cornell University, USA) &
surfaces are unirational. There exists a vast, unexplored world Alexander Teplyaev (University of Connecticut, USA)
of unirational surfaces. In this book, we explain the Frobenius
sandwiches as examples of unirational surfaces. This book introduces background and recent progress on these problems,
from both established leaders in the field and early career researchers. The
Readership: Graduate students and researchers in the fields book gives a broad introduction to several foundational techniques in fractal
of Algebraic Geometry, Fields and Rings, and Commutative mathematics, while also introducing some specific new and significant results
Algebra. of interest to experts, such as that waves have infinite propagation speed on
fractals. It contains sufficient introductory material that it can be read by new
456pp Jul 2020 researchers or researchers from other areas who want to learn about fractal
978-981-121-520-9 US$138 £120 methods and results.
Readership: Academic mathematicians and physicists, both pure and applied,
Arc Schemes and working on fractals or rough spaces or interested in fractal media; Scientists
Singularities from the many areas in which fractal models are important,
edited by David Bourqui (Université de
Rennes 1, France), Johannes Nicaise 596pp Mar 2020
(Imperial College London, UK & University 978-981-121-552-0 US$158 £140
of Leuven, Belgium) & Julien Sebag
(Universitéde Rennes 1, France) A Guide to Lie Systems with Compatible
This title introduces the theory of arc Geometric Structures
schemes in algebraic geometry and by Javier de Lucas (University of Warsaw, Poland)
singularity theory, with special emphasis on recent developments & Cristina Sardón Muñoz (Instituto de Ciencias
around the Nash problem for surfaces. The main challenges are Matemáticas, Spain)
to understand the global and local structure of arc schemes, and 9
how they relate to the nature of the singularities on the variety. The book presents a comprehensive guide to the study
Since the arc scheme is an infinite dimensional object, new tools of Lie systems from the fundamentals of differential
need to be developed to give a precise meaning to the notion geometry to the development of contemporary research
of a singular point of the arc scheme. topics. It embraces several basic topics on differential
geometry and the study of geometric structures while
Other related topics are also explored, including motivic developing known applications in the theory of Lie systems. The book also
integration and dual intersection complexes of resolutions of includes a brief exploration of the applications of Lie systems to superequations,
singularities. Written by leading international experts, it offers discrete systems, and partial differential equations. Offering a complete overview
a broad overview of different applications of arc schemes in from the topic’s foundations to the present, this book is an ideal resource for
algebraic geometry, singularity theory and representation theory. Physics and Mathematics students, doctoral students and researchers.
Readership: Graduate students interested in algebraic
Readership: The book is aimed at Physics and Mathematics students finishing
geometry and the theory of arc schemes and the solution of
their degree, doctoral students, and researchers.
the Nash problem for surfaces.
312pp Apr 2020 424pp Feb 2020
978-1-78634-719-0 US$108 £95 978-1-78634-697-1 US$148 £130Mathematics Catalogue 2021
Metacyclic Groups and the Singularities — Kagoshima 2017
D(2) Problem Proceedings of the 5th Franco-Japanese-
by Francis E A Johnson Vietnamese Symposium on Singularities
(University College London, UK) The 5th Franco-Japanese-Vietnamese
Symposium on Singularities
This book solves the D(2) problem for a large, Kagoshima, Japan, 27 Oct – 3 Nov 2017
possibly infinite, number of finite metacyclic Editors-in-chief: Masaharu Ishikawa (Keio
groups G(p, q). Prior to this the author had solved University, Japan) & Shoji Yokura (Kagoshima
the D(2) problem for the groups G(p, 2). However,
University, Japan)
for q > 2, the only previously known solutions
were for the groups G(7, 3), G(5, 4) and G(7, 6), The main theme of the symposium was Singularity
all done by difficult direct calculation by two of the author’s students, Theory in a broad sense, including complex and real algebraic varieties,
Jonathan Remez (2011) and Jason Vittis (2019). functions and mappings, and topology of singularities. This volume
includes three surveys of recent trends based on the lectures in the
The method employed is heavily algebraic and involves precise analysis mini-school organized in the first two days of the symposium and articles
of the integral representation theory of G(p, q). Some noteworthy features presenting recent progress in Singularity Theory.
are a new cancellation theory of modules (Chapters 10 and 11) and a
simplified treatment (Chapters 5 and 12) of the author’s theory of Swan Readership: Graduate students and researchers.
homomorphisms. 312pp Jul 2020
Readership: Academic mathematicians; postgraduate and higher. 978-981-120-602-3 US$128 £115
280pp Jan 2021
978-981-122-275-7 US$85 £75
Notable Titles in
Geometry and Topology
Lectures on the Geometry of
Manifolds (3rd Edition) Lectures on Convex Sets
by Liviu I Nicolaescu (2nd Edition)
(University of Notre Dame, USA) by Valeriu Soltan (George Mason University, USA)
“This is an extremely complete book on the
The goal of this book is to introduce the reader to
fundamentals of the algebraic and topological
some of the main techniques, ideas and concepts
properties of convex sets. This is a well-written
frequently used in modern geometry. It starts
book, which should be of considerable use to
from scratch and it covers basic topics such as
researchers in convex geometry.” Zentralblatt
differential and integral calculus on manifolds,
MATH
connections on vector bundles and their curvatures, basic Riemannian
geometry, calculus of variations, DeRham cohomology, integral geometry The second edition essentially extends and revises the original book.
(tube and Crofton formulas), characteristic classes, elliptic equations on Every chapter is rewritten, with many new theorems, examples,
manifolds and Dirac operators. The new edition contains a new chapter problems, and bibliographical references included. It contains three new
on spectral geometry presenting recent results which appear here for chapters and 100 additional problems with solutions.
the first time in printed form.
Readership: Undergraduate and graduate students in mathematics,
Readership: Graduate students and researchers in global analysis, optimization and operations research.
differential geometry.
612pp Jan 2020
680pp Sep 2020
978-981-120-211-7 US$148 £130
978-981-121-481-3 US$180 £160
978-981-120-351-0(pbk) US$78 £70
978-981-121-595-7(pbk) US$98 £85
Geometric Foundations of Design Bestselling Author
Old and New Differential Geometry of Curves
by Jay Kappraff
(New Jersey Institute of Technology, USA)
and Surfaces
by Masaaki Umehara & Kotaro Yamada
This book is meant to serve either as a textbook (Tokyo Institute of Technology, Japan)
for an interdisciplinary course in Mathematics translated by Wayne Rossman
of Design, or as a trade book for designers. It (Kobe University, Japan)
will also be of interest for people interested in
recreational mathematics showing the connection “The book will serve as a very useful reference
between mathematics and design. Topics from for a broad range of applied mathematicians, physicists, as well as
the book can also be adapted for use in pre-college mathematics. Each theoretical geophysicists seeking a precise, systematic presentation
chapter will provide the user with ideas that can be incorporated in a of the differential geometry underlying much of modern theory. After
10 design. Background materials will be provided to show the reader the reading the book the reader should have a good feeling for the
mathematical principles that lie behind the designs. material presented, provided that he has done all the exercises! For
Key Features: mathematically oriented readers, I recommend also the additional
○ The book is highly graphic oriented with many examples of material.” Pure and Applied Geophysics
incorporating mathematics in design
This engrossing volume on curve and surface theories is the result of
○ Additional designs will be offered to the purchaser in a website
many years of experience the authors have had with teaching the most
○ Many topics are novel and have not been presented elsewhere
essential aspects of this subject. Surface theory from the viewpoint of
○ Every effort has been made to make the topics accessible
manifolds theory is explained, and encompasses higher level material
to non-mathematicians while at the same time being of
interest to experienced mathematicians that is useful for the more advanced student.
Readership: General Public, undergraduates and designers who are Readership: Undergraduate and graduate students, and researchers
interested in seeing the connection between mathematics and design. interested in differential geometry of curve and surface theories.
275pp Oct 2020 328pp Jun 2017
978-981-121-970-2 US$98 £85 978-981-4740-23-4 US$88 £73
978-981-4740-24-1(pbk) US$48 £42For more information, visit: www.worldscientific.com WORLD SCIENTIFIC
Lecture Notes Series, Institute for Mathematical
Essential Textbooks
Sciences, National University of Singapore - Vol 37
Advanced Textbooks in Mathematics
Mathematics of Shapes and
Conformal Maps and Geometry
Applications by Dmitry Beliaev (University of Oxford, UK)
edited by Sergey Kushnarev (Singapore
University of Technology and Design, Singapore), Though Riemann mapping theorem is frequently
Anqi Qiu (National University of Singapore, explored, there are few texts that discuss general
Singapore) & Laurent Younes (Johns Hopkins theory of univalent maps, conformal invariants,
University, USA) and Loewner evolution. This textbook provides an
accessible foundation of the theory of conformal
The volume illustrates this wealth of subjects by maps and their connections with geometry.
providing new contributions on the metric structure of diffeomorphism
groups and shape spaces, recent developments on deterministic and It offers a unique view of the field, as it is one of the first to discuss general
stochastic models of shape evolution, new computational methods theory of univalent maps at a graduate level, while introducing more
manipulating shapes, and new statistical tools to analyze shape datasets. complex theories of conformal invariants and extremal lengths. This book
In addition to these contributions, applications of shape analysis to is an ideal resource for graduate courses in Complex Analysis or as an
medical imaging and computational anatomy are discussed, leading, in analytic prerequisite to study the theory of Schramm – Loewner evolution.
particular, to improved understanding of the impact of cognitive diseases Readership: Advanced undergraduate or graduate students in
on the geometry of the brain. mathematics, especially those interested in analysis or theory of
Readership: Graduate students, applied mathematicians, statisticians, Schramm – Loewner Evolution.
computer scientists and biomedical engineers. 240pp Dec 2019
220pp Nov 2019 978-1-78634-613-1 US$88 £75
978-981-120-012-0 US$88 £75
MATHEMATICAL ANALYSIS
Fundamental Concepts in
Modern Analysis (2nd Edition) Essential Advance Level Textbooks
An Introduction to Nonlinear Analysis
by Vagn Lundsgaard Hansen A Course in Analysis
(Technical University of Denmark, Denmark) Vol. V: Functional Analysis, Some
With: Poul G Hjorth Operator Theory, Theory of Distributions
by Niels Jacob & Kristian P Evans
Review of the First Edition: (Swansea University, UK)
“It is written in a dense but very deep and
conceptual style. Its evident instructive character The book is an advanced textbook and a
is also one of the advantages of this textbook.” Mathematics Abstracts reference text in functional analysis in the wide
sense. It provides advanced undergraduate and
In this book, students from both pure and applied subjects are offered an graduate students with a coherent introduction
opportunity to work seriously with fundamental notions from mathematical to the field, and leads them to more demanding
analysis that are important not only from a mathematical point of view topics such as the spectral theorem, Choquet theory, interpolation theory,
but also occur frequently in the theoretical parts of, for example, the analysis of operator semigroups, Hilbert – Schmidt operators and Hille
engineering sciences. It is a useful resource for many sciences that – Tamarkin operators, topological vector spaces and distribution theory,
depend on fundamental techniques from mathematical analysis. fundamental solutions, or the Schwartz kernel theorem.
In this edition, the notions of compactness and sequentially compactness Readership: Advanced undergraduate students, graduate students,
are developed with independent proofs for the main results. This edition researchers in analysis.
also covers a new section on partial derivatives, and new material has
been incorporated to make a more complete account of higher order 856pp Mar 2020
derivatives in Banach spaces, including full proofs for symmetry of higher 978-981-121-549-0 US$198 £175
order derivatives and Taylor’s formula. 978-981-121-633-6(pbk) US$98 £85
Readership: Lecturers and students in pure and applied mathematics,
theoretical engineering and the physical sciences. Bestselling Author
304pp Nov 2019 The Fractional Laplacian
978-981-120-940-6 US$98 £85 by Wenxiong Chen (Yeshiva University, USA),
Yan Li (Yeshiva University, USA) & Pei Ma
Bestseller (Nanjing Forestry University, China)
This is a unique book that provides a compre-
Differential Forms hensive understanding of nonlinear equations
by Victor Guillemin & Peter Haine
involving the fractional Laplacian as well as other
(Massachusetts Institute of Technology, USA) 11
nonlocal operators. Beginning from the definition
There already exist a number of excellent graduate of fractional Laplacian, it gradually leads the readers to the frontier of
textbooks on the theory of differential forms as current research in this area. The explanations and illustrations are
well as a handful of very good undergraduate elementary enough so that first year graduate students can follow easily,
textbooks on multivariable calculus in which this while it is advanced enough to include many new ideas, methods, and
subject is briefly touched upon but not elaborated results that appeared recently in research literature, which researchers
on enough. The goal of this textbook is to be readable and usable for would find helpful. It focuses on introducing direct methods on the
undergraduates. It is entirely devoted to the subject of differential forms nonlocal problems without going through extensions, such as the direct
and explores a lot of its important ramifications. methods of moving planes, direct method of moving spheres, direct
blowing up and rescaling arguments, and so on.
Readership: First-year graduate and advanced undergraduate students
in math programs. Readership: Graduate students and researchers interested in analysis
and differential equations.
272pp Mar 2019
978-981-3272-77-4 US$88 £75 344pp Jul 2020
978-981-121-377-9(pbk) US$48 £40 978-981-3223-99-8 US$128 £113Mathematics Catalogue 2021
Bounded Symmetric Domains in Banach Bestseller
Spaces Essential Textbooks in Mathematics
by Cho-Ho Chu (Queen Mary, University of London, UK)
A Friendly Approach to
This timely book exposes succinctly recent advances in Functional Analysis
the geometric and analytic theory of bounded symmetric by Amol Sasane (London School of
domains. A unique feature is the unified treatment to both Economics, UK)
finite and infinite dimensional symmetric domains, using
Jordan theory in tandem with Lie theory. The highlights “This is a nice and modern introduction
include a generalized Riemann mapping theorem, which to the topic ... If the reader is a student
realizes a bounded symmetric domain as the open unit ball who wants to be become proficient in the
of a complex Banach space with a Jordan structure. Far-reaching applications subject, then solving the exercises, or as many as possible, is
of this realization in complex geometry and function theory are discussed. an excellent way to acquire the necessary skills. The flexible
This monograph is intended to be a convenient reference for researchers and possibilities provided — the text can be used as lecture notes for
graduate students in geometric analysis, infinite dimensional holomorphy as well a course, or as a tool for self study, and even as a handbook to
as functional analysis and operator theory. look up some definitions or theorems.” European Mathematical
Society
Readership: Graduate students and researchers in diverse mathematical fields
including complex geometry, function theory, functional analysis and operator This book constitutes a concise introductory course on
theory. It would also appeal to algebraists who are interested in the applications Functional Analysis for students who have studied calculus
of Jordan and Lie algebras. and linear algebra. The topics covered are Banach spaces,
continuous linear transformations, Frechet derivative, geometry
404pp Oct 2020 of Hilbert spaces, compact operators, and distributions. In
978-981-121-410-3 US$98 £85 addition, the book includes selected applications of functional
analysis to differential equations, optimization, physics (classical
Lectures on Functional Analysis and and quantum mechanics), and numerical analysis. The book
contains 197 problems, meant to reinforce the fundamental
Applications (2nd Edition) concepts. The inclusion of detailed solutions to all the exercises
by V S Pugachev & I N Sinitsyn
makes the book ideal also for self-study.
(Russian Academy of Sciences, Russia)
Readership: Graduate students in functional analysis, operator
This volume is not only intended for mathematicians
theory and mathematical physics.
who deal with applications of functional analysis, but
also for those having only a moderate background 396pp Apr 2017
in mathematics in their areas of work. The materials 978-1-78634-333-8 US$118 £98
covered, which includes practically all the information 978-1-78634-334-5(pbk) US$68 £56
on functional analysis that may be necessary for those
working in various areas of mathematics applications, as well as the simplicity
Series on Number Theory and
of presentation, differentiates this book from others. The method and style of
Its Applications - Vol 14
presentation of materials make it digestible and easily understood by readers.
Problems and Solutions in
This second edition includes new and updated 300 examples and more than
500 problems to help readers understand and master the theories presented. In Real Analysis (2nd Edition)
addition, necessary improvements for bringing the contents more up to date with by Masayoshi Hata
current fundamental and applied developments in Chapters 1 – 10 were made. (Kyoto University, Japan)
Readership: Undergraduate and graduate students as well as researchers in This second edition introduces an
applied mathematics, and engineers. additional set of new mathematical
problems with their detailed solutions in
800pp Jun 2021 real analysis. It also provides numerous
978-981-3203-17-4 US$178 £148 improved solutions to the existing problems from the previous
978-981-3203-18-1(pbk) US$88 £73 edition, and includes very useful tips and skills for the readers
to master successfully. There are three more chapters that
expand further on the topics of Bernoulli numbers, differential
Krzyz• Conjecture: Theory and Methods equations and metric spaces.
A Research Diary of a Mathematician
by Ronen Peretz (Ben Gurion University of Problems and Solutions in Real Analysis can be treated as a
the Negev, Israel) collection of advanced exercises by undergraduate students
during or after their courses of calculus and linear algebra. It
This book is about one of the beautiful topics in is also instructive for graduate students who are interested in
mathematics. It describes an on-going research on analytic number theory. Readers will also be able to completely
bounded analytic functions which are defined on the grasp a simple and elementary proof of the Prime Number
unit disc. This is a very active topic that belongs to the Theorem through several exercises. This volume is also suitable
theory of complex analysis in a single complex variable. for non-experts who wish to understand mathematical analysis.
12 It contains the analytic theory of functions, the geometric
function theory among other theoretical areas, as well as many applications. Readership: Undergraduates and graduate students in
Some applications originate in other fields of mathematics: geometry, topology, mathematical analysis.
arithmetic and number theory in general, algebra etc. Other applications originate
376pp Feb 2017
in other scientific and engineering disciplines: physics, dynamical systems,
electrical engineering etc. 978-981-3142-81-7 US$88 £73
978-981-3142-82-4(pbk) US$48 £40
The book includes much more than just a review on the Krzyż Conjecture.
It includes topics on inner functions within the context of problems that are
different from the Krzyż Conjecture as well as other topics on general bounded
Save the
analytic functions.
Readership: Complex Analysis, Geometric Function Theory, Extremal
problems, for graduate students and experts in those areas. environment
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