Due 2018-10-23
1st ed. 2018, Approx. 190 p.
Printed book
Softcover
ISBN 978-3-319-92239-3
Covers both classical results from the 1960s and very recent results on highdimensional
approximation
Contains a number of short illustrative proofs
Provides the first comprehensive survey on hyperbolic cross approximation of
the mixed smoothness classes of multivariate functions
This book gives a systematic survey of classical and recent results on hyperbolic cross
approximation. Motivated by numerous applications, the last two decades have seen great
success in studying multivariate approximation. The multivariate problems turn out to be much
more difficult than their univariate counterparts. Recent findings have established that
multivariate mixed smoothness classes play a fundamental role in high-dimensional
approximation. The book presents results and discussions of linear and nonlinear
approximations of the mixed smoothness classes. Many important open problems in the book
will provide both students and professionals ideas for further research.
Due 2018-11-08
Approx. 500 p.
Printed book
Hardcover
ISBN 978-3-319-94219-3
Attempts to close the gap between the mathematical community’s
understanding of the B model and the A model
Brings together mathematical and physical perspectives in one reference,
providing a unique opportunity for the two communities to learn from one
another
Provides an overview of several methods by which mirrors have been
constructed
Details the “BCOV” B-model theory from a physical perspective
This book collects various perspectives, contributed by both mathematicians and physicists, on
the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in
both the mathematics and physics communities, but among mathematicians, the “A-model” half
of the story remains much better-understood than the B-model. This book aims to address that
imbalance. It begins with an overview of several methods by which mirrors have been
constructed, and from there, gives a thorough account of the “BCOV” B-model theory from a
physical perspective; this includes the appearance of such phenomena as the holomorphic
anomaly equation and connections to number theory via modularity. Following a mathematical
exposition of the subject of quantization, the remainder of the book is devoted to the B-model
from a mathematician’s point-of-view, including such topics as polyvector fields and primitive
forms, Givental’s ancestor potential, and integrable systems.
Due 2018-09-15
1st ed. 2018, XXII, 398 p.
19 illus., 4 illus. in color.
Printed book
Softcover
ISBN 978-3-319-94772-3
Provides a wide-ranging and up-to-date account on the history of abstract
algebra
Covers topics from number theory (especially quadratic forms) and Galois
theory as far as the origins of the abstract theories of groups, rings and fields
Develops the mathematical and the historical skills needed to understand the
subject
Presents material that is difficult to find elsewhere, including translations of
Gauss’s sixth proof of quadratic reciprocity, parts of Jordan’s Traite and
Dedekind’s 11th supplement, as well as a summary of Klein’s work on the
icosahedron
This textbook provides an accessible account of the history of abstract algebra, tracing a range
of topics in modern algebra and number theory back to their modest presence in the
seventeenth and eighteenth centuries, and exploring the impact of ideas on the development
of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book
progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether.
Approaching mathematical topics from a historical perspective, the author explores quadratic
forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory,
commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will
learn what Galois accomplished, how difficult the proofs of his theorems were, and how
important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach
to the solution of equations. The book also describes the relationship between Kummer’s ideal
numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor
problem was better than Kummer’s. Designed for a course in the history of modern algebra,
this book is aimed at undergraduate students with an introductory background in algebra but
will also appeal to researchers with a general interest in the topic. With exercises at the end of
each chapter and appendices providing material difficult to find elsewhere, this book is selfcontained
and therefore suitable for self-study.
Due 2018-11-02
1st ed. 2018, Approx. 550 p.
Printed book
Hardcover
ISBN 978-981-13-1228-1
Elucidates a truly global view of Radha Charan Gupta’s history of mathematics
Offers an immensely useful approach to the history of mathematics and,
particularly, Indian mathematics
Brings together original retyped articles and scanned figures (drawn by Prof.
Gupta himself)
This book includes 57 selected articles that highlight the major contributions of Professor
Radha Charan Gupta?a doyen of history of mathematics?written on a variety of important
topics pertaining to mathematics and astronomy in India. It is divided into ten parts. Part 1
presents two articles offering an overview of Professor Gupta’s oeuvre. The four articles in part
II convey the importance of studies in the history of mathematics. Parts III?VII constituting 33
articles, feature a number of articles on a variety of topics, such as geometry, trigonometry,
algebra, combinatorics and spherical trigonometry, which not only reveal the breadth and depth
of Professor Gupta’s work, but also highlight his deep commitment to the promotion of studies
in the history of mathematics. The ten articles of part VIII, present interesting bibliographical
sketches of a few veteran historians of mathematics and astronomy in India. Part IX examines
the dissemination of mathematical knowledge across different civilisations. The last part
presents an up-to-date bibliography of Gupta’s work. It also includes a tribute to him in
Sanskrit composed in eight verses.
Due 2018-09-17
1st ed. 2018, VIII, 493 p.
393 illus., 4 illus. in color.
Printed book
Hardcover
ISBN 978-3-319-94062-5
Freely accessible solutions to every-other-odd exercise are posted to the book’
s Springer website; Instructors contact the authors for a full solutions manual
Includes a plethora of worked examples and exercises with varying degrees of
difficulty
Designed for flexible use by instructors and students
Numerous graphics help illustrate even the most abstract concepts
This textbook is intended for a one semester course in complex analysis for upper level
undergraduates in mathematics. Applications, primary motivations for this text, are presented
hand-in-hand with theory enabling this text to serve well in courses for students in engineering
or applied sciences. The overall aim in designing this text is to accommodate students of
different mathematical backgrounds and to achieve a balance between presentations of
rigorous mathematical proofs and applications. The text is adapted to enable maximum
flexibility to instructors and to students who may also choose to progress through the material
outside of coursework. Detailed examples may be covered in one course, giving the instructor
the option to choose those that are best suited for discussion. Examples showcase a variety of
problems with completely worked out solutions, assisting students in working through the
exercises.The numerous exercises vary in difficulty from simple applications of formulas to
more advanced project-type problems. Detailed hints accompany the more challenging
problems. Multi-part exercises may be assigned to individual students, to groups as projects, or
serve as further illustrations for the instructor. Widely used graphics clarify both concrete and
abstract concepts, helping students visualize the proofs of many results. Freely accessible
solutions to every-other-odd exercise are posted to the book’s Springer website. Additional
solutions for instructors’ use may be obtained by contacting the authors directly.
*******************************************************
Due 2019-03-11
1st ed. 2019, XXXI, 325 p.
23 illus. in color.
Printed book
Softcover
ISBN 978-3-319-94237-7
Deals with new, challenging problems in nonlinear analysis and solves several
open problems and questions
Gives a good overview of existing methods and presents new ideas and
results as well
Proposes open problems, research ideas and suggestions
This book is devoted to the study of positive solutions to indefinite problems. The monograph
intelligibly provides an extensive overview of topological methods and introduces new ideas
and results. Sticking to the one-dimensional setting, the author shows that compelling and
substantial research can be obtained and presented in a penetrable way. In particular, the
book focuses on second order nonlinear differential equations. The author analyzes the
Dirichlet, Neumann and periodic boundary value problems associated with the equation and
provides existence, nonexistence and multiplicity results for positive solutions. The author
proposes a new approach based on topological degree theory that allows him to answer some
open questions and solve a conjecture about the dependence of the number of positive
solutions on the nodal behaviour of the nonlinear term of the equation. The new technique
developed in the book gives, as a byproduct, infinitely many subharmonic solutions and
globally defined positive solutions with chaotic behaviour. Furthermore, some future directions
for research, open questions and interesting, unexplored topics of investigation are proposed.
330pp Feb 2019
ISBN: 978-981-3238-84-8 (softcover)
The aim of the solutions manual is to provide comprehensive yet elementary solutions to each of the 489 problems that appeared in the textbook.
The solutions manual contains full solutions to each problem in the parent textbook. The solutions to each problem are written from a first principles approach, which would have further augment the understanding of the important and recurring concepts in each chapter. Moreover, the solutions are written in a relatively self-contained manner, with very little undergraduate mathematics assumed. In that regard, the solutions manual appeals to a wide range of readers, from secondary and junior college students, undergraduates, to teachers and professors.
Foreword
Preface
Solutions to Exercise 1
Solutions to Exercise 2
Solutions to Exercise 3
Solutions to Exercise 4
Solutions to Exercise 5
Solutions to Exercise 6
Readership: Students doing combinatorics.
208pp Jul 2019
ISBN: 978-981-3271-60-9 (hardcover)
This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg?Whitham equation, Vakhnenko equation, Camassa?Holm equation, several versions of the NLS equation, Kaup?Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.
Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied.
At the end, the paradifferential approach is used. This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics, quantum mechanics, amongst others.
Introduction
Traveling Waves and their Profiles
Solvability of PDEs from Physics and Geometry
Interaction of Peakons and Kinks
Dressing Method and Geometrical Applications
Hirota's Method in Soliton Theory
Special Type Solutions of Evolution PDEs
Regularity Properties of Nonlinear Hyperbolic PDEs
Readership: University and graduate students, mathematicians, physicists, engineers and specialists in the fields of evolution PDEs and their applications.