Format: Hardback, 313 pages, height x width: 235x155 mm, 14 Illustrations, color; 17 Illustrations, black and white
Series: Applied and Numerical Harmonic Analysis
Pub. Date: 03-May-2026
ISBN-13: 9783032126368
Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the second volume of a tribute to Strichartz' work and legacy, featuring chapters written by his colleagues and friends that explore his mathematical contributions, as well as some of the latest developments in these areas.
Preface.- The Einstein Relation on Metric Measure Spaces.- Numerical
investigation of Holder exponent for harmonic functions on Sierpinski
Carpets.- Fractal Complex Dimensions and Cohomology of the Weierstrass
Curve.- Surjectivity of spectral multipliers on p.c.f. fractals.- Scaling
limit of the sandpile identity element on the Sierpinski gasket.-
𝑝-Energy forms on fractals: recent progress.- Generalised
KrenFeller operators and gap diffusions via transformations of measure
spaces.- Strichartz inequalities: some recent developments.- Self-similar
energies on Fractals obtained by anti-attracting maps.- Fractal curvatures
and short-time asymptotics of heat content.
Format: Hardback, 170 pages, height x width: 235x155 mm, X, 170 p.
Series: Springer Monographs in Mathematics
Pub. Date: 22-Mar-2026
ISBN-13: 9783032175052
Coclass is a powerful invariant that reveals patterns in the intricate landscape of finite p-groups. This monograph offers a gentle introduction to coclass theory, presenting key developments from the past two decades within a unified framework and discussing open conjectures. Alongside a systematic exposition of established results, the book presents new findings and some corrections to the literature. Special emphasis is placed on coclass graphs and their remarkable periodic structures. Intended for readers with a graduate-level background in group theory and algebra, the book is accessible to newcomers, including graduate students, while also serving as a reliable reference for researchers.
1 Introduction to coclass graphs.- 2 Constructive methods and
visualisations.- 3 Number theory and group constructions.- 4 Matrix groups
and uniseriality.- 5 Cohomology theory and extensions.- 6 The number of
infinite paths in G¹ (p,r).- 7 Periodicity I.- 8 The skeletons of a coclass
tree.- 9 Groups of maximal class.- 10 Towards Periodicity II.- References.-
Index.- List of Symbols.
Format: Paperback / softback, 90 pages, height x width: 235x155 mm, 20 Illustrations, color; 1 Illustrations, black and white
Series: SpringerBriefs on PDEs and Data Science
Pub. Date: 20-Apr-2026
ISBN-13: 9789819570485
PDE constrained optimization problems are frequently encountered in many academic or industrial contexts. This book shows how to attack and solve a given PDE constrained optimization problem thanks to the efficient and expert tool FreeFEM.
This book is intended for students and researchers aiming at learning how to efficiently solve, with the software FreeFEM, optimization problems under partial differential equations (PDE) constraints. The readers are expected to have a basic knowledge in the analysis and numerical solving of partial differential equations with finite element methods, in optimization, in algorithmics and numerical implementation.
All the codes are available at FreeFEMs github and can hopefully serve as templates for the users.
Chapter.1.State of the art .
Chapter.2.PDE constrained optimization
with FreeFEM.
Chapter.3.Plateau problem.
Chapter.4.Shape optimization with
FreeFEM.- A Supplements.- B Identification of parameters with FreeFEM.-
Listings.
Format: Paperback / softback, 241 pages, height x width: 235x155 mm, 139 Illustrations, color; 11 Illustrations, black and white
Series: Mathematics Study Resources
Pub. Date: 31-Mar-2026
ISBN-13: 9783662729175
This book presents methods from the history of mathematics that have not become standard methods or even made it into classic textbooks. These alternative approaches were often popular at the time of their creation, but then lost attention compared to today's standard methods and eventually fell into oblivion. Often these methods still contain unused potential: It is worth developing them further and discovering where exactly their limits lie.
The book aims to provide prospective teachers with a view beyond the usual teaching content and provide content suggestions for working with interested and talented students. For example, Archimedes developed a method for calculating the area of a parabolic segment, which in a way anticipates a piece of integral calculus. However, Archimedes' method did not develop into the standard method found in today's textbooks. Instead, you will find the methods designed by Newton and Leibniz. This book develops the Archimedean method further and shows its "residual potential": Other curves, not just parabolas, can be similarly approached and it is interesting and instructive to see how far Archimedes' method can be developed and where it ultimately reaches its limits.
This book is a translation of the original German edition Seitenwege in der Mathematikgeschichte (2024). The translation was done with the help of an artificial intelligence machine translation tool. In the subsequent editing, the author and his colleague Helmer Aslaksen (Uni Oslo) carefully reviewed the translation. Still, the book may read stylistically differently from a conventional translation.
Preface.-
1. Area Determinations With Archimedes.-
2. Indian Roots.-
3. Integration and Differentiation A Generalization of the Method of Gregorius.-
4. Two Methods of Integration by Fermat.-
5. The Resection Method of Leibniz and Its Inversion.-
6. The Fan Method.-
7. A new round with 𝜋.
Format: Hardback, 613 pages, height x width: 235x155 mm, 138 Illustrations, color; 40 Illustrations, black and white
Series: Interdisciplinary Applied Mathematics
Pub. Date: 13-Apr-2026
ISBN-13: 9783032148841
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The books content lies at the interface of epidemiology, graph theory, stochastic processes and dynamical systems. This second edition has been substantially expanded from 11 to 15 chapters, adding comprehensive coverage of stochastic models, statistical inference, simple and complex contagions, and higher-order network structures. New material reflects recent theoretical advances, while maintaining the unified mathematical framework that made the first edition so valuable. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by:
Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches, including stochastic models, to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Introducing likelihood-based inference frameworks and Bayesian tools for parameter estimation from real epidemic data; Extending classical network epidemic models to higher-order structures and complex contagion processes; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve differential equation models or directly simulate epidemics on networks.
Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike.
Preface.- Introduction to Networks and Diseases.- Exact Propagation
Models: Top Down.- Exact Propagation Models: Bottom-Up.- Mean-Field
Approximations for Heterogeneous Networks.- Percolation-Based Approaches for
Disease Modelling.- Hierarchies of SIR Models.- Dynamic and Adaptive
Networks.- Non-Markovian Epidemics.- PDE Limits for Large Networks.- Disease
Spread in Networks with Large-scale Structure.- Appendix: Stochastic
Simulation.- Index.
*
Format: Hardback, 330 pages, height x width: 235x155 mm, 1 Illustrations, color; 13 Illustrations, black and white
Series: Indian National Science Academy
Pub. Date: 08-May-2026
ISBN-13: 9789819561513
This volume brings together fourteen essays authored by distinguished mathematicians from India, offering a panoramic view of current research directions as well as recent historical developments in mathematics in India. The articles cover diverse topicsnumber theory, operator algebra, operator theory, harmonic analysis, quantum learning, noncommutative geometry and random matricesshowcasing the breadth and depth of contemporary mathematical research. The book provides a vivid snapshot of mathematical thought as it evolves today, connecting tradition with innovation and offering both insight and inspiration to the next generation of mathematicians.
The volume opens with an illuminating essay by M. S. Raghunathan, Some Highlights of Indian Contributions to Mathematics in the 20th Century, a comprehensive historical account of post-Independence mathematical research in India that will inspire young readers and scholars alike. A special inclusion is the research article Symmetric Products and Moduli Spaces of Vector Bundles on Curves by Kyoung-Seog Lee and the late M. S. Narasimhan, completed shortly before Narasimhans passing in 2021. This paper, which has already attracted wide attention in the research community, stands as a fitting tribute to his enduring influence in algebraic geometry.
Some Highlights of Indian Contributions to Mathematics in the 20th
Century.- Convex Analysis-Statistical Theory of Decisions and of Machine
Learning Classical and Quantum.- Symmetric Products and Moduli Spaces of
Vector Bundles of Curves.- Classification of C algebras, Spaces of Operators
and Function Spaces using the Geometry of Banach Spaces.- Contribution to
Random Matrices by Indian statisticians and Probabilists: A Brief Survey.-
Normalisation of Scores, Multiple Choice Questions, over Multi-phase Tests.-
Recent Developments in Analytic Number Theory.- A brief history of
Noncommutative Geometry in India.- A Compendium of Research in Operator
Theory and Operator Algebra.- Hardy-Hilbert Spaces for General Domains.- The
Geometry of Bruhat-Tits Groups.- A Survey of Fourier Analysis on Riemannian
Symmetric Spaces: Contribution of Indian Mathematicians (20002025).-
Positivity and Negativity Preservers under the Entrywise Calculus.- A Survey
and a Result on Inhomogeneous Quadratic Forms.
Format: Hardback, 512 pages, height x width: 235x155 mm, X, 512 p.
Pub. Date: 04-Apr-2026
ISBN-13: 9783032171054
This book offers a historical and analytical study of the origins of holomorphic dynamicsa field linking analytic functions with the behavior of iterated orbits. Central to this account is the 19151918 Grand Prix des Sciences Mathématiques, whose winning manuscript extended local research to the entire Riemann sphere and highlighted the striking properties of boundaries between basins of convergence.
Viewed broadly, this event marked a convergence of research traditions from the eighteenth and nineteenth centuriesinfinitesimal calculus, singular points, infinite series, functional equations, root separation, complex analysis, multi-valued functions, and sequences of functionseach a cornerstone for the general theory that now holds a prominent place in modern analysis.
Drawing on unpublished archival material, original French sources, and the intellectual context of early twentieth-century mathematics, the book reconstructs how scientific ambitions and evolving techniques shaped foundational developments in the analysis of complex functions and their iterative dynamics. Blending historical narrative with critique and technical insight, it will appeal to scholars and students interested in the history of mathematics, holomorphic dynamics, and the interplay between ideas and their historical milieu.
1 Introduction.- 2 Tools of infinity.- 3 Overview of the educational
system.- 4 Parental bonds.- 5 Of functionals, notations, and iterates.- 6
Marvels of function composition.- 7 Now it is complex analysis.- 8 A truly
essential point.- 9 Prodigious theorems.- 10 Multi-valued functions.- 11
Confluence.- 12 We who are not as others.- 13 The inception of holomorphic
dynamics.- 14 On the eastern front.- 15 Assessments.- 16 Gearing up for new
discoveries.- 17 The Grand Prix of 1918.- 18 Epilogue.- 19 Insights and
Fill-ins.- 20 Contributions to complex analysis.- Julias memoir on the
iteration of meromorphic functions.- 21 Remarks on the memoir.- 22 The four
sealed envelopes.- Grand Prix des Mathématiques - Dossier.- 23 Presentation
of the dossier.- 24 The reports.- 25 The manuscript of Salvatore Pincherle.-
Appendices.- A Normal families: an exegesis of Julias and Fatous memoirs.-
B Baires theory.- C A stranger in a strange land.- D Incommensurable avec
2.- References.- Alphabetical Index.
Format: Hardback, 142 pages, height x width: 235x155 mm, 28 Illustrations, black and white
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Pub. Date: 12-Apr-2026
ISBN-13: 9783032150561
This book provides the first variorum translation into English of Isaac Newtons De motu corporum in gyrum, from the 1685 manuscript at Cambridge University Library (UCL Add. 3990).
It offers a unique perspective on the development of Newtons views on a number of critical issues before the publication of the first edition of the Principia in 1687.
The book fills a critical gap in Newton scholarship. The translation deliberately reflects the vocabulary and syntax of Newtons Latin as closely as possible, enabling the reader to track the text in the manuscript almost word-by-word, including the ubiquitous inserts and deletions that show where and how Newton changes his mind or struggles with the formulation of a point.
Preface.- Introduction.- De motu Corporum, Liber Secundus: A Variorum
Translation.- Notes on Newtons Latin Vocabulary.- Appendix 1: De motu
corporum in mediis regulariter cedentibus (pre Liber Secundus).- Appendix 2:
De motu Corporum, Liber Primus (pre Liber Secundus).- Appendix 3: A
Disconnected Fragment from Liber Primus (pre Liber Secundus).- Appendix 4:
De motu Corporum, Definitiones (post Liber Secundus).- Appendix 5: De motu
Corporum, Liber Primus (post Liber Secundus).- De Motu Corporum, Liber
Secundus: An Article-by-Article Commentary.
Format: Hardback, 388 pages, height x width: 235x155 mm, 89 Illustrations, black and white
Series: Springer Asia Pacific Mathematics Series
Pub. Date: 15-Apr-2026
ISBN-13: 9789819555628
This book presents finite difference methods for three types of classical linear PDEs, three types of nonlinear PDEs and fractional PDEs. Specific topics cover two-point boundary value problems, elliptic equations, parabolic equations, hyperbolic equations, high-dimensional evolution equations, Schr\''{o}dinger equations, the Burgers' equation, the Korteweg-de Vries equation, and fractional diffusion-wave equations.
The book strives to achieve:
(a) Featured content. Thorough and dedicated presentations are provided for the finite difference methods.
(b) Scattered difficulty. Starting from a simple two-point boundary value problem for an ODE, authors introduce core concepts and analytical techniques of the finite difference methods, then apply them to handle with various partial differential equations.
(c) Emphasis on practicability. For each algorithm, provided numerical examples enable students to learn how to apply it and verify theoretical results with numerical outcomes.
The book is suitable for advanced undergraduate and beginning graduate students in applied mathematics and engineering.
Finite Dierence Methods for Two-point Boundary Value Problems.- Finite
Dierence Methods for Elliptic Equations.- Finite Dierence Methods for
Parabolic Equations.- Finite Dierence Methods for Hyperbolic Equations.-
Alternative Directional Implicit Methods for High-dimensional Evolution
Equations.- Finite Dierence Methods for Fractional Dierential Equations.-
Finite Dierence Methods for the SchrØodinger Equation.- Finite Dierence
Methods for the Burgers Equation.- Finite Dierence Methods for the
Korteweg-de Vries Equation.- Bibliography.- Index.