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In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. The text concentrates in particular on Riemann's only work on prime numbers, including ideas – new at the time – such as analytical continuation into the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta-function is presented. The impact of Riemann's ideas on regularizing infinite values in field theory is also emphasized. This revised and enhanced new edition contains three new chapters, two on the application of Riemann's zeta-function regularization to obtain the partition function of a Bose (Fermi) oscillator and one on the zeta-function regularization in quantum electrodynamics. Appendix A2 has been re-written to make the calculations more transparent. A summary of Euler-Riemann formulae completes the book.

'The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems, and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time. In this printing of Ramanujan's collected papers, Bruce Berndt provides an annotated guide to Ramanujan's work and to the mathematics it inspired over the last three-quarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do'--Provided by publisher.

Cal Elgot was a very serious and thoughtful researcher, who with great determi­ nation attempted to find basic explanations for certain mathematical phenomena­ as the selection of papers in this volume well illustrate. His approach was, for the most part, rather finitist and constructivist, and he was inevitably drawn to studies of the process of computation. It seems to me that his early work on decision problems relating automata and logic, starting with his thesis under Roger Lyndon and continuing with joint work with Biichi, Wright, Copi, Rutledge, Mezei, and then later with Rabin, set the stage for his attack on the theory of computation through the abstract treatment of the notion of a machine. This is also apparent in his joint work with A. Robinson reproduced here and in his joint papers with John Shepherdson. Of course in the light of subsequent work on decision problems by Biichi, Rabin, Shelah, and many, many others, the subject has been placed on a completely different plane from what it was when Elgot left the area. But I feel that his papers, results-and style-were very definitely influential at the time and may well have altered the course of the investigation of these problems. As Sammy Eilenberg explains, the next big influence on Elgot's thinking was category theory, which gave him a way of expressing his ideas in a sharply algebraic manner. The joint book with Eilenberg is one illustration of this influence.

This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner onthe convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.

Even at the beginning of the 21st century, we are far from becoming paperless. Pen and paper is still the only truly ubiquitous information processing technology. Pen-and-paper user interfaces bridge the gap between paper and the digital world. Rather than replacing paper with electronic media, they seamlessly integrate both worlds in a hybrid user interface. Classical paper documents become interactive. This opens up a huge field of novel computer applications at our workplaces and in our homes. This book provides readers with a broad and extensive overview of the field, so as to provide a full and up-to-date picture of pen-and-paper computing. It covers the underlying technologies, reviews the variety of modern interface concepts and discusses future directions of pen-and-paper computing. Based on the author's award-winning dissertation, the book also provides the first theoretical interaction model of pen-and-paper user interfaces and an integrated set of interaction techniques for knowledge workers. The model proposes a ‘construction set'of core interactions that are helpful in designing solutions that address the diversity of pen-and-paper environments. The interaction techniques, concrete instantiations of the model, provide innovative support for working with printed and digital documents. They integrate well-established paper-based practices with concepts derived from hypertext and social media.Researchers, practitioners who are considering deploying pen-and-paper user interfaces in real-world projects, and interested readers from other research disciplines will find the book an invaluable reference source. Also, it provides an introduction to pen-and-paper computing for the academic curriculum. The present book was overdue: a thorough, concise, and well-organized compendium of marriages between paper-based and electronic documents.Max Mühlhäuser, Technische UniversitätDarmstadtEveryone interested in how to design for real-world activities would profit from reading this book.James D. Hollan, University of California, San Diego

The theory of nonlinear oscillations and stability of motion is a fundamental part of the study of numerous real world phenomena. These phenomena, particularly auto-oscillations of the first and second kind, capture, para­ metric, subharmonic and ultraharmonic resonance, asymptotic behavior and orbits'stability, constitute the core of problems treated in'Nonlinear Mechanics', and their study is connected with the names of H. Poincare, A. M. Lyapunov, N. M. Krylov and N. N. Bogolyubov. Professor Demetrios Magiros, a widely known scientist in the theories of oscillations and nonlinear differential equations, has devoted his numerous works to this significant part of modern physical science. His scientific results can be classified in the following way: I) creation of methods of analysis of subharmonic resonances under the nonlinear effect, 2) determination and analysis of the main modes of nonlinear oscillations on the basis of infinite determinants, 3) analysis of problems of celestial mechanics, 4) classification of stability of solutions of dynamic systems concepts, 5) mathematical analogs of physical and social systems. He has developed new methods and solutions for a great number of difficult problems of nonlinear mechanics making a significant contri­ bution to the theory and applications of the field. Urgency, depth of perception of the considered phenomena, and practi­ cal directness are characteristics of his work.

This open access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.

This volume comprises selected papers from the SIAM International Meshing Roundtable Workshop 2023, SIAM IMR 2023, held in Amsterdam, the Netherlands, March 6-9, 2023. The IMR was started by Sandia National Laboratories in 1992 and, since 2021, it has been held under the umbrella of the Society for Industrial and Applied Mathematics (SIAM). The SIAM IMR 2023 was the first in-situ conference to be held since 2019, after two online conferences. It consisted of short courses, technical presentations from keynotes, contributed talks and research notes, a poster session and meshing contest, and discussion panels. The papers in these proceedings present novel contributions that range from theoretical advances to technical applications in engineering, geometric modeling, computer graphics, visualization, and machine learning.

The book intends to be a collection of research papers on algebra and related topics, most of which were presented at the international'Workshop on Associative Rings and Algebras with additional structures (WARA22)'. The purpose of the workshop WARA22 was to present the current state of the art both in the Theory of Lie structures of associative rings and algebras and in the Theory of functional identities in rings. The conference has emerged as a powerful forum offering researchers the opportunity to meet, get to know each other and discuss advances in ring theory, inspiring further research directions. The main topics covered refer to rings with involution, Lie and Jordan structures, rings and algebras arising under various constructions, modules, bimodules and ideals in associative algebras, behavior of derivations, automorphisms and other kinds of additive maps in rings and algebras. All the contributing authors are leading international academicians and researchers in their respective fields. The papers cover a wide range of topics in ring theory, group theory, matrix algebra and graph theory. The book will serve both the specialist looking for the latest results and the novice looking for the appropriate references to access the study and understanding of the results presented here.

This volume features a selection of technical papers presented at the workshop “The Fifth Workshop on Interdisciplinary Sciences (WIS 2023)'. Contributions from esteemed researchers and academics in applied mathematics, AI, and statistics offer valuable insights into their latest research. The papers also delve into interdisciplinary applications, spanning fields such as agriculture and economics, with strong emphasis on data analysis techniques. We hope this proceedings volume will serve as a valuable resource for scholars, researchers, and practitioners interested in the recent advancements and emerging trends in interdisciplinary sciences.

This contributed volume is an exciting product of the 22nd MAVI conference, which presents cutting-edge research on affective issues in teaching and learning math. The teaching and learning of mathematics is highly dependent on students'and teachers'values, attitudes, feelings, beliefs and motivations towards mathematics and mathematics education. These peer-reviewed contributions provide critical insights through their theoretically and methodologically diverse analyses of relevant issues related to affective factors in teaching and learning math and offer new tools and strategies by which to evaluate affective factors in students'and teachers'mathematical activities in the classroom. Among the topics discussed: The relationship between proxies for learning and mathematically related beliefs.Teaching for entrepreneurial and mathematical competences.Prospective teachers'conceptions of the concepts mean, median, and mode.Prospective teachers'approach to reasoning and proofThe impact of assessment on students'experiences of mathematics. Through its thematic connections to teacher education, professional development, assessment, entrepreneurial competences, and reasoning and proof, Students'and Teachers'Values, Attitudes, Feelings and Beliefs in Mathematics Classrooms proves to be a valuable resource for educators, practitioners, and students for applications at primary, secondary, and university levels.

This book collects select papers presented at the 7th International Arab Conference on Mathematics and Computations (IACMC 2022), held from 11–13 May 2022, at Zarqa University, Zarqa, Jordan. These papers discuss a new direction for mathematical sciences. Researchers, professionals and educators will be exposed to research results contributed by worldwide scholars in fundamental and advanced interdisciplinary mathematical research such as differential equations, dynamical systems, matrix analysis, numerical methods and mathematical modelling. The vision of this book is to establish prototypes in completed, current and future mathematical and applied sciences research from advanced and developing countries. The book is intended to make an intellectual contribution to the theory and practice of mathematics. This proceedings would connect scientists in this part of the world to the international level.

This book reviews math topics relevant to non-mathematics students and scientists, but which they may not have seen or studied for a while. These math issues can range from reading mathematical symbols, to using complex numbers, dealing with equations involved in calculating medication equivalents, the General Linear Model (GLM) used in e.g. neuroimaging analysis, finding the minimum of a function, independent component analysis, or filtering approaches. Almost every student or scientist, will at some point run into mathematical formulas or ideas in scientific papers that may be hard to understand, given that formal math education may be some years ago. In this book we will explain the theory behind many of these mathematical ideas and expressions and provide readers with the tools to better understand them. We will revisit high school mathematics and extend and relate this to the mathematics you need to understand the math you may encounter in the course of your research. This book will help you understand the math and formulas in the scientific papers you read. To achieve this goal, each chapter mixes theory with practical pen-and-paper exercises such that you (re)gain experience with solving math problems yourself. Mnemonics will be taught whenever possible. To clarify the math and help readers apply it, each chapter provides real-world and scientific examples.In this new edition, two new chapters covering statistics and differential equations have been added, which have been workshopped in the'authors'popular lecture series in order to maximize the benefit for readers.

This volume contains eighteen papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Some of the topics explored includeArabic editions of Euclid's Elements from the thirteenth century and their role in the assimilation of Euclidean geometry into the Islamic intellectual traditionPortuguese sixteenth century recreational mathematics as found in the Tratado de Prática Darysmetica A Cambridge correspondence course in arithmetic for women in England in the late nineteenth centuryThe mathematical interests of the famous Egyptologist Thomas Eric (T. E.) Peet The history of Zentralblatt für Mathematik and Mathematical Reviews and their role in creating a publishing infrastructure for a global mathematical literatureThe use of Latin squares for agricultural crop experiments at the Rothamsted Experimental StationThe many contributions of women to the advancement of computing techniques at the Cavendish Laboratory at the University of Cambridge in the 1960sThe volume concludes with two short plays, one set in Ancient Mesopotamia and the other in Ancient Egypt, that are well suited for use in the mathematics classroom.Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

Articles, notes, generalizations, paradoxes, miscellaneous in mathematics, linguistics, and education.

This volume collects papers based on talks given at the conference “Geometrias'19: Polyhedra and Beyond”, held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference's theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.

This book is dedicated to V.A. Yankov's seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic.The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov's results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics.The book also contains an exposition of Yankov's revolutionary approach to constructive proof theory. The editors also include Yankov's contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

This book gathers papers presented at the 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, which was held in Kazan, Russia, in October 2020. The papers address the following topics: the theory of mesh methods for boundary-value problems in mathematical physics; non-linear mathematical models in mechanics and physics; algorithms for solving variational inequalities; computing science; and educational systems. Given its scope, the book is chiefly intended for students in the fields of mathematical modeling science and engineering. However, it will also benefit scientists and graduate students interested in these fields.

This volume contains eleven papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Société canadienne d'histoire et de philosophie des mathématiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Topics considered includeThe mathematics and astronomy in Nathaniel Torperly's only published work, Diclides Coelometricae, seu valvae astronomicae universalConnections between the work of Urbain Le Verrier, Carl Gustav Jacob Jacobi, and Augustin-Louis Cauchy on the algebraic eigenvalue problemAn evaluation of Ken Manders'argument against conceiving of the diagrams in Euclid's Elements in semantic termsThe development of undergraduate modern algebra courses in the United StatesWays of using the history of mathematics to teachthe foundations of mathematical analysisWritten by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

Frederick Mosteller has inspired numerous statisticians and other scientists by his creative approach to statistics and its applications. This volume brings together 40 of his most original and influential papers, capturing the variety and depth of his writings. The editors hope to share these with a new generation of researchers, so that they can build upon his insights and efforts. This volume of selected papers is a companion to the earlier volume A Statistical Model: Frederick Mosteller's Contributions to Statistics, Science, and Public Policy, edited by Stephen E. Fienberg, David C. Hoaglin, William H. Kruskal, and Judith M. Tanur (Springer-Verlag, 1990), and to Mosteller's forthcoming autobiography, which will also be published by Springer-Verlag. It includes a biography and a comprehensive bibliography of Mosteller's books, papers, and other writings. Stephen E. Fienberg is Maurice Falk University Professor of Statistics and Social Science, in the Departments of Statistics and Machine Learning at Carnegie Mellon University, Pittsburgh, PA. David C. Hoaglin is Principal Scientist at Abt Associates Inc., Cambridge, MA.

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2012), and provides an overview of the depth and breath of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography. ​

A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honours including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields. These two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selection will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own.

Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the disci

This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The book also addresses core research challenges such as the representation of large and complex datasets, and integrating numerical methods with robust combinatorial algorithms. In keeping with the focus of the TopoInVis 2017 Workshop, the contributions reflect the latest advances in finding experimental solutions to open problems in the sector. They provide an essential snapshot of state-of-the-art research, helping researchers to keep abreast of the latest developments and providing a basis for future work. Gathering papers by some of the world's leading experts on topological techniques, thebook represents a valuable contribution to a field of growing importance, with applications in disciplines ranging from engineering to medicine.

This book presents a selection of papers from the International Conference Geometrias'17, which was hosted by the Department of Architecture at the University of Coimbra from 16 to 18 June 2017. The Geometrias conferences, organized by Aproged (the Portuguese Geometry and Drawing Teachers'Association), foster debate and exchange on practical and theoretical research in mathematics, architecture, the arts, engineering, and related fields.Geometrias'17, with the leitmotif “Thinking, Drawing, Modelling”, brought together a group of recognized experts to discuss the importance of geometric literacy and the science of representation for the development of scientific and technological research and professional practices. The 12 peer-reviewed papers gathered here show how geometry, drawing, stereotomy, and the science of representation are still at the core of every act leading to the conception and materialization of form, and highlight their continuing relevance for scholars andprofessionals in the fields of architecture, engineering, and applied mathematics.

This volume convenes carefully selected, peer-reviewed papers presented at the BIOMAT 2023 International Symposium, which was virtually held on November 6-9, 2023, with an organization staff based in Rio de Janeiro, Brazil. In this volume, the reader will find studies on the epidemic model of the COVID-19 pandemic, aspects of risk-based testing and quarantine, as well as joint efforts in the search for the perfect vaccine. Additionally, the volume covers the influence of fear and the saturated fear cost in predator-prey dynamics, optimal control techniques applied to HPV infection and cervical cancer cells, generic epidemic models for disease propagation, discretized SIS model with no vertical transmission, dynamics of vibrio-phage interactions, and antibiotics treatment for septic arthritis. Comprehensive Reviews are also included on the applications of CHIRP ultrasound for the mathematical modeling of evaporation of nanodroplets and on Alternative Entropy Measures and their application in the studies of distributions of discrete probabilities of occurrence. These works aim to motivate Ph.D. students and new practitioners in the field of Biomathematics. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to foster the interdisciplinary exchange of results, ideas, and techniques, promoting truly international cooperation for problem discussion. BIOMAT volumes published from 2017 to 2022 are also available by Springer.

Kofi Annan, former Secretary General of the United Nations, argued that “We need to create a world that is equitable, that is stable and a world where we bear in mind the needs of others, and not only what we need immediately. We are all in the same boat.”American businessman, John Landgraf stated: “I hope that most of us believe that we actually would all benefit from living in a more equitable society. If that's not happening, we're squandering human potential.” For the world to be fair, one needs to know how to divide. Without the mathematics of division, humankind cannot function…Marie Antoinette, Queen of France (infamously) said “If people have no bread, let them eat cake,” and while Ahmes ― the scribe of the Rhind Mathematical Papyrus ― dealt with loaves of bread, prosperous people in the twentieth century dealt with cake division, although bread is also uniformly available. You'll be surprised, but there are at least four books and over 200 scientific (not gastronomical!) papers on cake division. Those authors were not overly concerned with obesity, one can guess, but whether distributing loaves, cakes, chores, or dividends, one needs to master division.This book deals with a wide spectrum of division problems, and provides the historical background, giving a sense of how pervasive division is in our lives. In particular, the second part focuses on a problem that remained open until 1985, when Professor Robert John Aumann (Nobel laureate in Economics, 2005) and Professor Michael Maschler solved it using game-theoretic techniques. Simple alternative solutions are given, which are suitable for high schools and other educational institutions.

Why do you lean in a bend? Why does a sprinter slow down before the finish line? Why do golf balls have dimples? Why do you swim better slightly underwater? Why, on a bike, the faster you go, the more stable you are? Why shouldn't you rely on doping tests too much? Is there a law of evolution of records?These are some of the 40 questions that Amandine Aftalion answers in this book using simple physics and mathematics, and some humor. Not only will it allow you to improve yourself in sports, but it will also but it will also give way to understanding how champions do.An easy book to read and the must to have if you are a sports addict or if you watch sports on TV and ask yourself “why?”.Amandine Aftalion is a French mathematician. She is a CNRS senior scientist and graduated from École normale supérieure in Paris. She has given talks all over the world, as a specialist of models coming from low temperature physics. She has written a book on vortices in Bose–Einstein condensates. More recently, she has used energy minimization to study an optimal control problem coming from human energy: optimizing running. She has written papers on sports aimed at coaches. Part of her latest results have inspired the first chapter of this book. She is the producer and director of a French YouTube channel for the popularization of mathematics, Videodimath, elected as one of the 5 best French YouTube channels for popular mathematics.

The special semester'Singularities and low dimensional topology'in the Spring of 2023 at the Erdős Center (Budapest) brought together algebraic geometers and topologists to discuss and explore the strong connection between surface singularities and topological properties of three- and four-dimensional manifolds. The semester featured a Winter School (with four lecture series) and several focused weeks. This volume contains the notes of the lecture series of the Winter School and some of the lecture notes from the focused weeks. Topics covered in this collection range from algebraic geometry of complex curves, lattice homology of curve and surface singularities to novel results in smooth four-dimensional topology and grid homology, and to Seiberg-Witten homotopy theory and ‘spacification'of knot invariants. Some of these topics are already well-documented in the literature, and the lectures aim to provide a new perspective and fresh connections. Other topics are rather new and have been covered only in research papers. We hope that this volume will be useful not only for advanced graduate students and early-stage researchers, but also for the more experienced geometers and topologists who want to be informed about the latest developments in the field.

The present book contains the proceedings of the 14th International Symposium on Continuum Models and Discrete Systems (CMDS14) held in Paris in June 2023. It contains 21 contributions that cover a broad range of topics in the wide field of mechanics and physics of heterogeneous media for discrete and continuous systems, from image analysis to models of random structures and to homogenization. The sessions in the CMDS conference series cover, in particular, the modeling of complex heterogeneous systems and metamaterials, structures and composites with extreme properties, deformable solids with microstructures, generalized continua, fracture and defect dynamics, fatigue, design of structured and architectured materials, micro and nanostructures, thermodynamics, transport theory and multiphysics coupling and methods ranging from homogenization theories to optimal design and machine-learning frameworks. Papers in the present volume are organized according to the following six main topics: probabilistic models, homogenization, solid mechanics, architectured materials, optics and metamaterials, machine learning methods.

This Festschrift, dedicated to Herman Geuvers on the occasion of his 60th birthday, contains papers written by many of his closest collaborators. Herman Geuvers is a full professor at Radboud University Nijmegen and holds a part-time professorship at Eindhoven University of Technology. He received his PhD from Radboud University in 1993 and he was promoted to full professor in Computer Assisted Reasoning in 2006. Prof. Geuvers is an internationally renowned researcher in the field of proof assistants, logic in computer science, lambda calculus, and type theory. He has been a steering committee chair of the TYPES and FSCD conferences, chair of related EU Cost Action projects, and program chair or editor of related conferences and special issues in the area of computer science logic. He is a successful, generous and inspiring advisor and educator. He has been director of education and director of research of the Computer Science Institute at Radboud University Nijmegen, and he is currently chair of the examination board of computer science and chair of the board of the Institute for Programming Research and Algorithmics, a Dutch national inter-university research school. The contributions in this volume reflect Prof. Geuvers'main research interests.

This book presents the refereed proceedings of the 15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held in Linz, Austria, and organized by the Johannes Kepler University Linz and the Austrian Academy of Sciences, in July 2022. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these highly active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, in particular arising in finance, statistics and computer graphics.

John Corcoran was a very well-known logician who worked on several areas of logic. He produced decisive works giving a better understanding of two major figures in the history of logic, Aristotle and Boole. Corcoran had a close association with Alfred Tarski, a prominent 20th-century logician. This collaboration manifested in Corcoran's substantial introduction to Tarski's seminal book, Logic, Semantics, Metamathematics (1956). Additionally, Corcoran's posthumous editorial involvement in'What are logical notions?'(1986) breathed new life into this seminal paper authored by Tarski. His scholarly pursuits extended to the intricate explication of fundamental concepts in modern logic, including variables, propositions, truth, consequences, and categoricity. Corcoran's academic curiosity extended further to the intersection of ethics and logic, reflecting his contemplation of their interrelation. Beyond these theoretical contributions, Corcoran was deeply engaged in the pedagogical dimensions of logic instruction. This volume serves as a compilation of articles contributed by Corcoran's students, colleagues, and international peers. By encompassing a diverse range of subjects, this collection aptly mirrors Corcoran's wide-ranging interests, offering insights that not only deepen our understanding of his work but also advance the theoretical frameworks he explored.

This volume is devoted to the most recent discoveries in mathematics and statistics. It also serves as a platform for knowledge and information exchange between experts from industrial and academic sectors. The book covers a wide range of topics, including mathematical analyses, probability, statistics, algebra, geometry, mathematical physics, wave propagation, stochastic processes, ordinary and partial differential equations, boundary value problems, linear operators, cybernetics and number and functional theory. It is a valuable resource for pure and applied mathematicians, statisticians, engineers and scientists.

This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of researchers with the national Centre of Excellence in Nonlinear Studies (CENS) at the Department of Cybernetics of Tallinn University of Technology in Estonia.The papers chiefly focus on the role of mathematics in the analysis of wave phenomena. They highlight the complexity of related topics concerning wave generation, propagation, transformation and impact in solids, gases, fluids and human tissues, while also sharing insights into selected mathematical methods for the analytical and numerical treatment of complex phenomena. In addition, the contributions derive advanced mathematical models, share innovative ideas on computing, and present novel applications for a number of research fields where both linear and nonlinear wave problems play an important role.The papers are written in a tutorial style, intended for non-specialist researchers and students. The authors first describe the basics of a problem that is currently of interest in the scientific community, discuss the state of the art in related research, and then share their own experiences in tackling the problem.Each chapter highlights the importance of applied mathematics for central issues in the study of waves and associated complex phenomena in different media. The topics range from basic principles of wave mechanics up to the mathematics of Planet Earth in the broadest sense, including contemporary challenges in the mathematics of society. In turn, the areas of application range from classic ocean wave mathematics to material science, and to human nerves and tissues. All contributions describe the approaches in a straightforward manner, making them ideal material for educational purposes, e.g. for courses, master class lectures, or seminar presentations.

Mathematical modelling and computer simulations are playing a crucial role in the solution of the complex problems arising in the field of biomedical sciences and provide a support to clinical and experimental practices in an interdisciplinary framework.Indeed, the development of mathematical models and efficient numerical simulation tools is of key importance when dealing with such applications.Moreover, since the parameters in biomedical models have peculiar scientific interpretations and their values are often unknown, accurate estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In the light of the new challenges brought by the biomedical applications, computational mathematics paves the way for the validation of the mathematical models and the investigation of control problems.The volume hosts high-quality selected contributions containing original research results as well as comprehensive papers and survey articles including prospective discussion focusing on some topical biomedical problems. It is addressed, but not limited to: research institutes, academia, and pharmaceutical industries.

This book discusses the modern theory of Laplace eigenfunctions through the lens of a new tool called geodesic beams. The authors provide a brief introduction to the theory of Laplace eigenfunctions followed by an accessible treatment of geodesic beams and their applications to sup norm estimates, L^p estimates, averages, and Weyl laws. Geodesic beams have proven to be a valuable tool in the study of Laplace eigenfunctions, but their treatment is currently spread through a variety of rather technical papers. The authors present a treatment of these tools that is accessible to a wider audience of mathematicians. Readers will gain an introduction to geodesic beams and the modern theory of Laplace eigenfunctions, which will enable them to understand the cutting edge aspects of this theory.

This book contains select papers presented at the International Conference on Applied Mathematics and Computational Intelligence (ICAMCI-2020), held at the National Institute of Technology Agartala, Tripura, India, from 19–20 March 2020. It discusses the most recent breakthroughs in intelligent techniques such as fuzzy logic, neural networks, optimization algorithms, and their application in the development of intelligent information systems by using applied mathematics. The book also explains how these systems will be used in domains such as intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and complicated problems in optimization. The book publishes new developments and advances in various areas of type-3 fuzzy, intuitionistic fuzzy, computational mathematics, block chain, creak analysis, supply chain, soft computing, fuzzy systems, hybrid intelligent systems, thermos-elasticity, etc. The book is targeted to researchers, scientists, professors, and students of mathematics, computer science, applied science and engineering, interested in the theory and applications of intelligent systems in real-world applications. It provides young researchers and students with new directions for their future study by exchanging fresh thoughts and finding new problems.

​This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021.The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines.The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium.The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

Samson Abramsky's wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky's work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky's work, reflecting its exceptionally broad scope and his ability to illuminate and unify diverse topics.Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky's work hasled to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power.The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky's enduring influence. It will provide an invaluable and unique resource for both students and established researchers.

This book convenes peer-reviewed, selected papers presented at the Ninth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Sozopol, Bulgaria, June 17–20, 2022. The works are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis.In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them for solving real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations.The NTADES 2022 conference was organized in cooperation with the Society of Industrial and Applied Mathematics (SIAM), the major international organization for Industrial and Applied Mathematics and for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering, finance, and neuroscience.

This volume presents peer-reviewed surveys on new developments in the study of Lyapunov exponents in dynamical systems and its applications to other areas, such as mathematical physics. Written by leading experts in their fields, the contributions are based upon the presentations given by invited speakers at the “New Trends in Lyapunov Exponents” workshop held in Lisbon, Portugal, February 7–11, 2022. The works focus on the concept of Lyapunov exponents in their various manifestations in dynamical systems along with their applications to mathematical physics and other areas of mathematics. The papers reflect the spirit of the conference of promoting new connections among different subjects in dynamical systems. This volume aims primarily at researchers and graduate students working in dynamical systems and related fields, serving as an introduction to active fields of research and as a review of recent results as well.

One of the greatest theoretical physicists of the 19th century, James Clerk Maxwell is best known for his studies of the electromagnetic field. The 101 scientific papers of this two-volume set, arranged chronologically, testify to Maxwell's profound scientific legacy and include the preliminary explorations that culminated in his most famous work, A Treatise on Electricity and Magnetism. One of the nineteenth century's most significant papers,'A Dynamical Theory of the Electromagnetic Field,'appears here, along with similarly influential expositions of Maxwell's dynamical theory of gases. The author's extensive range of interests is well represented, from his discussions of color blindness and the composition of Saturn's rings to his essays on geometrical optics, ether, and protecting buildings from lightning. His less technical writings are featured as well, including items written for the Encyclopedia Britannica and Nature magazine, book reviews, and popular lectures. Striking in their originality, these papers offer a wealth of stimulating and inspiring reading to modern students of mathematics and physics.

Every two years the members of GIRET (= Centre for International Re­ search on Economic Tendency Surveys) meet at conferences in order to promote the scientific discussion and to encourage the exchange of ideas. CIRET is an international study group for research in the field of business cycle surveys. CIRET was founded in 1960 and has at present about 350 full and corresponding members in 35 different coun­ tries. The members either carry out business, investment or consumer 1 surveys or are working on a practical or methodological level with the results of such surveys. The most important topics of the GIRET conferences are the predictive value of survey data as trade cycle indicators, the utilization of qualitative data in econometric models, forecasts of capital expenditures based on plans of private companies, the usefulness of consumer surveys for trade cycle analyses. In September 1977 the 13th CIRET Conference took place in Munich. On the occasion of the three-day conference 27 papers were presented.

Not only was E.P. Wigner one of the most active creators of 20th century physics, he was also always interested in expressing his opinion in philosophical, political or sociological matters. This volume of his collected works covers a wide selection of his essays about science and society, about himself and his colleagues. Annotated by J. Mehra, this volume will become an important source of reference for historians of science, and it will be pleasant reading for every physicist interested in forming ideas in modern physics.

This book presents a collection of selected papers that represent the current variety of research on the teaching and learning of probability. The respective chapters address a diverse range of theoretical, empirical and practical aspects underpinning the teaching and learning of probability, curricular issues, probabilistic reasoning, misconceptions and biases, as well as their pedagogical implications. These chapters are divided into THREE main sections, dealing with: TEACHING PROBABILITY, STUDENTS'REASONING AND LEARNING AND EDUCATION OF TEACHERS.In brief, the papers presented here include research dealing with teachers and students at different levels and ages (from primary school to university) and address epistemological and curricular analysis, as well as the role of technology, simulations, language and visualisation in teaching and learning probability. As such, it offers essential information for teachers, researchers and curricular designers alike.

This proceedings volume gathers selected, peer-reviewed papers presented at the 2nd International Conference on Mathematics and its Applications in Science and Engineering – ICMASE 2021, which was virtually held on July 1-2, 2021 by the University of Salamanca, Spain. Works included in this book cover applications of mathematics both in engineering research and in real-world problems, touching topics such as difference equations, number theory, optimization, and more. The list of applications includes the modeling of mechanical structures, the shape of machines, and the growth of a population, expanding to fields like information security and cryptography. Advances in teaching and learning mathematics in the context of engineering courses are also covered.This volume can be of special interest to researchers in applied mathematics and engineering fields, as well as practitioners seeking studies that address real-life problems in engineering.

Cooperation is pervasive throughout nature, but its origin remains an open question. For decades, social scientists, business leaders, and economists have struggled with an important question: why is cooperation so ubiquitous among unrelated humans? The answers would have profound effects because anything that promotes cooperation leads to more productive work environments and benefits society at large. Game theory provides an ideal framework for studying social dilemmas, or those situations in which people decide whether to cooperate with others (benefitting the group) or defect by prioritizing their self-interest (benefitting only the individual). The social dilemma is formulated as a mathematical game and then programmed into a computer model. Simulating the game allows researchers to investigate potential theories to explain how cooperation emerges and what promotes its persistence. Over the past 25 years, countless papers on social dilemma games have been published, yet arguably little progress has been made. The problem is the social dilemma game models are unrealistic in the sense they contain artificial constructs that deviate from the way humans act. This book describes the shortcomings in current social dilemma game modeling techniques and provides guidance on designing more effective models. A basic introduction to game theory is provided with an emphasis on the prisoner's dilemma, the most widely studied social dilemma game. Individual chapters are provided detailing the shortcomings of weak selection, spatial games, and the Moran process. Computer model validation is also discussed at length. The recommendations found in this book should help design more realistic social dilemma game models likely to produce a better understanding of human cooperation.

This volume is an effort to bring together important contributions to the mathe­ matical development of demography and to suggest briefly their historical context. We have tried to find who first thought of the several concepts and devices commonly used by demographers, what sort of problem he was facing to which the device or concept seemed the solution, and how his invention developed subsequently in the hands of others. Historically, the book starts with a Roman table of life expectancies from the third century a. d. about which we know little, and with John Graunt's explora­ tions in an area that was still popularly suspect when he wrote in 1662. These are followed by the astronomer Halley, who looked into the field long enough to invent the life table and to notice that Their Majesties would take a sizeable loss on the annuity scheme they had just launched; and by Euler, who was first to devise the formulas of stable population theory and to apply them to filling gaps in data To these we add the handful of further contributions in the 19th century and many pieces from the explosion of contributions that began in this century with Lotka. We doubt that we have managed to trace everything back to its ultimate beginning, and suspect that our nominees in some cases have been anticipated by predecessors who will be turned up by other students.