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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 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 book addresses the analysis of functions of a real variable and transitions from the standard calculus sequence to mathematical analysis. The author presents the limits and convergence of sequences of functions, illustrates the limitations of the Riemann integral, and discusses the need for a new integral: the Lebesgue integral. The fundamental concepts of the theory of calculus of one variable is presented in addition to limits, continuity, derivatives and its applications, and integrals and their applications. The tone and language of the book is kept as informal as possible along with the descriptions and examples to aid learning. The book is concise and presents single variable advanced calculus leading up to Fourier analysis. In addition, the book sets up sufficient background for a course in measure theory and Lebesgue integration.

Die Forschung zum Pädagogischen Argumentieren untersucht, wie Lehrpersonen ihr Wissen nutzen, um zu produktiven Unterrichtshandlungen zu kommen. Es wird insbesondere angenommen, dass fachliches und fachdidaktisches Wissen relevant ist, um Vor- und Nachteile alternativer Unterrichtshandlungen in typischen Anforderungssituationen zu analysieren und so zu professionellen Entscheidungen zu gelangen. In der vorliegenden Arbeit wird die Nutzung des mathematikbezogenen fachlichen und fachdidaktischen Wissens von angehenden Mathematiklehrpersonen (Novizen) und qualifizierten Mathematiklehrpersonen (Experten) verglichen. Die dazu durchgeführten Studien liefern empirische Belege dafür, dass sich Expertise von Mathematiklehrpersonen auch in der Fähigkeit zeigt, verschiedene fachliche und fachdidaktische Argumente flexibel auf potentielle Unterrichtshandlungen beziehen zu können. Das fachliche und fachdidaktische Wissen entfaltet demnach seine Wirkung für die Unterrichtspraxis insbesondere dann, wenn dieses in Form von fachlichen und fachdidaktischen Argumenten integrativ auf Unterrichtshandlungen bezogen werden kann.

This book collects a selection of the articles presented at the virtual conference “Game Theory and Applications”, organized in St. Petersburg in the summer of 2022. The articles in this collection cover all the main applications of game theory, interpolating mathematical methods with economics, biology, sociology, mobile systems, and social networks. Scholars in the field will find this to be a valuable contribution.

This monograph meticulously examines the contributions of French mathematician Michel Chasles to 19th-century geometry. Through an in-depth analysis of Chasles'extensive body of work, the author examines six pivotal arguments which collectively reshape the foundations of geometry. Chasles introduces a novel form of polarity, termed'parabolic,'to the graphic context, so expressing the metric properties by means of this specific polarity—a foundational argument. Beyond the celebrated'Chasles theorem,'he extends his analysis to the movement of a rigid body, employing concepts derived from projective geometry. This approach is consistently applied across diverse domains. Chasles employs the same methodology to analyze systems of forces. The fourth argument examined by the author concerns the principle of virtual velocities, which can also be addressed through a geometric analysis. In the fifth chapter, Chasles'philosophy of duality is explained. It is grounded on theduality principles of projective geometry. Finally, the author presents Chasles'synthetic solution for the intricate problem of ellipsoid attraction—the sixth and concluding chapter. Throughout these explorations, Chasles engages in a dynamic scientific dialogue with leading physicists and mathematicians of his era, revealing diverse perspectives and nuances inherent in these discussions.Tailored for historians specializing in mathematics and geometry, this monograph also beckons philosophers of mathematics and science, offering profound insights into the philosophical, epistemological, and methodological dimensions of Chasles'groundbreaking contributions. Providing a comprehensive understanding of Chasles'distinctive perspective on 19th-century geometry, this work stands as a valuable resource for scholars and enthusiasts alike.

This book is devoted to combinatorial aspects of the theory of symmetric functions. This rich, interesting and highly nontrivial part of algebraic combinatorics has numerous applications to algebraic geometry, topology, representation theory and other areas of mathematics. Along with classical material, such as Schur polynomials and Young diagrams, less standard subjects are also covered, including Schubert polynomials and Danilov–Koshevoy arrays. Requiring only standard prerequisites in algebra and discrete mathematics, the book will be accessible to undergraduate students and can serve as a basis for a semester-long course. It contains more than a hundred exercises of various difficulty, with hints and solutions. Primarily aimed at undergraduate and graduate students, it will also be of interest to anyone who wishes to learn more about modern algebraic combinatorics and its usage in other areas of mathematics.

This book provides an introductory overview of random variables and their transformations. The authors approach the topic with statistics students in mind, along with researchers in various fields who are interested in data analysis. The book begins with by defining and explaining mathematical expectation. The authors then discuss transformations of random variables, including distribution functions and special functions. The book also covers joint probability distribution and its applications. The authors have updated and expanded upon their writing on these topics, which they originally covered in their previous book, Statistics for Scientists and Engineers.

This book discusses many interesting results have been obtained in Leibniz algebras over the past two decades. The authors not only summarize recent results and methods successfully used in Leibniz algebras, but also show new prospective horizons. Any mathematical theories have a number of natural problems that arise in the process of its development, and these problems quite often have analogues in other areas such as differential geometry, homological algebra, classical algebraic topology, noncommutative geometry, etc. With this in mind the authors describe the general structure of Leibniz algebras that have already been discovered. This approach allows readers to see which parts of the theory should be developed further and also shows the significant differences of Leibniz algebras from Lie algebras. Recent results that constitute the naturally evolving general theory of the subject are then explored.

This new edition includes three new chapters, 7 through 9, that have very broad, practical applications in engineering and science. In addition, the author's latest research results incorporated into the new textbook demonstrates better performance than the popular METIS software for partitioning graphs, partitioning finite element meshes, and producing fill-reducing orderings for sparse matrices. The new Chapter 8, and its pre-requisite, Chapter 7, present a state-of-the-art algorithm for computing the shortest paths for real-life (large-scale) transportation networks with minimum computational time. This approach has not yet appeared in any existing textbooks and it could open the doors for other transportation engineering applications. Chapter 9 vastly expands the scope of the previous edition by including sensitivity (gradient) computation and MATLAB's built-in function “fmincon” for obtaining the optimum (or best) solution for general engineering problems.

Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will beof interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.

This book focuses on stability analysis and control design approaches for multi-agent systems under network-induced constraints. A hybrid system approach is introduced to address the cooperative control problem of networked multi-agent systems, and several important topics such as asynchronous sampled data cooperative control, hybrid event-triggered cooperative control, and reset-based cooperative control are studied under the hybrid system framework. The special feature of this book is that a hybrid systems approach is proposed for the cooperative control of multi-agent systems, which is beneficial for relaxing the conservativeness of stability analysis and network parameter computation. Interested readers can learn a novel approach to cooperative control of multi-agent systems, and this book can benefit researchers, engineers, and graduate students in the fields of multi-robot cooperation, unmanned aerial vehicle formation, control engineering, etc.

Dutch scientist Christiaan Huygens (1629-1695) left an indelible mark on the fields of mathematics, physics, astronomy, and geophysics. Despite his groundbreaking contributions, history has often overlooked his pivotal role. While two of the most famous achievements in physics are Newton's theory of gravity and Einstein's general theory of relativity, less well-known is that Huygens provided central elements to these theories. This book stands to correct that deficit. For example, we show how Huygens used symmetry arguments to derive conservation laws for momentum and for energy, and what Einstein later called the principle of equivalence to derive the formula for centrifugal force. In 1689, Huygens visited Newton. Together, they walked the streets of London. Newton had recently finished his masterpiece, Principia, expounding his laws of motion and the law of universal gravitation. Huygens had essentially completed his life's work by then, building on Archimedes, Leonardo da Vinci, Galileo, Descartes, Fermat, Pascal and his own ingenuity. He had established fame as an instrument maker (telescope, pendulum clock, planetarium). He had invented the 31 tone system. He had pioneered the first principles of remote sensing. He had discovered the rings of Saturn. He had formulated the wave theory of light. What would walking with Christiaan reveal? This book gives the result in nine chapters, namely: spontaneous order, the speed of light, Huygens'principle, the telescope, the pendulum clock, Huygens-Fresnel principle, special relativity, centrifugal force, and curvature. In addition, there is a chapter titled What Huygens could have written on diffraction, and a chapter titled Huygens and Geophysics. Mentally walking with Christiaan, browsing his collected works — a true treasure trove for puzzle enthusiasts — and rethinking his ideas creates a vivid impression of scientific life in the 17th century, an appreciation that it is remarkably similar to ours, and an understanding of Huygens'significant and lasting contributions to science.

This book addresses interconnections between contemporary advances in mathematics, especially algebra, with applications in the social sciences and the arts. It promotes the idea that knowledge cannot remain in disciplinary silos, rather, it belongs to all people, and is dedicated to associative relationships in a variety of mathematics applications, from sociology to linguistics, including anthropology, semiotics, education, and cognitive science. Contributions illuminate some of the ways in which algebra is developed, learned, understood, communicated, and applied in the social sciences and the humanities.The content in this book has its origins in a conference, Mathematics for Social Sciences and Arts–Algebraic Modelling, virtually hosted by the Faculty of Mechanical Engineering, University of Niš, Serbia, from the 24th to the 26th of May, 2021. This conference brought together scholars from various disciplines and geographic regions and focused on thejuxtaposition of algebra and social science applications. The conference organizers, higher education institutes from four different continents, invited leading scientists in social sciences and algebra, to contribute to this volume.The first part of this book addresses algebraic and mathematical thinking, specifically learning and practicing mathematics from a cognitive science perspective, as well as illustrative applications to distinctly human concerns, like education and semiotics. The second part focuses on algebraic semigroups and some of their generalizations. This book and the conference that engendered it provide an example of a fruitful collaboration, in which the skills and deep knowledge of algebraic structures, modeling, social sciences and arts brought in by the authors from different countries and continents merge in harmonious ways. These expositions are a rich resource and are of interest both to mathematicians and non-mathematicians.

This book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus. Beginning with some basic proof techniques and the notions of sets and functions, the book rigorously constructs the real numbers and their related structures from the natural numbers. During this construction, the readers will encounter the notions of infinity, limits, real sequences, and real series. These concepts are then formalised and focused on as stand-alone objects. Finally, they are expanded to limits, sequences, and series of more general objects such as real-valued functions. Once the fundamental tools of the trade have been established, the readers are led into the classical study of calculus (continuity, differentiation, and Riemann integration) from first principles. The book concludes with an introduction to the studyof measures and how one can construct the Lebesgue integral as an extension of the Riemann integral. This textbook is aimed at undergraduate students in mathematics. As its title suggests, it covers a large amount of material, which can be taught in around three semesters. Many remarks and examples help to motivate and provide intuition for the abstract theoretical concepts discussed. In addition, more than 600 exercises are included in the book, some of which will lead the readers to more advanced topics and could be suitable for independent study projects. Since the book is fully self-contained, it is also ideal for self-study.

Individual-based models (IBM) describe a population as a collection of different organisms whose local interactions determine the behaviour of the entire population. The individual description is convenient for computer simulations and the determination of various model parameters, and appropriate limit passages lead to the transport equations used in classical population dynamics models. The aim of this book is to provide a brief mathematical introduction to IBMs and their application to selected biological topics. The book is divided into seven chapters. In the first chapter we give a general description of IBMs and we present examples of models to illustrate their possible applications. Examples of applications include age, size and phenotype models, coagulation-fragmentation process, and models of genome evolution. The second chapter contains some theoretical results concerning limit passages from IBMs to phenotype and age-structured models. The rate of this convergence formulated as functional central limit theorems is presented in Chapter 3. As a result of the limit passage can be a superprocess, i.e., a stochastic process with values in a space of measures. Chapter 4 presented examples of such passages: from the branching Brownian motion to the Dawson--Watanabe superprocess and from the Moran's model of genetic drift with mutations to the Fleming--Viot superprocess. The next three chapters are devoted to models, in which we directly participated in the study. In Chapter 5 we study IBMs phenotype models and their limit passages. We show that random mating stabilises the distribution of traits, while assortative mating can lead to a polymorphic population. Formation of aggregates of phytoplankton and their movement is studied in Chapter 6. We present two types of models based on: fragmentation-coagulation processes; and diffusion with chemical signals leading to advanced superprocesses. Chapter 7 is devoted to rather advanced models with chemotaxis used to description of retinal angiogenesis and cell proliferations. The book is complemented by two appendices in which we have collected information about stochastic processes and various spaces we have used. The book is dedicated both to mathematicians and biologists. The first group will find here new biological models which leads to interesting and often new mathematical questions. Biologists can observe how to include seemingly different biological processes into a unified mathematical theory and deduce from this theory interesting biological conclusions. Apart from the sections on superprocesses, where quite advanced mathematical issues arise, such as stochastic partial equations, we try to keep the required mathematical and biological background to a minimum so that the topics are accessible to students.

Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. Besides selected ideas of Platon, Aristoteles, Leibniz, Kant, Frege and others, the results of Gödel and Tarski on incompleteness, undecidability and truth in deductive systems and their semantic models are covered. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory. Such theories contain identity types, which give a new understanding of equality, symmetry, equivalence and isomorphism in a conceptual way. The interaction of type theory and infinity category theory yields a new paradigm for a structural view on mathematics. This supports the tendencies towards formalising mathematics with the help of proof assistants. This book was first published in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.

In this book Lukas Graf studies dynamic network flows which are a model for individual car traffic in road networks. It is assumed that drivers choose their routes based on information about the current state of the network in such a way as to selfishly minimize their own arrival time at their destination. Whilst on their journey the drivers adapt their current route choices based on the changing state of the network. A dynamic flow wherein every (infinitesimally small) flow particle behaves in this way is then called an instantaneous dynamic equilibrium. After giving a mathematically precise definition of this equilibrium concept the author shows existence of those equilibrium flows, studies their computational complexity and derives bounds on their quality.

This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject. Spanning a broad spectrum of mathematical topics and historical periods, the book uses detailed case studies to investigate the different forms in which duality appeared and still appears in mathematics, to study their respective histories, and to analyze interactions between the different forms of duality. The chapters inquire into questions such as the contextual occurrences of duality in mathematics, the influence of chosen forms of representation, the impact of investigations of duality on mathematical practices, and the historical interconnections among various instances of duality. Together, they aim to answer a core question: Is there such a thing as duality in mathematics, or are there just several things called by the same name and similar in some respect? What emerges is that duality can be considered as a basic structure of mathematical thinking, thereby opening new horizons for the research on the history and the philosophy of mathematics and the reflection on mathematics in general. The volume will appeal not only to experts in the discipline but also to advanced students of mathematics, history, and philosophy intrigued by the complexities of this captivating subject matter.

This book presents a groundbreaking new mathematical paradigm and system (including inventing a new number) that enables a new approach to advancing the foundations of science and technology. The new approach allows connecting subjective and objective points of view that do not rely solely on the classical deductive approach. There is no need to fear paradoxical situations, because it's precisely in them wherein lies the key to a new understanding that is more connected to life itself. This new model also serves to advance the theory of consciousness. Life is more colorful and diverse than just the binary colors of black and white. For this purpose, the authors propose a new type of number called Soft Number. The basic idea is to distinguish between the different multiples of the number zero. Soft Logic is a continuous extension of the idea of giving different meanings to the zero. The authors create a tangible model of an infinitely small world. This seemingly inconceivable world is important for understanding the essence of the connection between the external world of reality and the inner world of human beings and offers a new language to express it. This book systematically and axiomatically describes the mathematical development of Soft Logic and Soft Numbers and points to possible directions for scientific and technological applications. This book is a valuable resource for researchers working in mathematics, physics, biology, engineering, computer science and artificial intelligence as well as advanced-level students majoring in computer science, engineering and mathematics. Practitioners, Data Scientists, AI developers and readers interested in a scientific understanding of the concept of consciousness will also want to purchase this book.

MATRIX is Australia's international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-2 weeks in duration. This book is a scientific record of the 24 programs held at MATRIX in 2021-2022, including tandem workshops with Mathematisches Forschungsinstitut Oberwolfach (MFO), with Research Institute for Mathematical Sciences Kyoto University (RIMS), and with Sydney Mathematical Research Institute (SMRI).

In this captivating historical novel, Daniele Struppa skillfully weaves a fictional autobiography, bringing Fibonacci to life with vivid details of his upbringing and adult years in Medieval Europe. As we explore the historical context of Fibonacci's time, we delve into the intriguing aspects of a bygone era, painting a compelling picture of a man whose contributions to mathematics continue to resonate today. From his groundbreaking work on congruent numbers to the famous numerical sequence that bears his name, the author invites readers to imagine the creative sparks that ignited Fibonacci's mathematical innovations. When historical evidence is elusive, accuracy and passion are seamlessly combined, offering plausible scenarios grounded in documented facts. A meticulously crafted apparatus of notes distinguishes fact from fiction, providing readers with a clear guide to navigate this enthralling reconstruction of Fibonacci's life. Step into the medieval world of Leonardo Fibonacci, one of the most celebrated mathematicians in history, and discover the man behind the mathematical genius. Mathematicians and curious readers alike will appreciate the allure of Fibonacci's mathematical brilliance.

This new edition presents the essential topics in probability and statistics from a rigorous standpoint. Any discipline involving randomness, including medicine, engineering, and any area of scientific research, must have a way of analyzing or even predicting the outcomes of an experiment. The authors focus on the tools for doing so in a thorough, yet introductory way. After providing an overview of the basics of probability, the authors cover essential topics such as confidence intervals, hypothesis testing, and linear regression. These subjects are presented in a one semester format, suitable for engineers, scientists, and STEM students with a solid understanding of calculus. There are problems and exercises included in each chapter allowing readers to practice the applications of the concepts.

Dieses Buch macht die überraschende Vielfalt der Personen und Tätigkeiten in der Radioaktivitätsforschung sichtbar. Dabei wird der Begriff der wissenschaftlichen Arbeit neu konzeptualisiert. Neben die Forschungsarbeit im Labor treten scheinbare Rand-, Neben- und Routinetätigkeiten, die für die Radioaktivitätsforschung als Disziplin von zentraler Bedeutung waren.Badeärzte, Industriechemiker und Bergbaubeamte waren an der Erforschung der neuen Substanzen und Strahlen ebenso beteiligt wie eine vergleichsweise hohe Zahl von Frauen. Die erste umfassende Studie zur deutschsprachigen Radioaktivitätsforschung im vorderen Teil des Buches offenbart die Ausnahmestellung der Hauptstädte Berlin und Wien für die Forschung ebenso wie fruchtbares akademisches Leben in der Provinz; sie zeigt, wie das neue Gebiet an den Hochschulen in die Lehre einzog und welchen Beitrag Professoren, Privatdozenten und Promovierende zur Forschung leisteten. Erstmals wird auch die Bedeutung der Wasseruntersuchungen aufgezeigt, die durch die Hoffnung auf radioaktive Heilquellen angetrieben wurden.Im zweiten Teil werden in internationaler Perspektive unsichtbare und in der Geschichtsschreibung oft wenig beachtete Facetten der „Arbeit mit dem Radium“ untersucht. So mussten Instrumente und radioaktive Präparate überhaupt erst hergestellt und in Umlauf gebracht werden. Auch die Etablierung von Nachweismethoden für Radioaktivität erforderte viel Arbeit, von der niemand sprach. Dienstleistungen wie die Entwicklung therapeutisch nutzbarer Präparate, Gutachtertätigkeiten, die Herausgabe einer Zeitschrift oder die Organisation eines Kongresses werden als integraler Bestandteil der wissenschaftlichen Arbeit in ihrer Bedeutung dargestellt. Eine Reflexion zur Arbeitsorganisation und zum disziplinären Status bündelt die Ergebnisse in einer neuen Gesamtsicht auf die frühe Radioaktivitätsforschung.

This book introduces readers to key concepts in group theory through engaging puzzles. The early sections of the book show how the rules of group theory emerge naturally from solving puzzles. Different classes of groups, such as cyclic, dihedral and permutation groups are introduced, accompanied by numerous puzzles to facilitate the understanding of the underlying group structures. Later chapters explain how further group theory principles can be applied to puzzle-solving. This book is intended as a highly motivating supplementary text for an undergraduate abstract algebra course. It is also ideal for anyone seeking a fun, hands-on approach to learning group theory. Additionally, the book's many puzzles will be enjoyable for readers already familiar with group theory.

This book, which is aimed at general readers interested in maths as well as professional mathematicians, addresses numerous aspects of this spell-binding science. In particular, the book shows how mathematics is structured and how it works. Practical examples are discussed as well as the general role of maths in culture and art, in nature and in everyday life. The topics covered range from forms of logical argumentation to numerical analysis, from simple applications in ancient civilisations to sophisticated tools in modern cultures, from natural shapes to artistic creations. Furthermore, it provides a comprehensible and comprehensive insight into the fascinating panorama of mathematics, emphasizing its importance in human history. It assumes only that readers have a grasp of the basic concepts of school maths, allowing them access to the exciting world of mathematics and to fall under its spell. Numerous examples and illustrations clarify the text. Rik Verhulst is Prof. emeritus in maths at the Karel de Grote University of Applied Sciences in Antwerp. He is the coordinator and co-author of several series of maths textbooks for secondary schools. He is well-known in professional circles for his numerous lectures at congresses and colloquia and for his contributions to various journals. As a collaborator and lecturer at the Belgian Centre for Methodology of Mathematics, the Vliebergh-Sencie courses, the Centre for Didactics of Mathematics at the Catholic University of Leuven and the Flemish Mathematical Olympiad, he has long been involved in the training of teachers and the preparation of pupils for the International Mathematical Olympiad.

Wozu braucht man eigentlich Mathematik? Haben Sie sich das auch schon gefragt oder sind Sie selbst Mathematiker/-in und hören dies oft?Mathematik ist weit mehr als die Suche nach der nächsten Primzahl oder dem x-ten Beweis des Satzes von Pythagoras. Mathematik ist eine zentrale Schlüsseltechnologie für viele Wissenschaftsbereiche. Die Frage, ob es einen Klimawandel gibt und wie man Veränderungen im Klima beobachtet, kann ohne Mathematik genauso wenig beantwortet werden wie die Frage, wie sich eine Pandemie ausbreitet. Viele weitere Beispiele werden in dem Buch angesprochen.In einem lockeren Erzählstil erläutert der Autor, wo überall Mathematik verborgen ist und wie man mit einfachen Mitteln schon verstehen kann, wie brisante Probleme gelöst werden. Vorausgesetzt werden (je nach Kapitel) teils gar keine Mathematik-Vorkenntnisse bis maximal zum Abitur-Wissen.

This textbook introduces bioinformatics to students in mathematics with no biology background assumed and it provides solid mathematical tools for biology students along with an understanding of how to implement them in bioinformatics problems. In addition to the basics, the text offers new approaches to understanding biological sequences. The concise presentation distinguishes itself from others on the subject, discussing and providing principles that relate to current open problems in bioinformatics as well as considering a variety of models. The convex hull principle is highlighted, opening a new interdisciplinary research area at the intersection of biology, mathematics, and computer science. Prerequisites include first courses in linear algebra, probability and statistics, and mathematical analysis. Researchers in mathematics, biology, and math-biology, will also find aspects of this text useful. This textbook is written based on the authors'research works that have been published in various journals along with the lecture notes used when teaching bioinformatics courses at the University of Illinois at Chicago and at Tsinghua University. The content may be divided into two parts. The first part includes three chapters, introducing some basic concepts. Chapter 1 provides biological background in molecular biology for mathematicians. Chapter 2 describes biological databases that are commonly used. Chapter 3 is concerned with alignment methods including global/local alignment, heuristic alignment, and multiple alignment. The second part consisting of five chapters, describes several bioinformatics principles using a rigorous mathematical formulation. Chapter 4 introduces the time-frequency spectral principle and its applications in bioinformatics. In Chapters 5 and 6, two strategies are used, the graphical representation and the natural vector method, to represent biological sequences, and conduct sequence comparison and phylogenetic analysis without alignment. Chapter 7 presents the convex hull principle and shows how it can be used to mathematically determine whether a certain amino acid sequence can be a protein. The last chapter summarizes additional mathematical ideas relating to sequence comparisons, such as new feature vectors and metrics. This part focuses on the governing principle in biology and provides plenty of alignment-free methods, which cannot be found in any other book.

Dieses Kaleidoskop zeigt, wie facettenreich und lebendig Mathematik ist – und lädt dazu ein, mehr über diese einzigartige Wissenschaft zu erfahren. Sorgfältig ausgewählte Beiträge spannen einen Bogen von zeitlosen Themen wie Zahlen, Unendlichkeiten, Dimensionen und Wahrscheinlichkeiten bis hin zu aktuellen Anwendungen in der Logistik, der Finanzwelt, der Kryptografie, der Medizin und anderen Feldern. Neben Ausschnitten aus klassischen mathematischen Texten werden aktuelle Beiträge präsentiert und durch eigens für diesen Band verfasste Abschnitte eingeordnet und abgerundet. Leicht verständliche, unterhaltsame Texte finden sich ebenso wie anspruchsvollere mathematische Herausforderungen. Ob Schülerinnen oder Schüler, Studierende, Lehrkräfte oder einfach nur alle, die bei „Pi“ nicht nur ein „e“ vermissen und an Torte denken wollen: Für jede und jeden ist etwas dabei, zum Stöbern und Schmökern, zum Ansehen und Durchblättern, zum Durcharbeiten und Mitdenken.Das Buch wurde fürden Abiturpreis der Deutschen Mathematiker-Vereinigung zusammengestellt und wird in diesem Rahmen traditionell als Preis an hervorragende Abiturientinnen und Abiturienten überreicht. Für die vorliegende dritte Auflage wurde das Buch aktualisiert und um einige Beiträge erweitert – insbesondere zu aktuellen Forschungs- und Anwendungsfeldern wie Künstliche Intelligenz, Quantencomputing und Epidemiologie.

The easy way to understand and retain all the concepts taught in pre-calculus classes Pre-Calculus All-in-One For Dummies is a great resource if you want to do you best in Pre-Calculus. Packed with lessons, examples, and practice problems in the book, plus extra chapter quizzes online, it gives you absolutely everything you need to succeed in pre-calc. Unlike your textbook, this book presents the essential topics clearly and concisely, so you can really understand the stuff you learn in class, score high on your tests (including the AP Pre-Calculus exam!), and get ready to confidently move ahead to upper-level math courses. And if you need a refresher before launching into calculus, look no further—this book has your back. Review what you learned in algebra and geometry, then dig into pre-calculus Master logarithms, exponentials, conic sections, linear equations, and beyond Get easy-to-understand explanations that match the methods your teacher uses Learn clever shortcuts, test-taking tips, and other hacks to make your life easierPre-Calculus All-in-One For Dummies is the must-have resource for students who need to review for exams or just want a little (or a lot of!) extra help understanding what's happening in class.

This book offers the first comprehensive account of how the logarithmic norm is used for matrices, nonlinear maps and linear differential operators, with a focus on initial and boundary value problems. Complementing the usual operator norm, the logarithmic norm is a versatile tool which provides unique additional information on the magnitude of an operator. It is instrumental in the stability theory of dynamical systems and in the theory of elliptic operator equations. The text adopts a unified approach to address a wide range of themes in applied mathematics. It explores the role of the logarithmic norm in scientific computing, compares the operator bounds with those of spectral theory, and illustrates the theory with classical models from science and engineering. Many previously unpublished results are presented alongside established material, supporting researchers in applied mathematics and computational engineering who seek a systematic approach to stability and perturbation bounds in initial value problems, boundary value problems and partial differential equations. Primarily intended as a reference text, the book can also serve as a graduate text for PhD students.

This is a personal story about being involved in the study of nonlinear phenomena for more than half a century. The focus is on the development of ideas and the resulting knowledge. This is the visible part of research, but much is usually hidden. The author describes how the ideas were generated and how an “invisible college” of friends and colleagues has emerged. The presentation is spiced by thoughts about the beauty of science and philosophical considerations on the complex world, where nonlinear interactions play an important role. The book is in some sense a biography but not so much about the personal life of the author – it is about science and its actors. Based on the author's experience in many European research centres and science policy institutions, it reflects on the development of knowledge in nonlinear dynamics as well as science policy actions over the second half of the 20th century and the first quarter of the 21st century. Graduates and postgraduates interested in the progress of research will find the book particularly engaging.

Microcirculation is a key area of interest within the realms of biology and medicine. As a vital discipline, microcirculatory biology forms a significant part of established medical fields like cardiovascular medicine and oncology, and is increasingly relevant in emerging fields such as neuroscience. With its multifaceted nature, the study of microcirculation has evolved from basic observations and experiments to embrace cutting-edge imaging technologies, quantitative methods, and the power of data science. This volume brings together a series of insightful chapters that highlight the latest trends in modeling microcirculation. It casts a spotlight on the vital role of microcirculation in brain function modeling and the innovative applications of microvascular models in oncology. Readers will be introduced to state-of-the-art methodologies of microcirculation modeling. A key focus is on mixed-dimensional models, mathematical methods adept at describing complex interactions within lower dimensional manifolds. Each chapter thoughtfully navigates the mathematical, computational, and practical challenges of these approaches, underscoring their effectiveness in capturing the essence of microcirculation. This book offers a window into the latest advancements and methodologies that are shaping the future of this vital field.

The book provides the latest research results on measuring Credit Rating Migration by mathematical methods. It brings about most popular mathematical models, methods and applications on this area, especially presents the latest development on structure models. It is systematically collects the models, methods and results in this area. The book first introduced the financial background and preliminary mathematical theory. Then two mainstream mathematical models for measuring default risks, the reduced form model and structure model, are presented. The structure model for measuring credit rating migration risks is the main part of the book and authors prove the existence, uniqueness, regularities, asymptotic behavior, traveling wave and other properties of the solutions of the model. The structural credit rating migration model is also extended to more general case, such as stochastic interest rate, multiple ratings, region switch and so on. Some credit derivatives, and numerical analysis, parameter calibration and estimate of the migration boundary of the models are given in the last two chapters. The book focuses on theoretical financial investigators, especially financial mathematical researchers and students. The book is involved various mathematical models, such as PDE, numerical simulation etc., some of them are interesting mathematical problems, so that, and a good reference book to study mathematical modeling in credit rating migration. It might also be used as a textbook for students in financial credit risks.

This volume is a collection of essays related to the work of Professor Yuriy Vasilievich Ivlev, a distinguished Russian logician and philosopher renowned for his expertise in many-valued and modal logics. Notably, his groundbreaking work on quasi-matrices for logics, now recognized as non-deterministic matrices and non-deterministic semantics, emerged in the 1970s. From a philosophical standpoint, Ivlev's research delves into the formal analysis of indeterminacy, offering a logical framework to understand how sequences of indeterminate events can yield determinate outcomes. The volume follows two complementary lines of research. Firstly, it serves as a platform for the exploration and discussion of Ivlev's seminal contributions to the algebraic characterization of both normal and non-normal modal logics, aimed at making these insights accessible to an international audience. Secondly, it features contributions from esteemed logicians and philosophers worldwide, offering diverseperspectives on the logical analysis of indeterminacy. This comprehensive volume will appeal to scholars and researchers in logic, philosophy, and mathematics who are engaged in the study of many-valued and modal methodologies for modeling situations of indeterminacy.

This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields. Arithmetic topology is now becoming a powerful guiding principle and driving force to obtain parallel results and new insights between 3-dimensional geometry and number theory.After an informative introduction to Gauss'work, in which arithmetic topology originated, the text reviews a background from both topology and number theory. The analogy between knots in 3-manifolds and primes in number rings, the founding principle of the subject, is based on the étale topological interpretation of primes and number rings. On the basis of this principle, the text explores systematically intimate analogies and parallel results of various concepts and theories between 3-dimensional topology and number theory. The presentation of these analogies begins at an elementary level, gradually building to advanced theories in later chapters. Many results presented here are new and original.References are clearly provided if necessary, and many examples and illustrations are included. Some useful problems are also given for future research. All these components make the book useful for graduate students and researchers in number theory, low dimensional topology, and geometry.This second edition is a corrected and enlarged version of the original one. Misprints and mistakes in the first edition are corrected, references are updated, and some expositions are improved. Because of the remarkable developments in arithmetic topology after the publication of the first edition, the present edition includes two new chapters. One is concerned with idelic class field theory for 3-manifolds and number fields. The other deals with topological and arithmetic Dijkgraaf–Witten theory, which supports a new bridge between arithmetic topology and mathematical physics.

This book is written in a style that uncovers the mathematical theories hidden in our daily lives, using examples of patterns that appear in nature, arts, traditional crafts, as well as mathematical mechanics in architectural techniques. The authors believe that through conversations between students and mathematicians, readers may learn about the methods used by the originators of these theories―their trials, errors, and triumphs―in reaching their various conclusions. The goal is to help readers refine their mathematical sense in terms of formulating valuable questions and pursuing them. In addition, the book aims to provide enjoyment in the application of mathematical principles to beautiful art and design by using examples that highlight the wonders and mysteries of these works found in our daily lives. To achieve these goals, the book tackles the latest exquisite results on polygons and polyhedra and the dynamic history of geometric research found around us. The term'intuitive geometry'was coined by Lászlo Fejes Tóth and refers to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the'man on the street.'This book enables readers to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity. In this second edition, many new results, and elegant proofs on a variety of topics have been added, enhancing the book's rich content even further.

This book presents contributions related to new research results presented at the 27th International Conference on Difference Equations and Applications, ICDEA 2022, that was held at CentraleSupélec, Université Paris-Saclay, France, under the auspices of the International Society of Difference Equations (ISDE), July 18–22, 2022. The book aims not only to disseminate these results but to foster further advances in the fields of difference equations and discrete dynamical systems. Also included are applications to economic growth modeling, population dynamics, epidemic modeling, game theory, control systems, and network analysis. The target audience for the book includes Ph.D. students, researchers, educators, and practitioners in these fields.

A rich, narrative explanation of the mathematics that has brought us machine learning and the ongoing explosion of artificial intelligence Machine learning systems are making life-altering decisions for us: approving mortgage loans, determining whether a tumor is cancerous, or deciding if someone gets bail. They now influence developments and discoveries in chemistry, biology, and physics—the study of genomes, extrasolar planets, even the intricacies of quantum systems. And all this before large language models such as ChatGPT came on the scene. We are living through a revolution in machine learning-powered AI that shows no signs of slowing down. This technology is based on relatively simple mathematical ideas, some of which go back centuries, including linear algebra and calculus, the stuff of seventeenth- and eighteenth-century mathematics. It took the birth and advancement of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see today. In this enlightening book, Anil Ananthaswamy explains the fundamental math behind machine learning, while suggesting intriguing links between artificial and natural intelligence. Might the same math underpin them both? As Ananthaswamy resonantly concludes, to make safe and effective use of artificial intelligence, we need to understand its profound capabilities and limitations, the clues to which lie in the math that makes machine learning possible.

This book provides a concise yet rigorous introduction to probability theory. Among the possible approaches to the subject, the most modern approach based on measure theory has been chosen: although it requires a higher degree of mathematical abstraction and sophistication, it is essential to provide the foundations for the study of more advanced topics such as stochastic processes, stochastic differential calculus and statistical inference. The text originated from the teaching experience in probability and applied mathematics courses within the mathematics degree program at the University of Bologna; it is suitable for second- or third-year students in mathematics, physics, or other natural sciences, assuming multidimensional differential and integral calculus as a prerequisite. The four chapters cover the following topics: measures and probability spaces; random variables; sequences of random variables and limit theorems; and expectation and conditional distribution. The text includes a collection of solved exercises.

The flourishing theory of classical optimal transport concerns mass transportation at minimal cost. This book introduces the reader to optimal transport on quantum structures, i.e., optimal transportation between quantum states and related non-commutative concepts of mass transportation. It contains lecture notes on classical optimal transport and Wasserstein gradient flowsdynamics and quantum optimal transportquantum couplings and many-body problemsquantum channels and qubits These notes are based on lectures given by the authors at the'Optimal Transport on Quantum Structures'School held at the Erdös Center in Budapest in the fall of 2022. The lecture notes are complemented by two survey chapters presenting the state of the art in different research areas of non-commutative optimal transport.