Search

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 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.

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.

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.

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.

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 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.