Matematik

Statistical Analysis for Civil Engineers: Mathematical Theory and Applied Experiment Design is a well-researched and topically organized reference book that guides its readers, both in academia and industry, to recognize how to describe unpredictable events in a quantitative way and to learn how these events can be incorporated into practical engineering analysis that facilitates data-driven problem solving and optimization-based decision-making.Written by experts in the field with a proven track record as educators and practicing consultancy specialists, this book has been developed in such a manner that it advances understanding of the mathematical theory underlying analytical methodology gradually. It also supports practical application through relevant worked examples in a variety of civil engineering branches, notably structural, materials, transportation, and geotechnical engineering. Through all stages of data analysis, numerical modeling and simulation, and implementation, the volume emphasizes the need to change the current perception with respect to the use of modern statistical techniques in the scientific as well as practical spheres of civil engineering.

This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the third edition of Steven Strogatz's classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.

El propósito de este libro, es compartir los resultados obtenidos en la investigación realizada en la Facultad de Ciencias Exactas y Naturales de la Universidad Nacional de Mar del Plata, respecto de los conocimientos y dificultades sobre aspectos básicos de Trigonometría de los estudiantes que cursan Álgebra en primer año de las carreras de Licenciatura en Química, Bioquímica, Profesorado y Licenciatura en Física y Profesorado y Licenciatura en Matemática, así como también, sobre el abordaje del tema Trigonometría realizado por los docentes de Sexto año de las escuelas secundarias en sus clases durante la pandemia. Asimismo, se presenta una secuencia didáctica relativa al tema para Sexto año de la Escuela Secundaria.Por otra parte, se relata una experiencia sobre una clase de primer año de la Facultad, utilizando GeoGebra, cuyo objetivo es reafirmar conceptos relacionados con las propiedades de los módulos y argumentos de Números Complejos (tema en el que se aplican conceptos de Trigonometría).

La preparación de los estudiantes de alto rendimiento en Matemática requiere de diferentes recursos y materiales para facilitar su aprendizaje y desarrollo, en los cuales se incluyen ejercicios desafiantes y relevantes.Este volumen está dedicado a las ecuaciones, inecuaciones y sistemas de ecuaciones, con ejercicios no tan habituales en los contenidos del currículo ordinario, y se presentan procedimientos ingeniosos para resolverlos. También se hacen consideraciones sobre la resolución de problemas según un estudio de la heurística de Polya. Además se abordan las ecuaciones funcionales que a no ser un tema del currículo ordinario de la Enseñanza Secundaria, lo es frecuente en las Olimpiadas de Matemática sobre todo internacionales.El libro está dirigido especialmente a docentes que participan en la preparación de estudiantes de alto rendimiento en Matemática. Es también de particular importancia para el autoestudio de los concursantes de las Olimpíadas de Matemáticas, para los candidatos a los exámenes para ingresar a las universidades, para estudiantes de cursos de Matemática Superior, y para cualquier autodidacta interesado en aprender o profundizar en estos temas matemáticos.

¿This book constitutes the proceedings of the 14th International Workshop on Statistical Atlases and Computational Models of the Heart, STACOM 2023, as well as the Cardiac MRI Reconstruction Challenge, CMRxRecon Challenge. There was a total of 53 submissions to the workshop. The 24 regular workshop papers included in this volume were carefully reviewed and selected from 29 paper submissions. They deal with cardiac segmentation, modelling, strain quantification, registration, statistical shape analysis, and quality control. In addition, 21 papers from the CMRxRecon challenge are included in this volume. They focus on fast CMR image reconstruction and provide a benchmark dataset that enables the broader research community to promote advances in this area of research.

This book uses game theory to analyze the strategies developed in negotiation processes. Offering a detailed analysis of competition and cooperation, it explores various bargaining strategies that result from the application of Nash equilibrium and mixed strategies. Employing a blend of game theory and real-world examples, the authors describe typical negotiation scenarios and unveil the art of negotiation strategy ¿ dissecting both competitive and cooperative tactics.This comprehensive analysis explores the multifaceted dimensions of negotiation, highlighting not only formal aspects but also the economic, social, political, and human factors at play. The authors discuss the basic structures of cooperative and non-cooperative games and conduct a comprehensive analysis of the language games that take place in negotiations. They examine how negotiators belonging to different forms of life can trade with each other when their respective language games are different and prone tomisinterpretation. The book also probes arbitration and mediation as conflict-resolution tools within this intricate landscape. Designed for the curious minds seeking insight into negotiation strategies, as well as students and scholars of diverse fields, this book fosters an understanding of negotiation's labyrinthine pathways. "Dynamics of Rational Negotiation" unlocks the door to negotiation's complexities, inviting readers to unravel the layers of human interaction.

This book presents recent advances in the theory and application of the Best-Worst Method (BWM). It includes selected papers from the Second International Workshop on Best-Worst Method (BWM2021), held in Delft, The Netherlands from 10-11 June, 2021, and provides valuable insights on why and how to use BWM in a diverse range of applications including health, energy, supply chain management, and engineering. The book highlights the use of BWM in different settings including single decision-making vs group decision-making, and complete information vs incomplete and uncertain situations. The papers gathered here will benefit academics and practitioners who are involved in multi-criteria decision-making and decision analysis.

This textbook provides an introduction to fundamental concepts of algebra at upper undergraduate to graduate level, covering the theory of rings, fields and modules, as well as the representation theory of finite groups.Throughout the book, the exposition relies on universal constructions, making systematic use of quotients and category theory ¿ whose language is introduced in the first chapter. The book is divided into four parts. Parts I and II cover foundations of rings and modules, field theory and generalities on finite group representations, insisting on rings of polynomials and their ideals. Part III culminates in the structure theory of finitely generated modules over Dedekind domains and its applications to abelian groups, linear maps, and foundations of algebraic number theory. Part IV is an extensive study of linear representations of finite groups over fields of characteristic zero, including graded representations and graded characters as well as a final chapter on the Drinfeld¿Lusztig double of a group algebra, appearing for the first time in a textbook at this level.Based on over twenty years of teaching various aspects of algebra, mainly at the École Normale Supérieure (Paris) and at Peking University, the book reflects the audiences of the author's courses. In particular, foundations of abstract algebra, like linear algebra and elementary group theory, are assumed of the reader. Each of the of four parts can be used for a course ¿ with a little ad hoc complement on the language of categories. Thanks to its rich choice of topics, the book can also serve students as a reference throughout their studies, from undergraduate to advanced graduate level.

In this book, various chaos maps are embedded in eleven efficient and well-known metaheuristics and a significant improvement in the optimization results is achieved. The two basic steps of metaheuristic algorithms consist of exploration and exploitation. The imbalance between these stages causes serious problems for metaheuristic algorithms, which are immature convergence and stopping in local optima. Chaos maps with chaotic jumps can save algorithms from being trapped in local optima and lead to convergence toward global optima. Embedding these maps in the exploration phase, exploitation phase, or both simultaneously corresponds to three efficient and useful scenarios. By creating competition between different modes and increasing diversity in the search space and creating sudden jumps in the search phase, improvements are achieved for chaotic algorithms. Four Chaotic Algorithms, including Chaotic Cyclical Parthenogenesis Algorithm, Chaotic Water Evaporation Optimization, Chaotic Tug-of-War Optimization, and Chaotic Thermal Exchange Optimization are developed.

This book starts with the rationale for creating an FCM by contrast to other techniques for participatory modeling, as this rationale is a key element to justify the adoption of techniques in a research paper. Fuzzy cognitive mapping is an active research field with over 20,000 publications devoted to externalizing the qualitative perspectives or ¿mental models¿ of individuals and groups. Since the emergence of fuzzy cognitive maps (FCMs) back in the 80s, new algorithms have been developed to reduce bias, facilitate the externalization process, or efficiently utilize quantitative data via machine learning. It covers the development of an FCM with participants through a traditional in-person setting, drawing from the experience of practitioners and highlighting solutions to commonly encountered challenges. The book continues with introducing principles of simulations with FCMs as a tool to perform what-if scenario analysis, while extending those principles to more elaborated simulation scenarios where FCMs and agent-based modeling are combined. Once an FCM model is obtained, the book then details the analytical tools available for practitioners (e.g., to identify the most important factors) and provides examples to aid in the interpretation of results. The discussion concerning relevant extensions is equally pertinent, which are devoted to increasing the expressiveness of the FCM formalism in problems involving uncertainty. The last four chapters focus on building FCM models from historical data. These models are typically needed when facing multi-output prediction or pattern classification problems. In that regard, the book smoothly guides the reader from simple approaches to more elaborated algorithms, symbolizing the noticeable progress of this field in the last 35 years. Problems, recent references, and functional codes are included in each chapter to provide practice and support further learning from practitioners and researchers.

This book aims at introducing students into the modern analytical foundations to treat problems and situations in the Calculus of Variations solidly and rigorously. Since no background is taken for granted or assumed, as the textbook pretends to be self-contained, areas like basic Functional Analysis and Sobolev spaces are studied to the point that chapters devoted to these topics can be utilized by themselves as an introduction to these important parts of Analysis. The material in this regard has been selected to serve the needs of classical variational problems, leaving broader treatments for more advanced and specialized courses in those areas. It should not be forgotten that problems in the Calculus of Variations historically played a crucial role in pushing Functional Analysis as a discipline on its own right. The style is intentionally didactic. After a first general chapter to place optimization problems in infinite-dimensional spaces in perspective, the first part of the book focuses on the initial important concepts in Functional Analysis and introduces Sobolev spaces in dimension one as a preliminary, simpler case (much in the same way as in the successful book of H. Brezis). Once the analytical framework is covered, one-dimensional variational problems are examined in detail including numerous examples and exercises. The second part dwells, again as a first-round, on another important chapter of Functional Analysis that students should be exposed to, and that eventually will find some applications in subsequent chapters. The first chapter of this part examines continuous operators and the important principles associated with mappings between functional spaces; and another one focuses on compact operators and their fundamental and remarkable properties for Analysis. Finally, the third part advances to multi-dimensional Sobolev spaces and the corresponding problems in the Calculus of Variations. In this setting, problems become much more involved and, for this same reason, much more interesting and appealing. In particular, the final chapter dives into a number of advanced topics, some of which reflect a personal taste. Other possibilities stressing other kinds of problems are possible. In summary, the text pretends to help students with their first exposure to the modern calculus of variations and the analytical foundation associated with it. In particular, it covers an extended introduction to basic functional analysis and to Sobolev spaces. The tone of the text and the set of proposed exercises will facilitate progressive understanding until the need for further challenges beyond the topics addressed here will push students to more advanced horizons.

The book concerns with solving about 650 ordinary and partial differential equations. Each equation has at least one solution and each solution has at least one coloured graph. The coloured graphs reveal different features of the solutions. Some graphs are dynamical as for Clairaut differential equations. Thus, one can study the general and the singular solutions. All the equations are solved by Mathematica. The first chapter contains mathematical notions and results that are used later through the book. Thus, the book is self-contained that is an advantage for the reader. The ordinary differential equations are treated in Chapters 2 to 4, while the partial differential equations are discussed in Chapters 5 to 10. The book is useful for undergraduate and graduate students, for researchers in engineering, physics, chemistry, and others. Chapter 9 treats parabolic partial differential equations while Chapter 10 treats third and higher order nonlinear partial differential equations, both with modern methods. Chapter 10 discusses the Korteweg-de Vries, Dodd-Bullough-Mikhailov, Tzitzeica-Dodd-Bullough, Benjamin, Kadomtsev-Petviashvili, Sawada-Kotera, and Kaup-Kupershmidt equations.

This text offers a unique balance of theory and a variety of standard and new applications along with solved technology-aided problems. The book includes the fundamental mathematical theory, as well as a wide range of applications, numerical methods, projects, and technology-assisted problems and solutions in Maple, Mathematica, and MATLAB. Some of the applications are new, some are unique, and some are discussed in an essay. There is a variety of exercises which include True/False questions, questions that require proofs, and questions that require computations. The goal is to provide the student with is a solid foundation of the mathematical theory and an appreciation of some of the important real-life applications. Emphasis is given on geometry, matrix transformations, orthogonality, and least-squares. Designed for maximum flexibility, it is written for a one-semester/two semester course at the sophomore or junior level for students of mathematics or science.

This book offers a comprehensive overview of the latest advancements in the field of applied mathematics as it relates to finance, marketing, and economics. It covers a range of topics including the effective utilization of applied mathematics and mathematical modeling in finance, economics, and marketing. Additionally, it explores the intersection between applied mathematics and practical applications in various scientific fields. The book targets a multidisciplinary audience, fostering the exchange of diverse ideas and showcasing the broad appeal of different subjects. It delves into recent developments in areas such as mathematical modeling in finance, mathematical modeling in marketing, the modeling of financial and economic fundamentals (e.g., interest rates, asset prices), market behavior modeling, modeling market imperfections, pricing financial derivative securities, hedging strategies, numerical methods, and financial engineering.The book features selected contributions presented at the first edition of the International Conference in Applied Mathematics to Finance, Marketing and Economics, which took place at the National School of Commerce and Management in El Jadida, Morocco, from November 26 to 27, 2020.

Commissioned by the Society for Modeling and Simulation International (SCS), this needed, useful new ¿Body of Knowledge¿ (BoK) collects and organizes the common understanding of a wide collection of professionals and professional associations.Modeling and simulation (M&S) is a ubiquitous discipline that lays the computational foundation for real and virtual experimentation, clearly stating boundaries¿and interactions¿of systems, data, and representations. The field is well known, too, for its training support via simulations and simulators. Indeed, with computers increasingly influencing the activities of today¿s world, M&S is the third pillar of scientific understanding, taking its place along with theory building and empirical observation.This valuable new handbook provides intellectual support for all disciplines in analysis, design and optimization. It contributes increasingly to the growing number of computational disciplines, addressing the broad variety of contributing as well as supported disciplines and application domains. Further, each of its sections provide numerous references for further information. Highly comprehensive, the BoK represents many viewpoints and facets, captured under such topics as:Mathematical and Systems Theory FoundationsSimulation Formalisms and ParadigmsSynergies with Systems Engineering and Artificial IntelligenceMultidisciplinary ChallengesEthics and PhilosophyHistorical PerspectivesExamining theoretical as well as practical challenges, this unique volume addresses the many facets of M&S for scholars, students, and practitioners. As such, it affords readers from all science, engineering, and arts disciplines a comprehensive and concise representation of concepts, terms, and activities needed to explain the M&S discipline.Tuncer Ören is Professor Emeritus at the University of Ottawa. Bernard Zeigler is Professor Emeritus at the University of Arizona. Andreas Tolk is Chief Scientist at The MITRE Corporation. All three editors are long-time members and Fellows of the Society for Modeling and Simulation International. Under the leadership of three SCS Fellows, Dr. Ören, University of Ottawa, Dr. Zeigler, The University of Arizona, and Dr. Tolk, The MITRE Corporation, more than 50 international scholars from 15 countries provided insights and experience to compile this initial M&S Body of Knowledge.

This book reports on cutting-edge theories and methods for analyzing complex systems, such as transportation and communication networks and discusses multi-disciplinary approaches to dependability problems encountered when dealing with complex systems in practice. The book presents the most relevant findings discussed at the 23rd International Multidisciplinary Conference on Reliability and Statistics in Transportation and Communication (RelStat 2023), which took place as a hybrid event on October 19 ¿ 21, 2023, in/from Riga, Latvia. It spans a broad spectrum of advanced theories and methods, giving a special emphasis to the digitalization of transport systems, as well as smart, artificial intelligence, and digital twins applications.

This book contains an Irish translation of the the second-edition English version (ISBN 9780244879822, https://logicpress.ie/2020-1/index.html) of a one-semester undergraduate course taught through the medium of Irish. I have given this course in Maynooth each year since 2006. The class is typically quite mixed, and the book aims to challenge students familiar with rigorous arguments while simultaneously providing comfort to other students that prefer procedural mathematics---not an easy balancing act! For instance, some exercises are targeted at one or other of these two groups of students and, while some material is done in the context of metric spaces, guidance is given to the reader who prefers to stick to the real line. This second edition of the book has no major new topics, but it is about twice as long as the first. Some topics are explored in greater depth (e.g. conjugacy and semiconjugacy, bifurcation) and some proofs have been added (notably for Sharkovsky's and Singer's theorems). Additional exercises have been given, and the most challenging ones are marked appropriately. There is a glossary giving translations of terms.

Learn the fundamentals of Bayesian modeling using state-of-the-art Python libraries, such as PyMC, ArviZ, Bambi, and more, guided by an experienced Bayesian modeler who contributes to these librariesKey Features- Conduct Bayesian data analysis with step-by-step guidance- Gain insight into a modern, practical, and computational approach to Bayesian statistical modeling- Enhance your learning with best practices through sample problems and practice exercises- Purchase of the print or Kindle book includes a free PDF eBook.Book DescriptionThe third edition of Bayesian Analysis with Python serves as an introduction to the main concepts of applied Bayesian modeling using PyMC, a state-of-the-art probabilistic programming library, and other libraries that support and facilitate modeling like ArviZ, for exploratory analysis of Bayesian models; Bambi, for flexible and easy hierarchical linear modeling; PreliZ, for prior elicitation; PyMC-BART, for flexible non-parametric regression; and Kulprit, for variable selection.In this updated edition, a brief and conceptual introduction to probability theory enhances your learning journey by introducing new topics like Bayesian additive regression trees (BART), featuring updated examples. Refined explanations, informed by feedback and experience from previous editions, underscore the book's emphasis on Bayesian statistics. You will explore various models, including hierarchical models, generalized linear models for regression and classification, mixture models, Gaussian processes, and BART, using synthetic and real datasets.By the end of this book, you will possess a functional understanding of probabilistic modeling, enabling you to design and implement Bayesian models for your data science challenges. You'll be well-prepared to delve into more advanced material or specialized statistical modeling if the need arises.What you will learn- Build probabilistic models using PyMC and Bambi- Analyze and interpret probabilistic models with ArviZ- Acquire the skills to sanity-check models and modify them if necessary- Build better models with prior and posterior predictive checks- Learn the advantages and caveats of hierarchical models- Compare models and choose between alternative ones- Interpret results and apply your knowledge to real-world problems- Explore common models from a unified probabilistic perspective- Apply the Bayesian framework's flexibility for probabilistic thinkingWho this book is forIf you are a student, data scientist, researcher, or developer looking to get started with Bayesian data analysis and probabilistic programming, this book is for you. The book is introductory, so no previous statistical knowledge is required, although some experience in using Python and scientific libraries like NumPy is expected.Table of Contents- Thinking Probabilistically- Programming Probabilistically- Hierarchical Models- Modeling with Lines- Comparing Models- Modeling with Bambi- Mixture Models- Gaussian Processes- Bayesian Additive Regression Trees- Inference Engines- Where to Go Next

This thesis deals with storage systems that are organized in last-in-first-out stacks. This approach for storing items is common, for example, in container terminals, and is therefore of great practical interest as well as high relevance in the literature. Furthermore, optimization problems that may arise in this context are presented and addressed by developing novel mathematical model formulations and customized solution methods.

En este estudio, se examina la subestructura matemática de las obras del artista gráfico neerlandés M.C. Escher. Los efectos matemáticos en las obras de Escher pueden clasificarse en ciertos temas. Los más importantes pueden ordenarse como la división regular del plano, las paradojas visuales y las ficciones sobre la estructura de la perspectiva y la topología geométrica. Para cada uno de estos temas, se puede decir que Escher está influenciado por ciertos nombres específicos. Los más importantes de ellos son Harold Coxeter, Roger Penrose y Albert Flocon.

Optimization should be the science of making the best possible decisions. Making decisions is a virtually universal human activity encountered by professionals (in any field) or people in their everyday lives. You would think, then, that the study of making good decisions is a subject that should be taught broadly to students throughout engineering, the physical and social sciences, business, and policy. Yet today, "optimization" is widely taught as a mathematically sophisticated subject, often limited to graduate students in specialized fields.In operations research (or industrial engineering), "optimization" is equivalent to deterministic math programming, starting with linear programs (and the simplex algorithm), and then transitioning through integer linear programs and nonlinear programs. If you are in departments like electrical or mechanical engineering, optimization means teaching optimal control. And if you are in computer science, optimization today could be interpreted in the context of machine learning (such as fitting models to data) or as reinforcement learning.This book claims that the traditional style of teaching optimization is misguided and out of date. First, while the simplex algorithm is a powerful strategy for solving linear programs, the details of the simplex algorithm are completely inappropriate in an introductory course in optimization. Second, while linear programs are appropriate for solving many problems, they are only applicable to a tiny fraction of all decisions. Third, linear programs (along with integer and nonlinear programs) are static models for problems with (typically) vector-valued decisions. By contrast, most decisions are sequential since they are made periodically over time as new information is arriving. In addition, the vast majority of these decisions are scalar (possibly continuous or discrete).This book is designed for instructors (or potential instructors) looking to introduce the science of making good decisions to the broadest possible audience. It should also be of interest to anyone who has already had a traditional course in optimization of any type. The presentation is organized around a series of topics that suggest a fundamentally different approach to teaching "optimization" spanning both sequential decision problems (which offer the simplest problem settings) before transitioning to more complex vector-valued decisions. It also makes the case that most problems which are modeled as linear (or integer, or nonlinear programs) are actually methods for making decisions in a sequential setting. For this reason, these topics are introduced with much less emphasis on algorithms than is traditionally used, both in static and sequential settings.

This book provides an in-depth roadmap for qualitative research methods and data analysis across disciplines using ATLAS.ti. It encompasses and rationalizes key qualitative research concepts and methods with innovative frameworks to enrich the reader¿s understanding of qualitative research methods and data analysis. The book contains multiple real-world projects that assist readers in developing conceptual and theoretical knowledge, as well as gaining insights from fieldwork, visualizing data collection, analysis, and methodological interpretations.This easy to use book provides a pragmatic approach to qualitative methods, proficiency in capturing field observations, user-friendly steps to data analysis starting from transcription, preparation of data, reading and identification of quotations, coding, memoing, commenting, code groups, creating smart codes and groups using set, semantic, and proximity operators resulting in generating numerous insightful thematic reports in avariety of formats.More notable features:- Demonstrates systematic roots to research from begin to end- Provides practical advice on how to overcome field challenges during data collection, ethical considerations, and step-by-step procedures for gaining access to participants and capturing holistic data- Includes numerous numerical arguments, interpretations, and explanations for concepts, themes, variables, networks, and emerging concepts- Includes several research frameworks and data analysis guideposts on real-world research projects with thorough procedures covering 267 images and 38 tables- Compelling for quantitative research and mixed methods approachesThe book's straightforward and user-friendly format makes it simple and easy to use, comprehend, and interpret for anyone working with ATLAS.ti.

This book is designed as a gentle introduction to the fascinating field of choice modeling and its practical implementation using the R language. Discrete choice analysis is a family of methods useful to study individual decision-making. With strong theoretical foundations in consumer behavior, discrete choice models are used in the analysis of health policy, transportation systems, marketing, economics, public policy, political science, urban planning, and criminology, to mention just a few fields of application. The book does not assume prior knowledge of discrete choice analysis or R, but instead strives to introduce both in an intuitive way, starting from simple concepts and progressing to more sophisticated ideas. Loaded with a wealth of examples and code, the book covers the fundamentals of data and analysis in a progressive way. Readers begin with simple data operations and the underlying theory of choice analysis and conclude by working with sophisticated models including latent class logit models, mixed logit models, and ordinal logit models with taste heterogeneity. Data visualization is emphasized to explore both the input data as well as the results of models. This book should be of interest to graduate students, faculty, and researchers conducting empirical work using individual level choice data who are approaching the field of discrete choice analysis for the first time. In addition, it should interest more advanced modelers wishing to learn about the potential of R for discrete choice analysis. By embedding the treatment of choice modeling within the R ecosystem, readers benefit from learning about the larger R family of packages for data exploration, analysis, and visualization.