Computational Methods for Coupled Problems in Science and Engineering
The ninth edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2021) was organized to take place on 13-16 June 2021. Due to the pandemic, COUPLED 2021 was a fully online and completely synchronous conference. The previous eight editions of this conference were held on the islands of Santorini (Greece) on 25-28 May 2005; Ibiza (Spain) on 21-23 May 2007; Ischia (Italy) on 8-11 June 2009; Kos (Greece) on 20-22 June 2011; Ibiza (Spain) on 17-19 June 2013; San Servolo, Venice (Italy), on 18-20 May 2015; Rhodes Island (Greece) on 12-14 June 2017; and Sitges (Spain) on 3-5 June 2019. The objectives of COUPLED PROBLEMS 2021 were to present and discuss the state of the art in mathematical models, numerical methods and computational techniques for solving coupling problems of a multidisciplinary character in science and engineering. The conference's goal was to make advances in the formulation and solution of real-life problems with a multidisciplinary perspective, accounting for all the complex couplings involved in the physical description of the problem. The conference was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS) and a Special Interest Conference of the International Association for Computational Mechanics (IACM). It was also supported by other scientific organizations in Europe and across the globe.
Risk Revealed
Explore the concept of risk through numerous examples and their statistical modeling, traveling from a historical perspective all the way to an up-to-date technical analysis. Written with a wide readership in mind, this book begins with accounts of a selection of major historical disasters, such as the North Sea flood of 1953 and the L'Aquila earthquake. These tales serve to set the scene and to motivate the second part of the book, which describes the mathematical tools required to analyze these events, and how to use them. The focus is on the basic understanding of the mathematical modeling of risk and what types of questions the methods allow one to answer. The text offers a bridge between the world of science and that of everyday experience. It is written to be accessible to readers with only a basic background in mathematics and statistics. Even the more technical discussions are interspersed with historical comments and plentiful examples.
Change Point Analysis for Time Series
This volume provides a comprehensive survey that covers various modern methods used for detecting and estimating change points in time series and their models. The book primarily focuses on asymptotic theory and practical applications of change point analysis. The methods discussed in the book go beyond the traditional change point methods for univariate and multivariate series. It also explores techniques for handling heteroscedastic series, high-dimensional series, and functional data. While the primary emphasis is on retrospective change point analysis, the book also presents sequential "on-line" methods for detecting change points in real-time scenarios. Each chapter in the book includes multiple data examples that illustrate the practical application of the developed results. These examples cover diverse fields such as economics, finance, environmental studies, and health data analysis. To reinforce the understanding of the material, each chapter concludes with several exercises.Additionally, the book provides a discussion of background literature, allowing readers to explore further resources for in-depth knowledge on specific topics. Overall, "Change Point Analysis for Time Series" offers a broad and informative overview of modern methods in change point analysis, making it a valuable resource for researchers, practitioners, and students interested in analyzing and modeling time series data.
Linear Algebra in Data Science
This textbook explores applications of linear algebra in data science at an introductory level, showing readers how the two are deeply connected. The authors accomplish this by offering exercises that escalate in complexity, many of which incorporate MATLAB. Practice projects appear as well for students to better understand the real-world applications of the material covered in a standard linear algebra course. Some topics covered include singular value decomposition, convolution, frequency filtering, and neural networks. Linear Algebra in Data Science is suitable as a supplement to a standard linear algebra course.
Tangles
Tangles offer a precise way to identify structure in imprecise data. By grouping qualities that often occur together, they not only reveal clusters of things but also types of their qualities: types of political views, of texts, of health conditions, or of proteins. Tangles offer a new, structural, approach to artificial intelligence that can help us understand, classify, and predict complex phenomena. This has become possible by the recent axiomatization of the mathematical theory of tangles, which has made it applicable far beyond its origin in graph theory: from clustering in data science and machine learning to predicting customer behaviour in economics; from DNA sequencing and drug development to text and image analysis. Such applications are explored here for the first time. Assuming only basic undergraduate mathematics, the theory of tangles and its potential implications are made accessible to scientists, computer scientists, and social scientists.
The families of prime numbers
The book introduces innovative approaches to conjectures and established knowledge in the realm of prime numbers. It explores how famous mathematicians like Sophie Germain and Mersenne, among others, conceptualized prime numbers Not only does the text clarify Fermat's Little Theorem, but it also offers an explanation for the existence of pseudoprimes. Furthermore, it sheds light on the effectiveness of the Lucas-Lehmer algorithm in discovering Mersenne Primes. By elucidating fundamental concepts, the book provides fresh insights into the study of prime numbers within Number Theory. While its primary audience consists of enthusiasts and mathematicians in search of new patterns and analytical methodologies for prime numbers, the book is designed to be accessible to a broader audience. With over 70 explanatory figures and clear prose, it appeals to anyone intrigued by the intricate world of prime numbers.
Ecosystem Modelling with EwE
This textbook provides a basis for courses in ecosystem modelling based on the Ecopath with Ecosim (EwE) modelling framework and software. EwE is a versatile approach with a low but very long (and gradually steeper) learning curve.The authors have been central to the development of EwE for more than thirty years, and during that time the simple Ecopath mass-balance approach it started with has through the addition of time and spatial-dynamic models, among others, been expanded to become a dynamic toolbox that can be used to address anything from simple fundamental research questions to very complex management and policy questions related to ecosystem based management.It's been a guiding principle throughout the development of EwE to provide an easy-to-access approach that does not require extensive mathematical or programming capabilities to get start. Model first, ask later is the philosophy. By just getting started with modelling, you gain insight and can start asking fundamental questions about how components of ecosystems interplay. Diving deeper is important, but this textbook makes the initial getting-started as simple and accessible as possible.
Harmonic Functions and Random Walks on Groups
Research in recent years has highlighted the deep connections between the algebraic, geometric, and analytic structures of a discrete group. New methods and ideas have resulted in an exciting field, with many opportunities for new researchers. This book is an introduction to the area from a modern vantage point. It incorporates the main basics, such as Kesten's amenability criterion, Coulhon and Saloff-Coste inequality, random walk entropy and bounded harmonic functions, the Choquet-Deny Theorem, the Milnor-Wolf Theorem, and a complete proof of Gromov's Theorem on polynomial growth groups. The book is especially appropriate for young researchers, and those new to the field, accessible even to graduate students. An abundance of examples, exercises, and solutions encourage self-reflection and the internalization of the concepts introduced. The author also points to open problems and possibilities for further research.
Probability Theory
This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author's 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: ProbabilitiesConditional Probabilities and IndependenceRandom Variables and Their DistributionOperations on Random VariablesExpected Value, Variance, and CovarianceNormally Distributed Random VectorsLimit Theorems Introduction to Stochastic ProcessesMathematical StatisticsAppendixBibliographyIndex
Practical Machine Learning with R
This textbook is a comprehensive guide to machine learning and artificial intelligence tailored for students in business and economics. It takes a hands-on approach to teach machine learning, emphasizing practical applications over complex mathematical concepts. Students are not required to have advanced mathematics knowledge such as matrix algebra or calculus.The author introduces machine learning algorithms, utilizing the widely used R language for statistical analysis. Each chapter includes examples, case studies, and interactive tutorials to enhance understanding. No prior programming knowledge is needed. The book leverages the tidymodels package, an extension of R, to streamline data processing and model workflows. This package simplifies commands, making the logic of algorithms more accessible by minimizing programming syntax hurdles. The use of tidymodels ensures a unified experience across various machine learning models.With interactive tutorials that students can download and follow along at their own pace, the book provides a practical approach to apply machine learning algorithms to real-world scenarios.In addition to the interactive tutorials, each chapter includes a Digital Resources section, offering links to articles, videos, data, and sample R code scripts. A companion website further enriches the learning and teaching experience: https: //ai.lange-analytics.com.This book is not just a textbook; it is a dynamic learning experience that empowers students and instructors alike with a practical and accessible approach to machine learning in business and economics. Key Features: Unlocks machine learning basics without advanced mathematics -- no calculus or matrix algebra required. Demonstrates each concept with R code and real-world data for a deep understanding -- no prior programming knowledge is needed. Bridges the gap between theory and real-world applications with hands-on interactive projects and tutorials in every chapter, guided with hints and solutions. Encourages continuous learning with chapter-specific online resources--video tutorials, R-scripts, blog posts, and an online community. Supports instructors through a companion website that includes customizable materials such as slides and syllabi to fit their specific course needs.
Linear Partial Differential and Difference Equations and Simultaneous Systems with Constant or Homogeneous Coefficients
Linear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology," which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass, and electricity; and their interactions. This is the third book of the volume.The book starts with six different methods of solution of linear partial differential equations (p.d.e.) with constant coefficients. One of the methods, namely characteristic polynomial, is then extended to a further five classes, including linear p.d.e. with homogeneous power coefficients and finite difference equations and simultaneous systems of both (simultaneous partial differential equations [s.p.d.e.] and simultaneous finite difference equations [s.f.d.e.]). The applications include detailed solutions of the most important p.d.e. in physics and engineering, including the Laplace, heat, diffusion, telegraph, bar, and beam equations. The free and forced solutions are considered together with boundary, initial, asymptotic, starting, and other conditions.The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical, and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.
Higher Special Functions
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaff矇, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
Math Mammoth The Four Operations (with a Touch of Algebra)
Math Mammoth The Four Operations (with a Touch of Algebra) is a mathematics worktext meant primarily for fifth and sixth grades. Being a worktext means that this book is a textbook and workbook together: the lessons include both the explanations of the concepts, as well as practice exercises.The main topics of this book are mental math strategies, simple equations and expressions, the order of operations, partial products, using all four operations in solving problems, and number patterns in the coordinate grid.Students encounter the exact definition of an equation and an expression. They practice the order of operations with problems that also reinforce the idea of the equal sign ("=") as denoting equality of the right and left sides of an equation. These kinds of exercises are needed because students may think that an equal sign signifies the act of finding the answer to a problem (such as 134 + 23 = ?), which is not so.Students solve simple equations with the help of a bar model. They also use the pan balance model to solve simple one and two-step equations and even some three-step equations.We review the thought of partial products (multiplying and dividing in parts), including how those partial products are seen in the multiplication algorithm, and how to use mental math to divide numbers in parts.Although the book is named "The Four Operations," the idea is not to practice each of the four operations separately, but rather to see how they are used together in solving problems and in simple equations. We are trying to develop the student's algebraic thinking, including the abilities to: translate problems into mathematical operations, comprehend the many operations needed to yield an answer to a problem, "undo" operations, and so on. Many of the ideas in this book are preparing students for algebra.The answers are appended.
Vector Calculus
A calculus book must tell the truth. This book is carefully written in the accepted language of mathematics in a readable exposition. It includes useful and fascinating applications, acquaints students with the history of the subject and offers a sense of what mathematics is all about.
Current topics in Logic and the Philosophy of Science. Papers from SILFS 2022 postgraduate conference
Logic and the Philosophy of Science are disciplines that avoid stopping and wandering around in circles on the same topics. Their role in dedicating themselves to scientific and applicative subjects always makes them extraordinarily fruitful and productive, in step with the developments of scientific and technological knowledge. The writings contained in this volume are proof of this. The set of research selected for this publication, starting from the 2022 Postgraduate Conference of SILFS (the Italian Society for Logic and the Philosophy of Science), testifies to a lively and rich knowledge widespread among young scholars of this area who combine pure logic and philosophy to the analysis of cutting-edge knowledge produced by current scientific and technological disciplines. The result is a kaleidoscope of research on updated logical and philosophical-scientific topics, which gives rise to promising developments on the part of young scholars who are contributing today to the logic and philosophy of science to create further perspectives in the future.
The Code of Mathematics
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 G繹del 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.
Bridging Gaps In Elementary Mathematics
Bridging Gaps in Elementary Mathematics is a Mathematics study supplement created to improve upon the appreciation and fundamental understanding of Mathematics by employing the "why" of Mathematics approach. It was also created to ensure that those who did not have an opportunity in their earlier years to study Mathematics, or those who did but need better understanding, would be able to "bridge" the gaps formed in their education. The material covers topics found in the curriculum at the Primary to the pre-Junior High School level. It is not intended to substitute for formally prescribed schooling study materials and textbooks. Still, it is a supplement that provides a more profound understanding, real-life applications and different perspectives of the universal elements of the Mathematics curriculum. It effectively approaches the subject from the root to help make it less abstract.
Inverse Gravity Cosmology
The book is about the inverse gravity cosmology hypothesis which is based on three of the author's published papers which past peer review. Hence, the book presents the inverse gravity concept, its mathematical structure, and its incorporation to established and proven aspects of physics. New developments and mathematics of the theoretical concept are expressed. Moreover, the book cites mistakes/deficiencies and omissions in previous publications. Lastly, the book's introduction includes information about the author's background that inspired the inception of the theoretical concept.
Mathematical Puzzles
Research in maths is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing maths. This book makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.
Topics in Model Theory
This book has two chapters. The first is a modern or contemporary account of stability theory. A focus is on the local (formula-by-formula) theory, treated a little differently from in the author's book Geometric Stability Theory. There is also a survey of general and geometric stability theory, as well as applications to combinatorics (stable regularity lemma) using pseudofinite methods.The second is an introduction to 'continuous logic' or 'continuous model theory, ' drawing on the main texts and papers, but with an independent point of view. This chapter includes some historical background, including some other formalisms for continuous logic and a discussion of hyperimaginaries in classical first order logic.These chapters are based around notes, written by students, from a couple of advanced graduate courses in the University of Notre Dame, in Autumn 2018, and Spring 2021.
Model-Based Monitoring and Statistical Control
Available in English for the first time, this classic and influential book by the late Kohei Otshu presents real examples of ships in motion under irregular ocean waves, helping to expalin fluctuations of stochastic phenomena through spectral analysis methods and statistical modeling.
Topics in Model Theory
This book has two chapters. The first is a modern or contemporary account of stability theory. A focus is on the local (formula-by-formula) theory, treated a little differently from in the author's book Geometric Stability Theory. There is also a survey of general and geometric stability theory, as well as applications to combinatorics (stable regularity lemma) using pseudofinite methods.The second is an introduction to 'continuous logic' or 'continuous model theory, ' drawing on the main texts and papers, but with an independent point of view. This chapter includes some historical background, including some other formalisms for continuous logic and a discussion of hyperimaginaries in classical first order logic.These chapters are based around notes, written by students, from a couple of advanced graduate courses in the University of Notre Dame, in Autumn 2018, and Spring 2021.
Causal Inference in Pharmaceutical Statistics
Causal Inference in Pharmaceutical Statistics introduces the basic concepts and fundamental methods of causal inference relevant to pharmaceutical statistics. This book covers causal thinking for different types of commonly used study designs in the pharmaceutical industry, including but not limited to randomized controlled clinical trials, longitudinal studies, singlearm clinical trials with external controls, and real-world evidence studies. The book starts with the central questions in drug development and licensing, takes the reader through the basic concepts and methods via different study types and through different stages, and concludes with a roadmap to conduct causal inference in clinical studies. The book is intended for clinical statisticians and epidemiologists working in the pharmaceutical industry. It will also be useful to graduate students in statistics, biostatistics, and data science looking to pursue a career in the pharmaceutical industry.Key Features: Causal inference book for clinical statisticians in the pharmaceutical industry Introductory level on the most important concepts and methods Align with FDA and ICH guidance documents Across different stages of clinical studies: plan, design, conduct, analysis, and interpretation Cover a variety of commonly used study designs
Risk Revealed
Explore the concept of risk through numerous examples and their statistical modeling, traveling from a historical perspective all the way to an up-to-date technical analysis. Written with a wide readership in mind, this book begins with accounts of a selection of major historical disasters, such as the North Sea flood of 1953 and the L'Aquila earthquake. These tales serve to set the scene and to motivate the second part of the book, which describes the mathematical tools required to analyze these events, and how to use them. The focus is on the basic understanding of the mathematical modeling of risk and what types of questions the methods allow one to answer. The text offers a bridge between the world of science and that of everyday experience. It is written to be accessible to readers with only a basic background in mathematics and statistics. Even the more technical discussions are interspersed with historical comments and plentiful examples.
Ordinal Data Analysis
This book is a step-by-step data story for analysing ordinal data from start to finish. The book is for researchers, statisticians and scientists who are working with data sets where the response is ordinal. This type of data is common in many disciplines, not just in surveys.
Partitions, Objective Indefiniteness, and Quantum Reality
This book presents a new 'partitional' approach to understanding or interpreting the math of standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, conversely, the math of partitions is a skeletonized set level version of the math of QM. Since at the set level, partitions are the mathematical tool to represent distinctions and indistinctions (or definiteness and indefiniteness), this approach shows how to interpret the key non-classical QM notion of superposition in terms of (objective) indefiniteness between definite alternatives (as opposed to seeing it as the sum of 'waves'). Thus, the book develops a new mathematical, or indeed, logical, approach to the century-old problem of interpreting quantum mechanics, ensure it is of interest to philosophers of science as well as mathematicians and physicists.
The Polls Weren't Wrong
This book will equip readers with the tools to navigate the mismatch of expectations. It is not intended to replace more technical applications of statistics but is accessible to those interested in learning about how poll data should be understood.
Integrated Computer Technologies in Mechanical Engineering - Synergetic Engineering
The best works were selected after the conference "Integrated Computer Technologies in Mechanical Engineering"-Synergetic Engineering (ICTM). The conference provided technical exchange between the scientific community in the form of keynote addresses, panel discussions, and a special session. In addition, participants were treated to a series of techniques that facilitated collaboration among fellow researchers. Moreover, ICTM 2021 received 110 applications from different countries.
Math Mammoth Factors & Factoring
Math Mammoth Factors & Factoring is a worktext that covers typical number theory topics for upper elementary school: divisibility rules, finding factors of a given number, prime numbers, prime factorization, the greatest common factor, and the least common multiple. These topics are usually covered in grades 4-6.The book begins with 4th grade topics, starting out with the concept of divisibility and the common divisibility rules. The lesson Prime Numbers brings out the concept of a prime number as one that is only divisible by 1 and by itself. Armed with the knowledge about divisibility, students now learn how to find factors of a given two-digit number in the lesson Finding Factors.The following lesson, Primes and Finding Factors, is a review lesson about factors, primes, and divisibility rules, originally intended for beginning of 5th grade. You can use it as a review of the first four lessons of this book, or for students that have some knowledge of these topics already.The next two lessons delve into prime factorization using a factor tree. The first lesson on the topic only uses two-digit numbers. In the latter, students are introduced the sieve of Eratosthenes and they factorize three-digit and larger numbers.The last topics in the book are the greatest common factor (GCF), the least common multiple (LCM), and factoring sums, intended mainly for 6th grade. Factoring sums means writing a sum such as 42 + 18 as 6(7 + 3). We first find a common factor of 42 and 18 (which is 6), and use that to factorize the sum. The lesson only deals with numeric examples, but it is actually preparing students for algebra, where the same process is done with variables; for example x2 + 2x is factored as x(x + 2).The book ends in a review lesson. Answers are appended.
Nonparametric Statistical Methods Using R
This thoroughly updated and expanded second edition covers traditional nonparametric methods and rank-based analyses. Two new chapters covering multivariate analyses and big data have been added. Core classical nonparametrics chapters on one- and two-sample problems have been expanded
Integrated Computer Technologies in Mechanical Engineering - Synergetic Engineering Ⅱ
The best works were selected after the conference titled "Integrated Computer Technologies in Mechanical Engineering"-Synergetic Engineering (ICTM) II. The conference provided technical exchange between the scientific community in the form of keynote addresses, panel discussions, and a special session. In addition, participants were treated to a series of techniques that facilitated collaboration among fellow researchers. Moreover, ICTM 2021 received 110 applications from different countries.
Math Mammoth Division 2
Math Mammoth Division 2 is a continuation from the Math Mammoth Division 1. It focuses on the topics of long division, remainder, problem solving, average, divisibility, and factors. The book is most suitable for fourth grade.We start out by reviewing basic division facts by single-digit numbers (such as 24 繩 4 or 56 繩 7). After that, we study terminology of division and dividing numbers by whole tens and hundreds (such as 400 繩 20). Next students practice the order of operations-this time with division as one of the operations.Then we study the concept of remainder, preparing students for the upcoming lessons on long division. At first, the concept of remainder is presented visually. Soon, students solve simple division problems with a remainder, written with the long division symbol (or long division "corner", as I like to call it).Next comes a set of lessons intended to teach long division in several small steps. We start with divisions where each of the digits in the dividend (thousands, hundreds, tens, and ones) can be divided evenly by the divisor (for example, 3096 繩 3). As the next step, there is a remainder in the ones. Then, the divisions have a remainder in the tens. Finally, there is a remainder in the hundreds and in the thousands, and this completes the step-by-step learning process for long division. The lessons also include lots of word problems to solve.After long division, we study the concept of average, which is a nice application of division, and problems that involve finding a fractional part of a quantity using division. For example, we can find 3/4 of a number by first finding 1/4 (dividing by 4) and then multiplying the result by 3. Students get help from visual bar models to solve the problems.The last section deals with elementary number theory. We study basic divisibility rules (though not all of them), prime numbers, and finding all factors of a given two-digit number.
Nonlinear Second Order Elliptic Equations
This book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions.While not all-encompassing, these topics represent major approaches to the theory of partial differential equations and systems, and should be of significant interest to graduate students and researchers. Two appendices have been included to provide a good gauge of the prerequisites for this book and make it reasonably self-contained.A notable strength of the book is that it contains a large number of substantial examples. Exercises for the reader are also included. Therefore, this book is suitable as a textbook for graduate students who havealready had an introductory course on PDE and some familiarity with functional analysis and nonlinear functional analysis, and as a reference for researchers.
Fundamentals of Order and Rank Statistics
This book is devoted to the fundamentals of order and rank statistics. Primarily focusing on theoretical properties, it also discusses practical aspects, including interesting applications of step and impulse functions for the distribution of random variables, magnitudes, and signs. New concepts are introduced, such as independent and semi-identically distributed random vectors and probability density-mass functions. This book also presents an investigation of relative magnitudes in order statistics, and of correlation coefficients among signs, ranks, and magnitudes. The basic concepts are described in clear terms, and step-by-step details are provided for most of the presented mathematical results. The exposition is accompanied by numerous examples and more than 100 exercises, for which a complete solution manual is available. Providing a useful reference, and requiring only a basic understanding of probability and random variables, the book will appeal to a wide readership.
Introduction to the Geometrical Foundations of General Relativity
This book is intended for physics students (undergraduate/transition to graduate) who want to prepare for lectures on general relativity. Some knowledge of linear algebra and analysis are required. This textbook starts with basic topics such as vector space and vectors (chapter 1), dual space and covectors (chapter 2), tensors (chapter 3), etc.. Great importance is always attached to the clarity of the explanations and derivations of the topics. 31 figures support these intentions. General relativity is in its deeper sense a geometric theory. Therefore, the emphasis in this textbook has been placed on understanding space in its geometric configuration. Space is a component of the representation of the physical real. And it is thus the stage on which the physical processes and procedures show themselves. Calculation tasks have been deliberately omitted. The focus is on understanding a topic. For this purpose, many examples and detailed extra introductions have been made. For exercises, there are enough examples in the relevant textbooks that can be used to deepen a topic. This book serves as a good basis for mastering tasks. If you have studied the book thoroughly, you will be prepared to start working on the physics of gravitation as described by general relativity.
Recent Trends in AI Enabled Technologies
This book constitutes the refereed proceedings of the First International Conference on Recent Trends in AI Enabled Technologies, ThinkAI 2023, which took place in Hyderabad, India, in December 2023. The 7 full papers presented in these proceedings were carefully reviewed and selected from 51 submissions. The conference focuses on on up to date topics and recent trends in artificial intelligence and related technologies.
The Power of Probability
"The Power of Probability: Making Sense of Uncertainty" is a comprehensive exploration of probability theory and probabilistic reasoning. From its historical origins to its practical applications in diverse domains, the book delves into the fundamental concepts, methodologies, and implications of understanding uncertainty. Through engaging discussions and practical examples, readers are empowered to embrace probabilistic thinking, make informed decisions, and navigate complexities in an uncertain world.
From Concepts to Code
The breadth of problems that can be solved with data science is astonishing, and this book provides the required tools and skills to a broad audience. The necessary background in computer science, mathematics, and statistics is provided in an approachable manner.
Math-Ish
From Stanford professor, author of Limitless Mind, youcubed.org founder, and leading expert in the field of mathematics education Jo Boaler comes a groundbreaking guide to finding joy and understanding by adopting a diverse approach to learning math."Every once in a while, someone revolutionizes an approach to a difficult subject and changes it forever. That is what Jo Boaler has done for math. Fresh, smart, and inclusive, Jo Boaler's strategy eschews the one-size-fits-a-few approach and instead allows math to be seen and solved by everyone. A huge achievement. Math-ish is the only math book I've ever enjoyed reading in my entire life. Honestly." -Bonnie Garmus, author of Lessons in ChemistryMathematics is a fundamental part of life, yet every one of us has a unique relationship with learning and understanding the subject. Working with numbers may inspire confidence in our abilities or provoke anxiety and trepidation. Stanford researcher, mathematics education professor, and the leading expert on math learning Dr. Jo Boaler argues that our differences are the key to unlocking our greatest mathematics potential.In Math-ish, Boaler shares new neuroscientific research on how embracing the concept of "math-ish"--a theory of mathematics as it exists in the real world--changes the way we think about mathematics, data, and ourselves. When we can see the value of diversity among people and multi-faceted approaches to learning math, we are free to truly flourish. Utilizing the latest research on math education, Jo guides us through seven principles that can radically reframe our relationship with the subject: - The power of mindset on learning- Utilizing a visual approach to math- The impact of physical movement and communication on understanding- Understanding the value of an "ish" perspective - in mathematics and beyond- The importance of connected and flexible knowledge- New data on diverse teaching modes that work with different learning styles, not against them- The value of diversity in learning mathematics--and beyondWhen mathematics is approached more broadly, inclusively, and with a greater sense of wonder and play--when we value the different ways people see, approach, and understand it--we empower ourselves and gain a beneficial understanding of its value in our lives.
Dynamic Network Flows with Adaptive Route Choice Based on Current Information
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.
Mathematical Structures
This textbook is intended to be accessible to any second-year undergraduate in mathematics who has attended courses on basic real analysis and linear algebra. It is meant to help students to appreciate the diverse specialized mathematics courses offered at their universities. Special emphasis is on similarities between mathematical fields and ways to compare them. The organizing principle is the concept of a mathematical structure which plays an important role in all areas of mathematics. The mathematical content used to explain the structural ideas covers in particular material that is typically taught in algebra and geometry courses. The discussion of ways to compare mathematical fields also provides introductions to categories and sheaves, whose ever-increasing role in modern mathematics suggests a more prominent role in teaching. The book is the English translation of the second edition of "Mathematische Strukturen" (Springer, 2024) written in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Math Mammoth Multiplication 2
Math Mammoth Multiplication 2 is a worktext focusing on multi-digit multiplication and related topics. It best suits fourth grade mathematics.The first lessons briefly review the concept of multiplication and the multiplication tables. Next, students encounter equations in disguise - presented with shapes on both sides of a pan balance - in the lesson Scales Puzzles. This lesson is intended to be fun and motivational.Then, the focus shifts to multi-digit multiplication (also called multiplication algorithm or multiplying in columns). We start out by learning to multiply numbers by multiples of ten and hundred (for example, 20 ? 4 or 500 ? 6). After this is mastered, students learn the very important concept of multiplying in parts, or partial products. This means that, for example, we multiply 4 ? 63 in two parts: first we multiply 4 ? 60 = 240 and 4 ? 3 = 12, and lastly the results are added: 240 + 12 = 252.This principle underlies all other multiplication algorithms, so it is important to master. We don't want children to "blindly" memorize the multiplication algorithm without understanding what is going on with it. The partial products algorithm (multiplying in parts) also ties in with an area model, and it is very important that students see the connection between this visual model and the procedure.The book contains two lessons about multiplying in columns the "easy way". This "easy way" is a simplified form of the traditional multiplication algorithm, based on partial products. You may skip these two lessons at your discretion. The method taught in those lessons is most useful for students who may have trouble with the traditional form of the algorithm. This method is also helpful in cementing the student's understanding of the partial products method.The traditional, or standard, form of multiplication algorithm is taught next, and is hopefully fairly easy, with the partial products as a foundation.Students also study estimation, the order of operations, and multiplying with money. There are numerous word problems in all of the lessons. Students are encouraged to write number sentences for the word problems-essentially learning to show their work and their thinking process.The lesson So Many of the Same Thing has to do with proportional reasoning. The idea is really simple, and prepares students for learning ratios and proportions in middle school.The last major topic in the book is multiplying two-digit numbers by two-digit numbers. Again, we first study partial products and tie that in with an area model. The lesson Multiplying in Parts: Another Way is optional. Lastly, the book teaches the standard algorithm for two-digit by two-digit multiplication. Students will practice multiplication with more digits in the book Mammoth Multiplication & Division 3.
Combinatorics Problems and Solutions
This book will help you learn combinatorics in the most effective way possible - through problem solving. It contains 263 combinatorics problems with detailed solutions. Combinatorics is the part of mathematics that involves counting. It is therefore an essential part of anyone's mathematical toolkit. The applications of combinatorics include probability, cryptography, error correcting, games, music and visual art. In this new edition we have expanded the introductory section by more than twice the original size, and the number of problems has grown by over 30%. There are new sections on the pigeon hole principle and integer partitions with accompanying problems. Many of the new problems are application oriented. There are also new combinatorial geometry problems. Someone with no prior exposure to combinatorics will find enough introductory material to quickly get a grasp of what combinatorics is all about and acquire the confidence to start tackling problems.
