Oblique Derivative Problems for Elliptic Equations in Conical Domains
The aim of our book is the investigation of the behavior of strong and weak solutions to the regular oblique derivative problems for second order elliptic equations, linear and quasi-linear, in the neighborhood of the boundary singularities. The main goal is to establish the precise exponent of the solution decrease rate and under the best possible conditions. The question on the behavior of solutions of elliptic boundary value problems near boundary singularities is of great importance for its many applications, e.g., in hydrodynamics, aerodynamics, fracture mechanics, in the geodesy etc. Only few works are devoted to the regular oblique derivative problems for second order elliptic equations in non-smooth domains. All results are given with complete proofs. The monograph will be of interest to graduate students and specialists in elliptic boundary value problems and their applications.
Statistical Inference Based on Kernel Distribution Function Estimators
This book presents a study of statistical inferences based on the kernel-type estimators of distribution functions. The inferences involve matters such as quantile estimation, nonparametric tests, and mean residual life expectation, to name just some. Convergence rates for the kernel estimators of density functions are slower than ordinary parametric estimators, which have root-n consistency. If the appropriate kernel function is used, the kernel estimators of the distribution functions recover the root-n consistency, and the inferences based on kernel distribution estimators have root-n consistency. Further, the kernel-type estimator produces smooth estimation results. The estimators based on the empirical distribution function have discrete distribution, and the normal approximation cannot be improved--that is, the validity of the Edgeworth expansion cannot be proved. If the support of the population density function is bounded, there is a boundary problem, namely the estimator does not have consistency near the boundary. The book also contains a study of the mean squared errors of the estimators and the Edgeworth expansion for quantile estimators.
Measurement Uncertainty
This reprint focuses on a very important topic in metrology, which is represent by measurement uncertainty. Any good metrologist or scientist in engineering knows that no measurement makes sense without an associated uncertainty value: without an uncertainty value, no decision can be taken; no comparisons can be made; no conformity can be assessed. Any decision, comparison or conformity assessment made without considering the measurement uncertainty affecting the measurement value is completely useless and meaningless. Stated that, it becomes very clear that uncertainty in measurement plays indeed a very important rule in our everyday life. This is the reason why there is a great need to have a fruitful academic and scientific discussion on this topic.We have been speaking about measurement uncertainty for less than 30 years, since the concept of "measurement uncertainty" has been introduced in 1995 by the "Guide to the expression of uncertainty in measurement" (GUM). Thirty years seems to be many, but still the concept of measurement uncertainty has not been spread worldwide and the GUM is a document that is not known everywhere. On the other hand, this document should be considered not only in academic scenario, but also in any technical and industrial scenario, where it is pivotal to know the meaning of measurement uncertainty, identify the uncertainty contributions and know how these contributions affect the final measurement result.
Numerical Methods Fundamentals
The book is designed to cover all major aspects of applied numerical methods, including numerical computations, solution of algebraic and transcendental equations, finite differences and interpolation, curve fitting, correlation and regression, numerical differentiation and integration, matrices and linear system of equations, numerical solution of ordinary differential equations, and numerical solution of partial differential equations. It uses a numerical problem-solving orientation with numerous examples, figures, and end of chapter exercises. Presentations are limited to very basic topics to serve as an introduction to more advanced topics.
An Introduction to Bond Graph Modeling with Applications
An Introduction to Bond Graph Modeling with Applications presents a collection of exercises on dynamical systems, modeling and control for university students in the areas of engineering, physics and applied mathematics. We can find several books on bond graphs, but most merely a small set of exercises and, in a few cases, some commands for computer packages like MATLAB or Mathematica. It is difficult to find books with a broad set of solved exercises and proposed exercises with solutions, guiding researchers starting their work with bond graphs, or students who are just beginning their study of the topic. This book aims to fill that gap, and provide a comprehensive, reader-friendly introduction to the Bond Graph modeling tool. Features Gives in-depth theoretical background coupled with practical, hands-on instructions. Provides a clear pedagogical framework, with numerous exercises and problems. Suitable for students and researchers who work with bond graphs: principally such as applied mathematicians, physicist and engineers.
An Introduction to R and Python for Data Analysis
An Introduction to R and Python for Data Analysis helps teach students to code in both R and Python simultaneously. As both R and Python can be used in similar manners, it is useful and efficient to learn both at the same time, helping lecturers and students to teach and learn more and save time.
An Introduction to Numerical Methods
An Introduction to Numerical Methods: A MATLAB(R) Approach, Fifth Edition continues to offer readers an accessible and practical introduction to numerical analysis. It presents a wide range of algorithms for scientific and engineering applications, using MATLAB to illustrate each numerical method.
Stochastic Differential Equations for Science and Engineering
The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while also discussing applications to estimation, stability analysis, and control. The book includes numerous examples and challenging exercises.
Game Theory: A Nontechnical Introduction to the Analysis of Strategy (Fourth Edition)
As with the previous editions, this fourth edition relies on teaching by example and the Karplus Learning Cycle to convey the ideas of game theory in a way that is approachable, intuitive, and interdisciplinary. Noncooperative equilibrium concepts such as Nash equilibrium, mixed strategy equilibria, and subgame perfect equilibrium are systematically introduced in the first half of the book. Bayesian Nash equilibrium is briefly introduced. The subsequent chapters discuss cooperative solutions with and without side payments, rationalizable strategies and correlated equilibria, and applications to elections, social mechanism design, and larger-scale games. New examples include panic buying, supply-chain shifts in the pandemic, and global warming.
A Journey Into the World of Exponential Functions
This book illustrates why abstract mathematical entities are needed to represent some aspects of physical reality. It provides an overview of different types of numbers and functions along with their historical background and applications.
Intermittent Convex Integration for the 3D Euler Equations
A new threshold for the existence of weak solutions to the incompressible Euler equations To gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions with intermittency, which are necessary for the construction of dissipative weak solutions for the Navier-Stokes equations. In this book, weak solutions to the 3D Euler equations are constructed for the first time with both non-negligible regularity and intermittency. These solutions enjoy a spatial regularity index in L^2 that can be taken as close as desired to 1/2, thus lying at the threshold of all known convex integration methods. This property matches the measured intermittent nature of turbulent flows. The construction of such solutions requires technology specifically adapted to the inhomogeneities inherent in intermittent solutions. The main technical contribution of this book is to develop convex integration techniques at the local rather than global level. This localization procedure functions as an ad hoc wavelet decomposition of the solution, carrying information about position, amplitude, and frequency in both Lagrangian and Eulerian coordinates.
More (Almost) Impossible Integrals, Sums, and Series
This book, the much-anticipated sequel to (Almost) Impossible, Integrals, Sums, and Series, presents a whole new collection of challenging problems and solutions that are not commonly found in classical textbooks. As in the author's previous book, these fascinating mathematical problems are shown in new and engaging ways, and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Classical problems are shown in a fresh light, with new, surprising or unconventional ways of obtaining the desired results devised by the author. This book is accessible to readers with a good knowledge of calculus, from undergraduate students to researchers. It will appeal to all mathematical puzzlers who love a good integral or series and aren't afraid of a challenge.
Chaos, Complexity, and Nonlinear Economic Theory
What do economic chaos and uncertainties mean in rational or irrational economic theories? How do simple deterministic interactions among a few variables lead to unpredictable complex phenomena? Why is complexity of economies causing so many conflicts and confusions worldwide?This book provides a comprehensive introduction to recent developments of complexity theory in economics. It presents different models based on well-accepted economic mechanisms such as the Solow model, Ramsey model, and Lucas model. It is focused on presenting complex behaviors, such as business cycles, aperiodic motion, bifurcations, catastrophes, chaos, and hidden attractors, in basic economic models with nonlinear behavior. It shows how complex nonlinear phenomena are identified from various economic mechanisms and theories. These models demonstrate that the traditional or dominant economic views on evolution of, for instance, capitalism market, free competition, or Keynesian economics, are not generally valid. Markets are unpredictable and nobody knows with certainty the consequences of policies or other external factors in economic systems with simple interactions.
Guide to Advanced Statistical Analysis in R
Features- Worked examples- Clear programming code, usable by R novices- Without mathematical formulae- structural equation modeling- survival analysis- longitudinal analysis- multivariate analysis- GLM, Poisson regression, multilevel modeling- power analysis, reliability- Further reading recommendations in each chapter- Data sets on the website
Guide to Advanced Statistical Analysis in R
Features- Worked examples- Clear programming code, usable by R novices- Without mathematical formulae- structural equation modeling- survival analysis- longitudinal analysis- multivariate analysis- GLM, Poisson regression, multilevel modeling- power analysis, reliability- Further reading recommendations in each chapter- Data sets on the website
Multidimensional Stationary Time Series
This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction.
Statistical Testing with jamovi Sport
FeaturesWorked examples from sportClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Foundations of Quantitative Finance
Published under the collective title of Foundations of Quantitative Finance, this set of ten books presents the advanced mathematics finance professionals need to advance their careers. These books develop the theory most do not learn in Graduate Finance programs, or in most Financial Mathematics undergraduate and graduate courses.
Statistical Testing with jamovi Sport
Features Worked examples from sportClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Corruption, Infrastructure Management and Public-Private Partnership
Public-Private Partnerships (PPP or 3Ps) allow the public sector to seek alternative funding and expertise from the private sector during procurement processes. Such partnerships, if executed with due diligence, often benefit the public immensely. Unfortunately, Public-Private Partnerships can be vulnerable to corruption. This book looks at what measures we can put in place to check corruption during procurement and what good governance strategies the public sector can adopt to improve the performance of 3Ps.The book applies mathematical models to analyze 3Ps. It uses game theory to study the interaction and dynamics between the stakeholders and suggests strategies to reduce corruption risks in various 3Ps stages. The authors explain through game theory-based simulation how governments can adopt a evaluating process at the start of each procurement to weed out undesirable private partners and why the government should take a more proactive approach.Using a methodological framework rooted in mathematical models to illustrate how we can combat institutional corruption, this book is a helpful reference for anyone interested in public policymaking and public infrastructure management.
Forecasting and Analytics with the Augmented Dynamic Adaptive Model (Adam)
Forecasting and Analytics with ADAM focuses on a time series model in Single Source of Error state space form, called "ADAM" (Augmented Dynamic Adaptive Model). The book demonstrates a holistic view to forecasting and time series analysis using dynamic models to solve real life problems.
Statistical Testing with jamovi Health
FeaturesWorked examples from health settingsClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Statistical Testing with jamovi Health
FeaturesWorked examples from health settingsClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Applied Functional Analysis
This textbook offers a concise and thorough introduction to the topic of applied functional analysis. Targeted to graduate students of mathematics, it presents standard topics in a self-contained and accessible manner. Featuring approximately 300 problems sets to aid in understanding the content, this text serves as an ideal resource for independent study or as a textbook for classroom use. With its comprehensive coverage and reader-friendly approach, it is equally beneficial for both students and teachers seeking a detailed and in-depth understanding of the subject matter.
Near Extensions and Alignment of Data in R^n
Near Extensions and Alignment of Data in Rn Comprehensive resource illustrating the mathematical richness of Whitney Extension Problems, enabling readers to develop new insights, tools, and mathematical techniques Near Extensions and Alignment of Data in Rn demonstrates a range of hitherto unknown connections between current research problems in engineering, mathematics, and data science, exploring the mathematical richness of near Whitney Extension Problems, and presenting a new nexus of applied, pure and computational harmonic analysis, approximation theory, data science, and real algebraic geometry. For example, the book uncovers connections between near Whitney Extension Problems and the problem of alignment of data in Euclidean space, an area of considerable interest in computer vision. Written by a highly qualified author, Near Extensions and Alignment of Data in Rn includes information on: Areas of mathematics and statistics, such as harmonic analysis, functional analysis, and approximation theory, that have driven significant advances in the field Development of algorithms to enable the processing and analysis of huge amounts of data and data sets Why and how the mathematical underpinning of many current data science tools needs to be better developed to be useful New insights, potential tools, and mathematical techniques to solve problems in Whitney extensions, signal processing, shortest paths, clustering, computer vision, optimal transport, manifold learning, minimal energy, and equidistribution Providing comprehensive coverage of several subjects, Near Extensions and Alignment of Data in Rn is an essential resource for mathematicians, applied mathematicians, and engineers working on problems related to data science, signal processing, computer vision, manifold learning, and optimal transport.
Statistical Testing with jamovi Criminology
FeaturesWorked examples from CriminologyClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Advanced Topics in Fractional Differential Equations
This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers' understanding of the concepts presented. Includes illustrations in order to support readers understanding of the presented concepts - Approaches the topic of fractional differential equations while employing fixed point theorems as tools - Presents novel results, which build upon previous literature and many years of research by the authors
Twisted Isospectrality, Homological Wideness, and Isometry
The question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics. This book focusses on the case of compact Riemannian manifolds, and, in particular, the question whether one can find finitely many natural operators that determine whether two such manifolds are isometric (coverings).The methods outlined in the book fit into the tradition of the famous work of Sunada on the construction of isospectral, non-isometric manifolds, and thus do not focus on analytic techniques, but rather on algebraic methods: in particular, the analogy with constructions in number theory, methods from representation theory, and from algebraic topology.The main goal of the book is to present the construction of finitely many "twisted" Laplace operators whose spectrum determines covering equivalence of two Riemannian manifolds.The book has a leisure pace and presents details and examples that are hard to find in the literature, concerning: fiber products of manifolds and orbifolds, the distinction between the spectrum and the spectral zeta function for general operators, strong isospectrality, twisted Laplacians, the action of isometry groups on homology groups, monomial structures on group representations, geometric and group-theoretical realisation of coverings with wreath products as covering groups, and "class field theory" for manifolds. The book contains a wealth of worked examples and open problems. After perusing the book, the reader will have a comfortable working knowledge of the algebraic approach to isospectrality. This is an open access book.
On the Synthesis of the Distribution amongst the Integers of the Prime Number Counting Function, pi(k), viewed as a Geometric Object
Academic Paper from the year 2023 in the subject Mathematics - Analysis, grade: 2.00, language: English, abstract: A method is devised in which the prime number counting function, pi(k) is viewed as having the properties of a staircase. The terminology appropriate to a staircase is used to describe the parts of the distribution amongst the integers. Strings of limited extent of consecutive numbers which may contain prime numbers are generated from an iterative equation which contains Gauss' prime number counting function. In honour of Gauss we call these strings of numbers, Gauss strings., and they are used in the construction of the staircase. Further, we show that the prime number counting function may be represented in number space by an infinite set of connected trapezia, the individual areas of which are numerically equal to the gap between the primes that are situated on two of the borders of any given trapezium.
A Topology of Mind
This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication. It examines mathematics in mind from the perspective of the spiral, cyclic and hyperlinked structures of the human mind in terms of its language, its thoughts and its various modes of communication in science, philosophy, literature and the arts including a chapter devoted to the spiral structure of the thought of Marshall McLuhan. In it, the authors examine the topological structures of hypertext, hyperlinking, and hypermedia made possible by the Internet and the hyperlinked structures that existed before its emergence. It also explores the cognitive origins of mathematical thinking of the human mind and its relation to the emergence of spoken language, and studies the emergence of mathematical notation and its impact on education. Topics addressed include: -The historical context of any topic that involves how mathematical thinking emerged, focusing on archaeological and philological evidence. - Connection between math cognition and symbolism, annotation and other semiotic processes. - Interrelationships between mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution. - Whether mathematics is an innate faculty or forged in cultural-historical context- What, if any, structures are shared between mathematics and language
Roc Analysis for Classification and Prediction in Practice
This book will present a unified and up-to date introduction to ROC methodologies, covering both diagnosis (classification) and prediction. The book will emphasize the practical implementation of these methods using standard statistical software such as R and STATA.
Sparse Polynomial Optimization
Many applications, including computer vision, computer arithmetic, deep learning, entanglement in quantum information, graph theory and energy networks, can be successfully tackled within the framework of polynomial optimization, an emerging field with growing research efforts in the last two decades. One key advantage of these techniques is their ability to model a wide range of problems using optimization formulations. Polynomial optimization heavily relies on the moment-sums of squares (moment-SOS) approach proposed by Lasserre, which provides certificates for positive polynomials. On the practical side, however, there is 'no free lunch' and such optimization methods usually encompass severe scalability issues. Fortunately, for many applications, including the ones formerly mentioned, we can look at the problem in the eyes and exploit the inherent data structure arising from the cost and constraints describing the problem.This book presents several research efforts to resolve this scientific challenge with important computational implications. It provides the development of alternative optimization schemes that scale well in terms of computational complexity, at least in some identified class of problems. It also features a unified modeling framework to handle a wide range of applications involving both commutative and noncommutative variables, and to solve concretely large-scale instances. Readers will find a practical section dedicated to the use of available open-source software libraries.This interdisciplinary monograph is essential reading for students, researchers and professionals interested in solving optimization problems with polynomial input data.
Learning Pandas 2.0
Mastering Data Wrangling and Analysis for Modern Data Science"Learning Pandas 2.0" is an essential guide for anyone looking to harness the power of Python's premier data manipulation library. With this comprehensive resource, you will not only master core Pandas 2.0 concepts but also learn how to employ its advanced features to perform efficient data manipulation and analysis.Throughout the book, you will acquire a deep understanding of Pandas 2.0's data structures, indexing, and selection techniques. Gain expertise in loading, storing, and cleaning data from various file formats and sources, ensuring data integrity and consistency. As you progress, you will delve into advanced data transformation, merging, and aggregation methods to extract meaningful insights and generate insightful reports."Learning Pandas 2.0" also covers specialized data processing needs like time series data, DateTime operations, and geospatial analysis. Furthermore, this book demonstrates how to integrate Pandas 2.0 with machine learning libraries like Scikit-learn, TensorFlow, and PyTorch for predictive analytics. This will empower you to build powerful data-driven models to solve complex problems and enhance your decision-making capabilities.What sets "Learning Pandas 2.0" apart from other books is its focus on numerous practical examples, allowing you to apply your newly acquired skills to tricky scenarios. By the end of this book, you will have the confidence and knowledge needed to perform efficient and robust data analysis using Pandas 2.0, setting you on the path to becoming a data analysis powerhouse.Key LearningsMaster core Pandas 2.0 concepts, including data structures, indexing, and selection for efficient data manipulation.Load, store, and clean data from various file formats and sources, ensuring data integrity and consistency.Perform advanced data transformation, merging, and aggregation techniques for insightful analysis and reporting.Harness time series data, DateTime operations, and geospatial analysis for specialized data processing needs.Visualize data effectively using Seaborn, Plotly, and advanced geospatial visualization tools.Integrate Pandas 2.0 with machine learning libraries like Scikit-learn, TensorFlow, and PyTorch for predictive analytics.Table of ContentIntroduction to Pandas 2.0Data Read, Storage, and File FormatsIndexing and Selecting DataData Manipulation and TransformationTime Series and DateTime OperationsPerformance Optimization and ScalingMachine Learning with Pandas 2.0Text Data and Natural Language ProcessingGeospatial Data AnalysisAudienceWhether you're a seasoned data professional or just starting your journey in data science, "Learning Pandas 2.0" is the perfect resource to help you harness the power of this cutting-edge library. This book is an absolute resource for implementing Pandas 2.0 in every possible data manipulation and analysis project.
Applied Probability
This textbook presents the basics of probability and statistical estimation, with a view to applications. The didactic presentation follows a path of increasing complexity with a constant concern for pedagogy, from the most classical formulas of probability theory to the asymptotics of independent random sequences and an introduction to inferential statistics. The necessary basics on measure theory are included to ensure the book is self-contained. Illustrations are provided from many applied fields, including information theory and reliability theory. Numerous examples and exercises in each chapter, all with solutions, add to the main content of the book.Written in an accessible yet rigorous style, the book is addressed to advanced undergraduate students in mathematics and graduate students in applied mathematics and statistics. It will also appeal to students and researchers in other disciplines, including computer science, engineering, biology, physics and economics, who are interested in a pragmatic introduction to the probability modeling of random phenomena.
Wavelet Analysis
Wavelet Analysis: Basic Concepts and Applications provides a basic and self-contained introduction to the ideas underpinning wavelet theory and its diverse applications. This book is suitable for master's or PhD students, senior researchers, or scientists working in industrial settings, where wavelets are used to model real-world phenomena and data needs (such as finance, medicine, engineering, transport, images, signals, etc.). Features: Offers a self-contained discussion of wavelet theory Suitable for a wide audience of post-graduate students, researchers, practitioners, and theorists Provides researchers with detailed proofs Provides guides for readers to help them understand and practice wavelet analysis in different areas
Counterexamples in Operator Theory
This text is the first of its kind exclusively devoted to counterexamples in operator theory and includes over 500 problems on bounded and unbounded linear operators in Hilbert spaces. This volume is geared towards graduate students studying operator theory, and the author has designated the difficulty level for each counterexample, indicating which ones are also suitable for advanced undergraduate students.The first half of the book focuses on bounded linear operators, including counterexamples in the areas of operator topologies, matrices of bounded operators, square roots, the spectrum, operator exponentials, and non-normal operators. The second part of the book is devoted to unbounded linear operators in areas such as closedness and closability, self-adjointness, normality, commutativity, and the spectrum, concluding with a chapter that features some open problems. Chapters begin with a brief "Basics" section for the readers' reference, and many of the counterexamples included are the author's original work. Counterexamples in Operator Theory can be used by students in graduate courses on operator theory and advanced matrix theory. Previous coursework in advanced linear algebra, operator theory, and functional analysis is assumed. Researchers, quantum physicists, and undergraduate students studying functional analysis and operator theory will also find this book to be a useful reference.
Spatial Data Science
Spatial Data Science introduces fundamental aspects of spatial data that every data scientist should know before they start working with spatial data. These aspects include how geometries are represented, coordinate reference systems (projections, datums), the fact that the Earth is round and its consequences for analysis, and how attributes of geometries can relate to geometries. In the second part of the book, these concepts are illustrated with data science examples using the R language. In the third part, statistical modelling approaches are demonstrated using real world data examples. After reading this book, the reader will be well equipped to avoid a number of major spatial data analysis errors.The book gives a detailed explanation of the core spatial software packages for R: sf for simple feature access, and stars for raster and vector data cubes - array data with spatial and temporal dimensions. It also shows how geometrical operations change when going from a flat space to the surface of a sphere, which is what sf and stars use when coordinates are not projected (degrees longitude/latitude). Separate chapters detail a variety of plotting approaches for spatial maps using R, and different ways of handling very large vector or raster (imagery) datasets, locally, in databases, or in the cloud. The data used and all code examples are freely available online from https: //r-spatial.org/book/. The solutions to the exercises can be found here: https: //edzer.github.io/sdsr_exercises/.
Introduction to the Basics of Real Analysis
This book presents an introduction to the key topics in Real Analysis and makes the subject easily understood by the learners. The book is primarily useful for students of mathematics and engineering studying the subject of Real Analysis. It includes many examples and exercises at the end of chapters. This book is very authentic for students, instructors, as well as those doing research in areas demanding a basic knowledge of Real Analysis. It describes several useful topics in Real Analysis such as sets and functions, completeness, ordered field, neighborhoods, limit points of a set, open sets, closed sets, countable and uncountable sets, sequences of real numbers, limit, continuity and differentiability of real functions, uniform continuity, point-wise and uniform convergence of sequences and series of real functions, Riemann integration, improper integrals and metric spaces.
Problem Solving Methods and Strategies in High School Mathematical Competitions
This book not only introduces important methods and strategies for solving problems in mathematics competition, but also discusses the basic principles behind them and the mathematical way of thinking.It may be used as a valuable textbook for a mathematics competition course or a mathematics education course at undergraduate and graduate level. It can also serve as a reference book for students and teachers in primary and secondary schools.The materials of this book come from a book series of Mathematical Olympiad Competition. It is a collection of problems and solutions of the major mathematical competitions in China. The translation is done by Yongming Liu.The authors are mathematical competition teachers and researchers, many China's national team coaches and national team leaders. Many techniques and approaches in the book come directly from their own research results.
Statistics with Rust
Are you an experienced statistician or data professional looking for a powerful, efficient, and versatile programming language to turbocharge your data analysis and machine learning projects? Look no further! "Statistics with Rust" is your comprehensive resource to unlock Rust's true potential in modern statistical methods.This book is tailored specifically for statisticians and data professionals who are already familiar with the fundamentals of statistics and want to leverage the speed and reliability of Rust in their projects. Over 11 in-depth chapters, you will discover how Rust outperforms Python in various aspects of data analysis and machine learning and learn to implement popular statistical methods using Rust's unique features and libraries."Statistics with Rust" begins by introducing you to Rust's programming environment and essential libraries for data professionals. You'll then dive into data handling, preprocessing, and visualization techniques that form the backbone of any statistical analysis. As you progress through the book, you'll explore descriptive and inferential statistics, probability distributions, regression analysis, time series analysis, Bayesian statistics, multivariate statistical methods, and nonlinear models. Additionally, the book covers essential machine-learning techniques, model evaluation and validation, natural language processing, and advanced techniques in emerging topics.To ensure you get the most out of this book, each chapter includes hands-on examples and exercises to reinforce your understanding of the concepts presented. You'll also learn to optimize your Rust code and select the best tools and libraries for each task, maximizing your productivity and efficiency.Key LearningsDiscover Rust's unique advantages for statistical analysis and machine learning projects.Learn to efficiently handle, preprocess, and visualize data using Rust libraries.Implement descriptive and inferential statistics with Rust for powerful data insights.Master probability distributions and random variables in Rust for robust simulations.Perform advanced regression analysis with Rust's capabilities.Explore Bayesian statistics and Markov Chain Monte Carlo methods in Rust.Uncover multivariate techniques, including PCA and Factor Analysis, using Rust libraries.Implement cutting-edge machine learning algorithms and model evaluation techniques in Rust.Delve into text analysis, natural language processing, and network analysis with Rust.
Problem Solving Methods and Strategies in High School Mathematical Competitions
This book not only introduces important methods and strategies for solving problems in mathematics competition, but also discusses the basic principles behind them and the mathematical way of thinking.It may be used as a valuable textbook for a mathematics competition course or a mathematics education course at undergraduate and graduate level. It can also serve as a reference book for students and teachers in primary and secondary schools.The materials of this book come from a book series of Mathematical Olympiad Competition. It is a collection of problems and solutions of the major mathematical competitions in China. The translation is done by Yongming Liu.The authors are mathematical competition teachers and researchers, many China's national team coaches and national team leaders. Many techniques and approaches in the book come directly from their own research results.
Closure Properties for Heavy-Tailed and Related Distributions
A Toolbox of Averaging Theorems
This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/ε.Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs).In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practical tools and theoretical insights to help you tackle a range of mathematical problems.
Heat Kernel on Lie Groups and Maximally Symmetric Spaces
This monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form - and derives them - for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics - such as global analysis, spectral geometry, stochastic processes, and financial mathematics - as well in areas of mathematical and theoretical physics - including quantum field theory, quantum gravity, string theory, and statistical physics.
