For courses in Introductory Statistics. Encourages statistical thinking using technology, innovative methods, and a sense of humour Inspired by the 2016 GAISE Report revision, Stats: Data and Models, 5th Edition by De Veaux, Velleman, and Bock uses innovative strategies to help students think critically about data, while maintaining the book's core concepts, coverage, and most importantly, readability. The authors make it easier for instructors to teach and for students to understand more complicated statistical concepts later in the course (such as the Central Limit Theorem). In addition, students get more exposure to large data sets and multivariate thinking, which better prepares them to be critical consumers of statistics in the 21st century. The 5th Edition's approach to teaching Stats: Data and Models is revolutionary, yet it retains the book's lively tone and hallmark pedagogical features such as its Think/Show/Tell Step-by-Step Examples. Samples Download the detailed table of contents Preview sample pages from Stats: Data and Models, Global Edition

Hoermander operators are a class of linear second order partial differential operators with nonnegative characteristic form and smooth coefficients, which are usually degenerate elliptic-parabolic, but nevertheless hypoelliptic, that is highly regularizing. The study of these operators began with the 1967 fundamental paper by Lars Hoermander and is intimately connected to the geometry of vector fields.Motivations for the study of Hoermander operators come for instance from Kolmogorov-Fokker-Planck equations arising from modeling physical systems governed by stochastic equations and the geometric theory of several complex variables. The aim of this book is to give a systematic exposition of a relevant part of the theory of Hoermander operators and vector fields, together with the necessary background and prerequisites.The book is intended for self-study, or as a reference book, and can be useful to both younger and senior researchers, already working in this area or aiming to approach it.

This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.

The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical disciplines in recent decades. Moreover, it turns out to be very useful for graduates when they encounter differential equations in their work; usually those equations are very complicated and cannot be solved by standard methods.The main idea of the qualitative analysis of differential equations is to be able to say something about the behavior of solutions of the equations, without solving them explicitly. Therefore, in the first place such properties like the stability of solutions stand out. It is the stability with respect to changes in the initial conditions of the problem. Note that, even with the numerical approach to differential equations, all calculations are subject to a certain inevitable error. Therefore, it is desirable that the asymptotic behavior of the solutions is insensitive to perturbations of the initial state.Each chapter contains a series of problems (with varying degrees of difficulty) and a self-respecting student should solve them. This book is based on Raul Murillo's translation of Henryk Zoladek's lecture notes, which were in Polish and edited in the portal Matematyka Stosowana (Applied Mathematics) in the University of Warsaw.

The scientific field of data analysis is constantly expanding due to the rapid growth of the computer industry and the wide applicability of computational and algorithmic techniques, in conjunction with new advances in statistical, stochastic and analytic tools. There is a constant need for new, high-quality publications to cover the recent advances in all fields of science and engineering. This book is a collective work by a number of leading scientists, computer experts, analysts, engineers, mathematicians, probabilists and statisticians who have been working at the forefront of data analysis and related applications. The chapters of this collaborative work represent a cross-section of current concerns, developments and research interests in the above scientific areas. The collected material has been divided into appropriate sections to provide the reader with both theoretical and applied information on data analysis methods, models and techniques, along with related applications.

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results. In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.

This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains.The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators.New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory.

Advances in techniques that reduce or eliminate the type of meshes associated with finite elements or finite differences are reported in the papers that form this volume. As design, analysis and manufacture become more integrated, the chances are that software users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily within the aforementioned integrated process. The maturity of BEM since 1978 has resulted in a substantial number of industrial applications of the method; this demonstrates its accuracy, robustness and ease of use. The range of applications still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general. The included papers originate from the 45th conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM) and describe theoretical developments and new formulations, helping to expand the range of applications as well as the type of modelled materials in response to the requirements of contemporary industrial and professional environments.

Addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by:* Presenting examples of the power and versatility of operator-splitting methods.* Providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly non-smooth) problems from science and engineering.* Showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems.

Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find: Numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed. Extensions from single-player optimization to noncooperative games, under delays and pdes, are provided. The delays and pdes are compensated in the control designs using the pde backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory. Accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.

This work is devoted to fixed point theory as well as the theory of accretive operators in Banach spaces. The goal is to develop, in self-contained way, the main results in both theories. Special emphasis is given to the study how both theories can be used to study the existence and uniqueness of solution of several types of partial differential equations and integral equations.

This book is a general introduction to the statistical analysis of networks, and can serve both as a research monograph and as a textbook. Numerous fundamental tools and concepts needed for the analysis of networks are presented, such as network modeling, community detection, graph-based semi-supervised learning and sampling in networks. The description of these concepts is self-contained, with both theoretical justifications and applications provided for the presented algorithms.Researchers, including postgraduate students, working in the area of network science, complex network analysis, or social network analysis, will find up-to-date statistical methods relevant to their research tasks. This book can also serve as textbook material for courses related to thestatistical approach to the analysis of complex networks.In general, the chapters are fairly independent and self-supporting, and the book could be used for course composition "a la carte". Nevertheless, Chapter 2 is needed to a certain degree for all parts of the book. It is also recommended to read Chapter 4 before reading Chapters 5 and 6, but this is not absolutely necessary. Reading Chapter 3 can also be helpful before reading Chapters 5 and 7. As prerequisites for reading this book, a basic knowledge in probability, linear algebra and elementary notions of graph theory is advised. Appendices describing required notions from the above mentioned disciplines have been added to help readers gain further understanding.

Containing the proceedings from the 41st conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM), this book is a collection of high quality papers that report on advances in techniques that reduce or eliminate the type of meshes associated with such methods as finite elements or finite differences. As design, analysis and manufacture become more integrated the chances are that the users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily in the integrated process. The maturity of BEM since 1978 has resulted in a substantial number of industrial applications that demonstrate the accuracy, robustness and easy use of the technique. Their range still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general. The papers in this volume help to expand the range of applications as well as the type of materials in response to industrial and professional requirements.

This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches. The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs - Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere. Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces Lp (Rn). Chapter 4 gives a gentle introduction to these results, using the Riesz - Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry - Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the L2 theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.

The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.

In 1940 G. H. Hardy published A Mathematician's Apology, a meditation on mathematics by a leading pure mathematician. Eighty-two years later, An Applied Mathematician's Apology is a meditation and also a personal memoir by a philosophically inclined numerical analyst, one who has found great joy in his work but is puzzled by its relationship to the rest of mathematics.

For a two-semester or three-semester course in Calculus for Life Sciences. Calculus for Biology and Medicine, Third Edition, addresses the needs of students in the biological sciences by showing them how to use calculus to analyze natural phenomena-without compromising the rigorous presentation of the mathematics. While the table of contents aligns well with a traditional calculus text, all the concepts are presented through biological and medical applications. The text provides students with the knowledge and skills necessary to analyze and interpret mathematical models of a diverse array of phenomena in the living world. Since this text is written for college freshmen, the examples were chosen so that no formal training in biology is needed.

This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.

This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincare's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time--pure and applied alike--ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques. The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman-Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincare-Hopf index theorem. The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.

For courses in Differential Equations and Linear Algebra. The right balance between concepts, visualisation, applications, and skills Differential Equations and Linear Algebra provides the conceptual development and geometric visualisation of a modern differential equations and linear algebra course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena - a comprehensive approach that makes accessible a wider range of more realistic applications. The book combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout.

Jump-start your career as a data scientist--learn to develop datasets for exploration, analysis, and machine learning SQL for Data Scientists: A Beginner's Guide for Building Datasets for Analysis is a resource that's dedicated to the Structured Query Language (SQL) and dataset design skills that data scientists use most. Aspiring data scientists will learn how to how to construct datasets for exploration, analysis, and machine learning. You can also discover how to approach query design and develop SQL code to extract data insights while avoiding common pitfalls. You may be one of many people who are entering the field of Data Science from a range of professions and educational backgrounds, such as business analytics, social science, physics, economics, and computer science. Like many of them, you may have conducted analyses using spreadsheets as data sources, but never retrieved and engineered datasets from a relational database using SQL, which is a programming language designed for managing databases and extracting data. This guide for data scientists differs from other instructional guides on the subject. It doesn't cover SQL broadly. Instead, you'll learn the subset of SQL skills that data analysts and data scientists use frequently. You'll also gain practical advice and direction on "how to think about constructing your dataset." Gain an understanding of relational database structure, query design, and SQL syntax Develop queries to construct datasets for use in applications like interactive reports and machine learning algorithms Review strategies and approaches so you can design analytical datasets Practice your techniques with the provided database and SQL code In this book, author Renee Teate shares knowledge gained during a 15-year career working with data, in roles ranging from database developer to data analyst to data scientist. She guides you through SQL code and dataset design concepts from an industry practitioner's perspective, moving your data scientist career forward!