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An Invitation to Model Theory
by Jonathan KirbyModel theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
An Invitation to Morse Theory (Universitext)
by Liviu NicolaescuThis self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.
An Invitation to Probability and Data Analysis for Physicists (UNITEXT for Physics)
by Roberto PiazzaThis book is an introduction to probability, statistics, data analysis, and hypothesis testing in physics. It is designed to be taught at different levels, from basic to advanced, and to be enjoyed by anyone doing research in the physical sciences or related subjects. It aims to be a companion in a journey leading the reader to appreciate and enjoy the major role of these subjects in all aspects of the physical sciences. With specific examples, the book encourages readers to meditate on the distinctive meaning of probability in classical and quantum physics. The author draws on his teaching experience in statistical physics and data analysis, as well as his research work in fields like complex systems and soft matter, to provide a comprehensive introduction to statistical methods.
An Invitation to Statistics in Wasserstein Space (SpringerBriefs in Probability and Mathematical Statistics)
by Victor M. Panaretos Yoav ZemelThis open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.
An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space (Graduate Texts in Mathematics #285)
by Konrad SchmüdgenThis textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules.Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.
An Invitation to Web Geometry (IMPA Monographs #2)
by Jorge Vitório Pereira Luc PirioThis book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chern's bound and Trépreau's algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.
An Invitation to the Rogers-Ramanujan Identities (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Andrew V. SillsThe Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.
An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method: Projections, Estimates, Tools (SpringerBriefs in Mathematics)
by Francisco-Javier Sayas Shukai DuThis monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method.
An Isogeometric Approach to Beam Structures: Bridging the Classical to Modern Technique
by Buntara S. GanThis book proposes a novel, original condensation method to beam formulation based on the isogeometric approach to reducing the degrees of freedom to conventional two-node beam elements. In this volume, the author defines the Buntara Condensation Formulation: a unique formulation in condensing the dynamic equilibrium equation for beam structures, suitable for reducing the number of unlimited dynamic equations necessary to yield a classic two-node beam element. Professor Buntara's method overcomes the problem of the isogeometric approach where the number of degrees of freedom is increased along with the complexity of the geometrical beam element and facilitates implementation of the codes into the existing beam structures programs, and CAD geometrical data into the conventional FE beam element codes. The book proposes a new reduction method where the beam element can be treated as under the conventional beam element theory that has only two nodes at both ends.
An Object-Oriented Python Cookbook in Quantum Information Theory and Quantum Computing
by M.S. Ramkarthik Pranay BarkatakiThis first-of-a-kind textbook provides computational tools in state-of-the-art OOPs Python that are fundamental to quantum information, quantum computing, linear algebra and one-dimensional spin half condensed matter systems. Over 104 subroutines are included, and the codes are aided by mathematical comments to enhance clarity. Suitable for beginner and advanced readers alike, students and researchers will find this textbook to be a helpful guide and a compendium which they can readily use.Features Includes over 104 codes in OOPs Python, all of which can be used either as a standalone program or integrated with any other main program without any issues. Every parameter in the input, output and execution has been provided while keeping both beginner and advanced users in mind. The output of every program is explained thoroughly with detailed examples. Detailed mathematical commenting is done alongside the code which enhances clarity about the flow and working of the code.
An Objective Theory of Probability (Routledge Revivals)
by Donald GilliesThis reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises’ views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises’ definition of probability in terms of limiting frequency and claims that probability should be taken as a primitive or undefined term in accordance with modern axiomatic approaches. This of course raises the problem of how the abstract calculus of probability should be connected with the ‘actual world of experiments’. It is suggested that this link should be established, not by a definition of probability, but by an application of Popper’s concept of falsifiability. In addition to formulating his own interesting theory, Dr Gillies gives a detailed criticism of the generally accepted Neyman Pearson theory of testing, as well as of alternative philosophical approaches to probability theory. The reissue will be of interest both to philosophers with no previous knowledge of probability theory and to mathematicians interested in the foundations of probability theory and statistics.
An October to Remember 1968: The Tigers-Cardinals World Series as Told by the Men Who Played in It
by Brendan DonleyAn October to Remember 1968: The Tigers-Cardinals World Series as Told by the Men Who Played in It recalls one of baseball's most celebrated championship series from the voices of the players who still remain--a collected narrative from a bygone era of major-league baseball as they reflect fifty years later.Modeled after Lawrence S. Ritter's celebrated book, The Glory of Their Times--for which the author traversed the country to record stories of baseball's deadball era--An October to Remember 1968 will likewise preserve the days of baseball past, gathering the memories of the remaining players of the great Tigers and Cardinals teams to assemble their accounts into a vibrant baseball collection. The 1968 World Series came at a time of great cultural change--the fading days of fans dressing up for ballgames, the first years of widespread color TV--and was an historic matchup of two legendary teams, pitting star power head-to-head and going the distance of seven hard-fought games. From the voices of the players themselves, An October to Remember 1968 illustrates in detail what it was like to be a 1968 Tiger, a 1968 Cardinal: what it was like to win it all and to lose it all: what it was like to face Bob Gibson peering in from the mound, Al Kaline digging in at the plate; what it was like, in the player's own words, to remember the days of that most special period in the history of America's national pastime.
An R Companion for Applied Statistics I: Basic Bivariate Techniques
by Danney RascoAn R Companion for Applied Statistics I: Basic Bivariate Techniques breaks the language of the R software down into manageable chunks in order to help students learn how to use it. R is a powerful, flexible, and free tool. However, the flexibility—which eventually becomes a great asset—can make the initial learning curve appear steep. This book introduces a few key aspects of the R tool. As readers become comfortable with these aspects, they develop a foundation from which to more thoroughly explore R and the packages available for it. This introduction does not explain every possible way to analyze data or perform a specific type of analysis. Rather, it focuses on the analyses that are traditionally included in an undergraduate statistics course and provides one or two ways to run these analyses in R. Datasets and scripts to run the examples are provided on an accompanying website. The book has been designed to be an R companion to Warner′s Applied Statistics I, Third Edition, and includes end-of-chapter instructions for replicating the examples from that book in R. However, this text can also be used as a stand-alone R guide, without reference to the Warner text.
An R Companion for Applied Statistics I: Basic Bivariate Techniques
by Danney RascoAn R Companion for Applied Statistics I: Basic Bivariate Techniques breaks the language of the R software down into manageable chunks in order to help students learn how to use it. R is a powerful, flexible, and free tool. However, the flexibility—which eventually becomes a great asset—can make the initial learning curve appear steep. This book introduces a few key aspects of the R tool. As readers become comfortable with these aspects, they develop a foundation from which to more thoroughly explore R and the packages available for it. This introduction does not explain every possible way to analyze data or perform a specific type of analysis. Rather, it focuses on the analyses that are traditionally included in an undergraduate statistics course and provides one or two ways to run these analyses in R. Datasets and scripts to run the examples are provided on an accompanying website. The book has been designed to be an R companion to Warner′s Applied Statistics I, Third Edition, and includes end-of-chapter instructions for replicating the examples from that book in R. However, this text can also be used as a stand-alone R guide, without reference to the Warner text.
An R Companion for Applied Statistics II: Multivariable and Multivariate Techniques
by Danney RascoAn R Companion for Applied Statistics II: Multivariable and Multivariate Techniques breaks the language of the R software down into manageable chunks in order to help students learn how to use R to analyze multivariate data. The book focuses on the statistics generally covered in an intermediate or multivariate statistics course and provides one or two ways to run each analysis in R. The book has been designed to be an R companion to Rebecca M. Warner′s Applied Statistics II: Third Edition, and includes end-of-chapter instructions for replicating the examples from that book in R. However, this text can also be used as a stand-alone R guide for a multivariate statistics course, without reference to the Warner text. Datasets and scripts to run the examples are provided on an accompanying website.
An R Companion for Applied Statistics II: Multivariable and Multivariate Techniques
by Danney RascoAn R Companion for Applied Statistics II: Multivariable and Multivariate Techniques breaks the language of the R software down into manageable chunks in order to help students learn how to use R to analyze multivariate data. The book focuses on the statistics generally covered in an intermediate or multivariate statistics course and provides one or two ways to run each analysis in R. The book has been designed to be an R companion to Rebecca M. Warner′s Applied Statistics II: Third Edition, and includes end-of-chapter instructions for replicating the examples from that book in R. However, this text can also be used as a stand-alone R guide for a multivariate statistics course, without reference to the Warner text. Datasets and scripts to run the examples are provided on an accompanying website.
An R Companion to Applied Regression
by John Fox Sanford WeisbergAn R Companion to Applied Regression is a broad introduction to the R statistical computing environment in the context of applied regression analysis. John Fox and Sanford Weisberg provide a step-by-step guide to using the free statistical software R, an emphasis on integrating statistical computing in R with the practice of data analysis, coverage of generalized linear models, and substantial web-based support materials. The Third Edition has been reorganized and includes a new chapter on mixed-effects models, new and updated data sets, and a de-emphasis on statistical programming, while retaining a general introduction to basic R programming. The authors have substantially updated both the car and effects packages for R for this edition, introducing additional capabilities and making the software more consistent and easier to use. They also advocate an everyday data-analysis workflow that encourages reproducible research. To this end, they provide coverage of RStudio, an interactive development environment for R that allows readers to organize and document their work in a simple and intuitive fashion, and then easily share their results with others. Also included is coverage of R Markdown, showing how to create documents that mix R commands with explanatory text. "An R Companion to Applied Regression continues to provide the most comprehensive and user-friendly guide to estimating, interpreting, and presenting results from regression models in R." –Christopher Hare, University of California, Davis
An R Companion to Applied Regression
by John Fox Sanford WeisbergAn R Companion to Applied Regression is a broad introduction to the R statistical computing environment in the context of applied regression analysis. John Fox and Sanford Weisberg provide a step-by-step guide to using the free statistical software R, an emphasis on integrating statistical computing in R with the practice of data analysis, coverage of generalized linear models, and substantial web-based support materials. The Third Edition has been reorganized and includes a new chapter on mixed-effects models, new and updated data sets, and a de-emphasis on statistical programming, while retaining a general introduction to basic R programming. The authors have substantially updated both the car and effects packages for R for this edition, introducing additional capabilities and making the software more consistent and easier to use. They also advocate an everyday data-analysis workflow that encourages reproducible research. To this end, they provide coverage of RStudio, an interactive development environment for R that allows readers to organize and document their work in a simple and intuitive fashion, and then easily share their results with others. Also included is coverage of R Markdown, showing how to create documents that mix R commands with explanatory text. "An R Companion to Applied Regression continues to provide the most comprehensive and user-friendly guide to estimating, interpreting, and presenting results from regression models in R." –Christopher Hare, University of California, Davis
An R Companion to Linear Statistical Models
by Christopher Hay-JahansThis work was prepared to serve as an R supplement for textbooks on Linear Statistical Models. It provides computational and coding details on the use of R that textbooks do not. Topics covered include simple and multiple linear regression models, models for one- and two-factor fixed-effects designs, covariance models, and models for randomized complete block designs. The text can serve as both a course supplement and a fairly detailed self-help resource. The development of grass-roots code alongside demonstrations of pre-packaged routines provides users with illustrations on how to develop their own programs with R.
An SPSS Companion to Political Analysis
by Philip H. PollockIn this much-anticipated revision of Pollock's popular SPSS workbook, students dive headfirst into actual political data and work with a software tool that prepares them for future political science research. Students learn by doing with guided examples, more than 120 screenshots, and step-bystep instructions.
An Undergraduate Primer in Algebraic Geometry (UNITEXT #129)
by Ciro CilibertoThis book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems.The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology.This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic. The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter.
An Unsolved Proof: The Math Kids (Book 9) (The Math Kids)
by David ColeHidden cameras, secret operations, and new math concepts await in the Math Kids' ninth adventure!Justin has been accused of stealing from the comic book shop! To earn back the trust of his parents and the store manager, he'll have to work at the shop for four whole weekends. And that puts a damper on his plans to play video games and hang out with fellow Math Kids, Jordan, Catherine, and Stephanie. With the end of summer approaching, the four friends realize that finding proof of Justin's innocence is their only way to save Justin's good name. To get it, they'll need to uncover who really stole the comics. Their primary suspects are the two older boys who accused Justin, but catching them red-handed will require more than just teamwork. Solving this problem will require knowledge of proofs and patterns, and if the Math Kids aren't successful, it won't be just Justin's reputation at risk.
An Unusual Pattern: The Math Kids (Book 3) (The Math Kids)
by David ColeThe Math Kids are at it again! When their new friend, Special Agent Carlson, asks them to take a look at a cryptic poem written by a dying bank robber, they know they will need all of their math skills to crack the case. The poem isn't their only problem, though. Their favourite school janitor is fired for stealing from student lockers. The Math Kids know Old Mike would never do anything like that, but how can they prove it, especially with the new janitor watching their every move? Jordan, Stephanie, Justin, and Catherine will need math, bravery, and a little bit of luck if they hope to solve the bank robbery case and get Old Mike his job back. Will they be able to figure out the unusual pattern in time? The Math Kids: An Unusual Pattern is the third book in David Cole's fast-moving math adventure series.
An den Grenzen des Endlichen: Das Hilbertprogramm im Kontext von Formalismus und Finitismus (Mathematik im Kontext)
by Christian TappDer Mathematiker David Hilbert entwickelte mit seiner Beweistheorie ein Programm zur Grundlegung der Mathematik. In der ersten deutschsprachigen Monographie zum Thema bietet der Autor neue Deutungen des Hilbertprogramms. Ausgehend von den historischen Quellen stellt er die Frage neu, ob Hilbert eine formalistische Philosophie der Mathematik voraussetzte. Er macht die Fülle der Ideen sichtbar, die Hilbert und seine Schüler formulierten, diskutiert anspruchsvolle philosophische Implikationen und räumt mit einer Reihe von Fehlinterpretationen auf.
Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons, from Theory to Experiment (Lecture Notes in Physics #870)
by Ugo Moschella Vittorio Gorini Sergio Cacciatori Francesco Belgiorno Stefano Liberati Daniele FaccioAnalogue Gravity Phenomenology is a collection of contributions that cover a vast range of areas in physics, ranging from surface wave propagation in fluids to nonlinear optics. The underlying common aspect of all these topics, and hence the main focus and perspective from which they are explained here, is the attempt to develop analogue models for gravitational systems. The original and main motivation of the field is the verification and study of Hawking radiation from a horizon: the enabling feature is the possibility to generate horizons in the laboratory with a wide range of physical systems that involve a flow of one kind or another. The years around 2010 and onwards witnessed a sudden surge of experimental activity in this expanding field of research. However, building an expertise in analogue gravity requires the researcher to be equipped with a rather broad range of knowledge and interests. The aim of this book is to bring the reader up to date with the latest developments and provide the basic background required in order to appreciate the goals, difficulties, and success stories in the field of analogue gravity. Each chapter of the book treats a different topic explained in detail by the major experts for each specific discipline. The first chapters give an overview of black hole spacetimes and Hawking radiation before moving on to describe the large variety of analogue spacetimes that have been proposed and are currently under investigation. This introductory part is then followed by an in-depth description of what are currently the three most promising analogue spacetime settings, namely surface waves in flowing fluids, acoustic oscillations in Bose-Einstein condensates and electromagnetic waves in nonlinear optics. Both theory and experimental endeavours are explained in detail. The final chapters refer to other aspects of analogue gravity beyond the study of Hawking radiation, such as Lorentz invariance violations and Brownian motion in curved spacetimes, before concluding with a return to the origins of the field and a description of the available observational evidence for horizons in astrophysical black holes.