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A Primer for Undergraduate Research: From Groups and Tiles to Frames and Vaccines (Foundations for Undergraduate Research in Mathematics)
by Christopher Lee Valerie Peterson Aaron WoottonThis highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading.The content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations research), yet have few enough prerequisites that the interested student can start exploring them under the guidance of a faculty member. Whether trying to start an undergraduate thesis, embarking on a summer REU, or preparing for graduate school, this book is appropriate for a variety of students and the faculty who guide them.
A Primer in Biological Data Analysis and Visualization Using R
by Gregg HartvigsenR is the most widely used open-source statistical and programming environment for the analysis and visualization of biological data. Drawing on Gregg Hartvigsen's extensive experience teaching biostatistics and modeling biological systems, this text is an engaging, practical, and lab-oriented introduction to R for students in the life sciences.Underscoring the importance of R and RStudio in organizing, computing, and visualizing biological statistics and data, Hartvigsen guides readers through the processes of entering data into R, working with data in R, and using R to visualize data using histograms, boxplots, barplots, scatterplots, and other common graph types. He covers testing data for normality, defining and identifying outliers, and working with non-normal data. Students are introduced to common one- and two-sample tests as well as one- and two-way analysis of variance (ANOVA), correlation, and linear and nonlinear regression analyses. This volume also includes a section on advanced procedures and a chapter introducing algorithms and the art of programming using R.
A Primer in Biological Data Analysis and Visualization Using R
by Gregg HartvigsenR is the most widely used open-source statistical and programming environment for the analysis and visualization of biological data. Drawing on Gregg Hartvigsen’s extensive experience teaching biostatistics and modeling biological systems, this text is an engaging, practical, and lab-oriented introduction to R for students in the life sciences.Underscoring the importance of R and RStudio in organizing, computing, and visualizing biological statistics and data, Hartvigsen guides readers through the processes of correctly entering and analyzing data and using R to visualize data using histograms, boxplots, barplots, scatterplots, and other common graph types. He covers testing data for normality, defining and identifying outliers, and working with non-normally distributed data. Students are introduced to common one- and two-sample tests as well as one- and two-way analysis of variance (ANOVA), correlation, and linear and nonlinear regression analyses. This volume also includes a section on advanced procedures and a chapter outlining algorithms and the art of programming using R.This second edition has been revised to be current with the versions of R software released since the book’s original publication. It features updated terminology, sources, and examples throughout.
A Primer in Fluid MechanicsDynamics of Flows in One Space Dimension
by Jr. BrowerThis distinctive text presents the basic principles of fluid mechanics by means of one-dimensional flow examples - differing significantly in style and content from other books. A Primer in Fluid Mechanics contains:an overview of fluid properties and the kinetic theory of gases information on the fundamental equations of fluid mechanics, including historical references and background information introductory discussions on fluid properties and fluid statics a comprehensive chapter on compressible flow a variety of applications on non-steady flow, including non-steady gas dynamics a brief introduction to acousticsNovel provisos in the text include an analysis of the static stability of a floating two-dimensional parabolic section viscous flow through an elastic duct several geometries in non-steady tank draining, including a singular perturbation problemChapters also discuss physical properties, atmospheric stability, thermodynamics, energy and momentum equations, dimensional analysis, and historical perspectives of flows in pipes and conduits.A Primer in Fluid Mechanics offers a rigorous text for the curious student and for the research engineer seeking a readily available guide to the more refined treatments in the literature - supporting classical and current discussions as well as theoretical and practical concepts.
A Primer In Probability (Statistics: A Series Of Textbooks And Monographs #Vol. 111)
by Kathleen SubrahmaniamSomewhat revised/expanded new edition of a problem-oriented introductory undergraduate text, the first edition of which appeared about a decade ago. The author writes with courteous clarity, and imposes only modest demands upon the mathematical skills of her readers.
A Primer in Probability (Statistics: A Series of Textbooks and Monographs)
by Kathleen SubrahmaniamSomewhat revised/expanded new edition of a problem-oriented introductory undergraduate text, the first edition of which appeared about a decade ago. The author writes with courteous clarity, and imposes only modest demands upon the mathematical skills of her readers. Problems at the end of each of t
A Primer in Tensor Analysis and Relativity (Undergraduate Lecture Notes in Physics)
by Ilya L. ShapiroThis undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course.The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity.Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, including an understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject.
A Primer of Algebraic Geometry: Constructive Computational Methods (Pure and Applied Mathematics #227)
by Huishi Li Freddy Van OystaeyenPresents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more.
A Primer of Permutation Statistical Methods
by Kenneth J. Berry Janis E. Johnston Paul W. Mielke, Jr.The primary purpose of this textbook is to introduce the reader to a wide variety of elementary permutation statistical methods. Permutation methods are optimal for small data sets and non-random samples, and are free of distributional assumptions. The book follows the conventional structure of most introductory books on statistical methods, and features chapters on central tendency and variability, one-sample tests, two-sample tests, matched-pairs tests, one-way fully-randomized analysis of variance, one-way randomized-blocks analysis of variance, simple regression and correlation, and the analysis of contingency tables. In addition, it introduces and describes a comparatively new permutation-based, chance-corrected measure of effect size. Because permutation tests and measures are distribution-free, do not assume normality, and do not rely on squared deviations among sample values, they are currently being applied in a wide variety of disciplines. This book presents permutation alternatives to existing classical statistics, and is intended as a textbook for undergraduate statistics courses or graduate courses in the natural, social, and physical sciences, while assuming only an elementary grasp of statistics.
A Primer on Hilbert Space Operators (Compact Textbooks in Mathematics)
by Piotr SołtanThe book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators. The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.
A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups (UNITEXT for Physics)
by Carlo Alabiso Ittay WeissThis book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups (UNITEXT for Physics)
by Carlo Alabiso Ittay WeissThis book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
A Primer on Linear Models (Chapman & Hall/CRC Texts in Statistical Science)
by John F. MonahanA Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods.
A Primer on Machine Learning Applications in Civil Engineering
by Paresh Chandra DekaMachine learning has undergone rapid growth in diversification and practicality, and the repertoire of techniques has evolved and expanded. The aim of this book is to provide a broad overview of the available machine-learning techniques that can be utilized for solving civil engineering problems. The fundamentals of both theoretical and practical aspects are discussed in the domains of water resources/hydrological modeling, geotechnical engineering, construction engineering and management, and coastal/marine engineering. Complex civil engineering problems such as drought forecasting, river flow forecasting, modeling evaporation, estimation of dew point temperature, modeling compressive strength of concrete, ground water level forecasting, and significant wave height forecasting are also included. Features Exclusive information on machine learning and data analytics applications with respect to civil engineering Includes many machine learning techniques in numerous civil engineering disciplines Provides ideas on how and where to apply machine learning techniques for problem solving Covers water resources and hydrological modeling, geotechnical engineering, construction engineering and management, coastal and marine engineering, and geographical information systems Includes MATLAB® exercises
A Primer on Mapping Class Groups (Princeton Mathematical Series #41)
by Benson Farb Dan MargalitThe study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.
A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)
by Joe Hair G. Tomas Hult Christian M. Ringle Marko SarstedtThe third edition of A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) guides readers through learning and mastering the techniques of this approach in clear language. Authors Joseph H. Hair, Jr., G. Tomas M. Hult, Christian Ringle, and Marko Sarstedt use their years of conducting and teaching research to communicate the fundamentals of PLS-SEM in straightforward language to explain the details of this method, with limited emphasis on equations and symbols. A running case study on corporate reputation follows the different steps in this technique so readers can better understand the research applications. Learning objectives, review and critical thinking questions, and key terms help readers cement their knowledge. This edition has been thoroughly updated, featuring the latest version of the popular software package SmartPLS 3. New topics have been added throughout the text, including a thoroughly revised and extended chapter on mediation, recent research on the foundations of PLS-SEM, detailed descriptions of research summarizing the advantages as well as limitations of PLS-SEM, and extended coverage of advanced concepts and methods, such as out-of-sample versus in-sample prediction metrics, higher-order constructs, multigroup analysis, necessary condition analysis, and endogeneity.
A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)
by Joe Hair G. Tomas Hult Christian M. Ringle Marko SarstedtThe third edition of A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) guides readers through learning and mastering the techniques of this approach in clear language. Authors Joseph H. Hair, Jr., G. Tomas M. Hult, Christian Ringle, and Marko Sarstedt use their years of conducting and teaching research to communicate the fundamentals of PLS-SEM in straightforward language to explain the details of this method, with limited emphasis on equations and symbols. A running case study on corporate reputation follows the different steps in this technique so readers can better understand the research applications. Learning objectives, review and critical thinking questions, and key terms help readers cement their knowledge. This edition has been thoroughly updated, featuring the latest version of the popular software package SmartPLS 3. New topics have been added throughout the text, including a thoroughly revised and extended chapter on mediation, recent research on the foundations of PLS-SEM, detailed descriptions of research summarizing the advantages as well as limitations of PLS-SEM, and extended coverage of advanced concepts and methods, such as out-of-sample versus in-sample prediction metrics, higher-order constructs, multigroup analysis, necessary condition analysis, and endogeneity.
A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)
by G. Tomas Hult Marko Sarstedt Dr Joe Hair Dr Christian M. RingleA Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) by Joseph F. Hair, Jr., G. Tomas M. Hult, Christian Ringle, and Marko Sarstedt is a practical guide that provides concise instructions on how to use partial least squares structural equation modeling (PLS-SEM), an evolving statistical technique, to conduct research and obtain solutions. Featuring the latest research, new examples using the SmartPLS software, and expanded discussions throughout, the Second Edition is designed to be easily understood by those with limited statistical and mathematical training who want to pursue research opportunities in new ways.
A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)
by G. Tomas Hult Marko Sarstedt Dr Joe Hair Dr Christian M. RingleA Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) by Joseph F. Hair, Jr., G. Tomas M. Hult, Christian Ringle, and Marko Sarstedt is a practical guide that provides concise instructions on how to use partial least squares structural equation modeling (PLS-SEM), an evolving statistical technique, to conduct research and obtain solutions. Featuring the latest research, new examples using the SmartPLS software, and expanded discussions throughout, the Second Edition is designed to be easily understood by those with limited statistical and mathematical training who want to pursue research opportunities in new ways.
A Primer on PDEs: Models, Methods, Simulations (UNITEXT)
by Anna Zaretti Federico Vegni Paolo Zunino Sandro SalsaThis book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.
A Primer on Population Dynamics Modeling: Basic Ideas for Mathematical Formulation (Theoretical Biology)
by Hiromi SenoThis textbook provides an introduction to the mathematical models of population dynamics in mathematical biology. The focus of this book is on the biological meaning/translation of mathematical structures in mathematical models, rather than simply explaining mathematical details and literacies to analyze a model. In some recent usages of the mathematical model simply with computer numerical calculations, the model includes some inappropriate mathematical structure concerning the reasonability of modeling for the biological problem under investigation. For students and researchers who study or use mathematical models, it is important and helpful to understand what mathematical setup could be regarded as reasonable for the model with respect to the relation between the biological factors involved in the assumptions and the mathematical structure of the model. Topics covered in this book are; modeling with geometric progression, density effect in population dynamics, deriving continuous time models from discrete time models, basic modeling for birth-death stochastic processes, continuous time models, modeling interspecific reaction for the continuous time population dynamics model, competition and prey-predator dynamics, modeling for population dynamics with a heterogeneous structure of population, qualitative analysis on the discrete time dynamical system, necessary knowledge about fundamental mathematical theories to understand the dynamical nature of continuous time models. The book includes popular topics in ecology and mathematical biology, as well as classic theoretical topics. By understanding the biological meaning of modeling for simple models, readers will be able to derive a specific mathematical model for a biological problem by reasonable modeling. The contents of this book is made accessible for readers without strong Mathematical background.
A Primer On String Theory
by Volker SchomerusSince its conception in the 1960s, string theory has been hailed as one of the most promising routes we have to unify quantum mechanics and general relativity. This book provides a concise introduction to string theory explaining central concepts, mathematical tools and covering recent developments in physics including compactifications and gauge/string dualities. With string theory being a multidisciplinary field interfacing with high energy physics, mathematics and quantum field theory, this book is ideal for both students with no previous knowledge of the field and scholars from other disciplines who are looking for an introduction to basic concepts.
A Primer on the Dirichlet Space
by Omar El-FallahThe Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.
A Primer on the Geometry of Carbon Nanotubes and Their Modifications (SpringerBriefs in Applied Sciences and Technology)
by Andreas Öchsner Sadegh Imani Yengejeh Seyedeh Alieh KazemiThis volume presents a comprehensive system for categorizing carbon nanotubes and their modifications in terms of nano sheets, nanotubes, microscopic and atomic modifications. In addition, the material and geometric properties of these nano-configurations are addressed. Lastly, it introduces a number of common software packages for geometry generation and several commercial finite element programs.
A Primer on Wavelets and Their Scientific Applications (Studies in Advanced Mathematics)
by James S. WalkerIn the first edition of his seminal introduction to wavelets, James S. Walker informed us that the potential applications for wavelets were virtually unlimited. Since that time thousands of published papers have proven him true, while also necessitating the creation of a new edition of his bestselling primer. Updated and fully revised to include th