- Table View
- List View
New Trends in Applied Harmonic Analysis, Volume 2: Harmonic Analysis, Geometric Measure Theory, and Applications (Applied and Numerical Harmonic Analysis)
by Akram Aldroubi Carlos Cabrelli Stéphane Jaffard Ursula MolterThis contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include:Gabor framesFalconer distance problemHausdorff dimensionSparse inequalitiesFractional Brownian motionFourier analysis in geometric measure theoryThis volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.
Using IBM® SPSS® Statistics: An Interactive Hands-On Approach
by James O. AldrichUsing IBM® SPSS® Statistics: An Interactive Hands-On Approach, Third Edition gives readers an accessible and comprehensive guide to walking through SPSS®, providing them with step-by-step knowledge for effectively analyzing their data. From entering data to working with existing databases, and working with the help menu through performing factor analysis, Using IBM® SPSS® Statistics covers every aspect of SPSS® from introductory through intermediate statistics. The book is divided into parts that focus on mastering SPSS® basics, dealing with univariate statistics and graphing, inferential statistics, relational statistics, and more. Written using IBM® SPSS® version 25 and 24, and compatible with the earlier releases, this book is one of the most comprehensive SPSS® guides available.
Using IBM® SPSS® Statistics: An Interactive Hands-On Approach
by James O. AldrichUsing IBM® SPSS® Statistics: An Interactive Hands-On Approach, Third Edition gives readers an accessible and comprehensive guide to walking through SPSS®, providing them with step-by-step knowledge for effectively analyzing their data. From entering data to working with existing databases, and working with the help menu through performing factor analysis, Using IBM® SPSS® Statistics covers every aspect of SPSS® from introductory through intermediate statistics. The book is divided into parts that focus on mastering SPSS® basics, dealing with univariate statistics and graphing, inferential statistics, relational statistics, and more. Written using IBM® SPSS® version 25 and 24, and compatible with the earlier releases, this book is one of the most comprehensive SPSS® guides available.
Technology in Mathematics Teaching: Selected Papers of the 13th ICTMT Conference (Mathematics Education in the Digital Era #13)
by Gilles Aldon Jana TrgalováThis book comprises chapters featuring a state of the art of research on digital technology in mathematics education. The chapters are extended versions of a selection of papers from the Proceedings of the 13th International Conference on Technology in Mathematics Teaching (ICTMT-13), which was held in Lyon, France, from July 3rd to 6th. ICTMT-13 gathered together over one hundred participants from twenty countries sharing research and empirical results on the topical issues of technology and its potential to improve mathematics teaching and learning. The chapters are organised into 4 themed parts, namely assessment in mathematics education and technology, which was the main focus of the conference, innovative technology and approaches to mathematics education, teacher education and professional development toward the technology use, and mathematics teaching and learning experiences with technology. In 13 chapters contained in the book, prominent mathematics educators from all over the world present the most recent theoretical and practical advances on these themes This book is of particular interest to researchers, teachers, teacher educators and other actors interested in digital technology in mathematics education.
Mathematics and Technology
by Gilles Aldon Fernando Hitt Luciana Bazzini Uwe GellertThis volume collects most recent work on the role of technology in mathematics education. It offers fresh insight and understanding of the many ways in which technological resources can improve the teaching and learning of mathematics. The first section of the volume focuses on the question how a proposed mathematical task in a technological environment can influence the acquisition of knowledge and what elements are important to retain in the design of mathematical tasks in computing environments. The use of white smart boards, platforms as Moodle, tablets and smartphones have transformed the way we communicate both inside and outside the mathematics classroom. Therefore the second section discussed how to make efficient use of these resources in the classroom and beyond. The third section addresses how technology modifies the way information is transmitted and how mathematical education has to take into account the new ways of learning through connected networks as well as new ways of teaching. The last section is on the training of teachers in the digital era. The editors of this volume have selected papers from the proceedings of the 65th, 66th and 67th CIEAEM conference, and invited the correspondent authors to contribute to this volume by discussing one of the four important topics. The book continues a series of sourcebooks edited by CIEAEM, the Commission Internationale pour l'#65533;tude et l'Am#65533;lioration de l'Enseignement des Math#65533;matiques / International Commission for the Study and Improvement of Mathematics Education.
National 5 Maths with Answers, Second Edition
by David AlcornExam Board: SQALevel: National 5Subject: MathematicsFirst Teaching: September 2017First Exam: Summer 2018National 5 Maths Second Edition offers updated, rearranged and complete coverage of the SQA syllabus for the examination of the same name from 2017/18 onwards. - Provides thorough preparation for the exam, as revised for the updated syllabus.- Covers all the topics necessary for the revised examination.- Offers a suggested approach through all five sections (Number, Algebra, Geometry, Trigonometry and Statistics), flexibly structured so that teachers and students are also free to select alternative routes to suit individual needs.- Organised content makes it easy to plan, manage and monitor progress.- Each chapter consists of:>Worked Examples with explanatory notes showing how skills are applied >Practice Exercises that are graded to build confidence >Key Points that summarise key points and skills>Review Exercise that provides the opportunity to consolidate topics introduced in the chapter- Includes Revision Exercises, for non-calculator and calculator papers, provide opportunities to consolidate skills acquired during the course.- Exam Practice provides further questions in preparation for the extended examination(s) of the revised syllabus.
Data Science in Practice (Chapman & Hall/CRC Data Science Series)
by Tom AlbyData Science in Practice is the ideal introduction to data science. With or without math skills, here, you get the all-round view that you need for your projects. This book describes how to properly question data, in order to unearth the treasure that data can be. You will get to know the relevant analysis methods, and will be introduced to the programming language R, which is ideally suited for data analysis. Associated tools like notebooks that make data science programming easily accessible are included in this introduction. Because technology alone is not enough, this book also deals with problems in project implementation, illuminates various fields of application, and does not forget to address ethical aspects. Data Science in Practice includes many examples, notes on errors, decision-making aids, and other practical tips. This book is ideal as a complementary text for university students, and is a useful learning tool for those moving into more data-related roles. Key Features: Success factors and tools for all project phases Includes application examples for various subject areas Introduces many aspects of Data Science, from requirements analysis to data acquisition and visualization
Left to Their Own Devices: How Digital Natives Are Reshaping the American Dream
by Julie M. AlbrightA sociologist explores the many ways that digital natives' interaction with technology has changed their relationship with people, places, jobs, and other stabilizing structures and created a new way of life that is at odds with the American Dream of past generations.Digital natives are hacking the American Dream. Young people brought up with the Internet, smartphones, and social media are quickly rendering old habits, values, behaviors, and norms a distant memory--creating the greatest generation gap in history. In this eye-opening book, digital sociologist Julie M. Albright looks at the many ways in which younger people, facilitated by technology, are coming "untethered" from traditional aspirations and ideals, and asks: What are the effects of being disconnected from traditional, stabilizing social structures like churches, marriage, political parties, and long-term employment? What does it mean to be human when one's ties to people, places, jobs, and societal institutions are weakened or broken, displaced by digital hyper-connectivity? Albright sees both positives and negatives. On the one hand, mobile connectivity has given digital nomads the unprecedented opportunity to work or live anywhere. But, new threats to well-being are emerging, including increased isolation, anxiety, and loneliness, decreased physical exercise, ephemeral relationships, fragmented attention spans, and detachment from the calm of nature.In this time of rapid, global, technologically driven change, this book offers fresh insights into the unintended societal and psychological implications of lives exclusively lived in a digital world.
Mathematical Modeling with Excel (Textbooks in Mathematics)
by Brian Albright William P FoxThis text presents a wide variety of common types of models found in other mathematical modeling texts, as well as some new types. However, the models are presented in a very unique format. A typical section begins with a general description of the scenario being modeled. The model is then built using the appropriate mathematical tools. Then it is implemented and analyzed in Excel via step-by-step instructions. In the exercises, we ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios.
Elementare Koordinatengeometrie: Mit einer Einführung in Maxima (Mathematik Primarstufe und Sekundarstufe I + II)
by Helmut AlbrechtDieses strukturell und didaktisch gut durchdachte Lehrbuch für die Ausbildung von Lehrerinnen und Lehrern im Fach Mathematik möchte den Studierenden die klassische Geometrie, die in der Schule leider ein Schattendasein fristet, unter einem etwas veränderten, neuartigen Blickwinkel nahe bringen. Von besonderem Reiz ist in diesem Zusammenhang die alte, ursprüngliche Descartes'sche Idee einer algebraischen Lösung geometrischer Probleme – ohne dabei die Geometrie durch den Formalismus der linearen Algebra und durch das Jonglieren mit Matrizen zu verdecken. Für die rechnerische Lösung der geometrischen Probleme sind nur einfache algebraische Verfahren nötig, wobei der gezielte Einsatz eines Computer-Algebra-Systems langwierige Berechnungen vermeidet und gleichzeitig die erworbenen Kenntnisse vertieft. Das Buch gibt hierfür eine praxis- und anwendungsbezogene Anleitung in den sinnvollen Gebrauch des Computer-Algebra-Systems Maxima. Eine vielfältige Aufgabensammlung rundet das Buch ab, Lösungen findet man kostenlos auf der Internetseite des Verlages.
Geometrie und GPS: Mathematische, physikalische und technische Grundlagen der Satellitenortung verständlich erklärt (Mathematik Primarstufe und Sekundarstufe I + II)
by Helmut AlbrechtAls am 4. Oktober 1957 der erste Satellit in eine Erdumlaufbahn gebracht wurde, dachte noch niemand an eine Positionsbestimmung mit Hilfe von Satelliten, und doch war „Sputnik I“ der Wegbereiter der heutigen Satellitennavigationssysteme. Ursprünglich als rein militärische Anwendung konzipiert, wird die Satellitenortung heute überwiegend zivil genutzt, und neben dem amerikanischen GPS gibt es heute mit Galileo, Glonass und Beidou weitere gleichartige Systeme.Das grundsätzliche Funktionsprinzip der Satellitenortung kann man überall nachlesen – aber damit beginnen erst die wirklich interessanten Fragen:Woher kennt man den genauen Standort der Satelliten?Wie kann man exakte Entfernungen zu Satelliten bestimmen, die über 20.000 km entfernt sind?Warum nennt man diese Entfernungen „Pseudoentfernungen“?Wieso werden an Bord der Satelliten Atomuhren mitgeführt?Was ermöglicht einem Empfänger, die empfangenen Daten zu unterscheiden, wo doch alle Satelliten auf ein und derselben Frequenz senden?Wie kann man aus den Entfernungen und den Satellitenorten die Empfängerposition berechnen?Warum taugt das Kugelmodell der Erde nicht für eine exakte Positionsbestimmung?Was ist, wenn Daten von mehr als den benötigten vier Satelliten zur Verfügung stehen?Warum sind sogar relativistische Effekte zu berücksichtigen?Dieses Buch gibt nicht nur verständliche und erschöpfende Antworten auf diese und viele weitere Fragen, sondern ermöglicht es interessierten Leserinnen und Lesern, die notwendigen Berechnungen von der Datengewinnung bis hin zur verblüffend exakten Positionsbestimmung mit Hilfe des Computer-Algebra-Systems Maxima Schritt für Schritt selbst nachzuvollziehen. Nicht zuletzt liefert es eine überzeugende Antwort auf die allgegenwärtige Frage von Schülern und Studierenden, wozu man denn all die Geometrie, Analysis und lineare Algebra überhaupt benötigt.Schließlich greift das Buch über die Mathematik hinaus Themen aus der Physik, der Astronomie, der Nachrichtentechnik und der Datenverarbeitung auf und motiviert so zu einer spannenden Anwendung innerhalb des MINT-Bereichs.
Introduction to Quantitative Methods for Financial Markets
by Hansjoerg Albrecher Volkmar Lautscham Andreas Binder Philipp MayerSwaps, futures, options, structured instruments - a wide range of derivative products is traded in today's financial markets. Analyzing, pricing and managing such products often requires fairly sophisticated quantitative tools and methods. This book serves as an introduction to financial mathematics with special emphasis on aspects relevant in practice. In addition to numerous illustrative examples, algorithmic implementations are demonstrated using "Mathematica" and the software package "UnRisk" (available for both students and teachers). The content is organized in 15 chapters that can be treated as independent modules. In particular, the exposition is tailored for classroom use in a Bachelor or Master program course, as well as for practitioners who wish to further strengthen their quantitative background.
Reinsurance: Actuarial and Statistical Aspects
by Hansjöerg Albrecher Jan Beirlant Jozef L. TeugelsReinsurance: Actuarial and Statistical Aspects provides a survey of both the academic literature in the field as well as challenges appearing in reinsurance practice and puts the two in perspective. The book is written for researchers with an interest in reinsurance problems, for graduate students with a basic knowledge of probability and statistics as well as for reinsurance practitioners. The focus of the book is on modelling together with the statistical challenges that go along with it. The discussed statistical approaches are illustrated alongside six case studies of insurance loss data sets, ranging from MTPL over fire to storm and flood loss data. Some of the presented material also contains new results that have not yet been published in the research literature. An extensive bibliography provides readers with links for further study.
Topics in Banach Space Theory
by Fernando Albiac Nigel J. KaltonThis text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book. . . succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly. . . It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments. . . I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book. . . " --Gilles Godefroy, Mathematical Reviews
Trails in Kinetic Theory: Foundational Aspects and Numerical Methods (SEMA SIMAI Springer Series #25)
by Giacomo Albi Sara Merino-Aceituno Alessia Nota Mattia ZanellaIn recent decades, kinetic theory - originally developed as a field of mathematical physics - has emerged as one of the most prominent fields of modern mathematics. In recent years, there has been an explosion of applications of kinetic theory to other areas of research, such as biology and social sciences. This book collects lecture notes and recent advances in the field of kinetic theory of lecturers and speakers of the School “Trails in Kinetic Theory: Foundational Aspects and Numerical Methods”, hosted at Hausdorff Institute for Mathematics (HIM) of Bonn, Germany, 2019, during the Junior Trimester Program “Kinetic Theory”. Focusing on fundamental questions in both theoretical and numerical aspects, it also presents a broad view of related problems in socioeconomic sciences, pedestrian dynamics and traffic flow management.
Complexity and Emergence: Lake Como School of Advanced Studies, Italy, July 22–27, 2018 (Springer Proceedings in Mathematics & Statistics #383)
by Sergio Albeverio Elisa Mastrogiacomo Emanuela Rosazza Gianin Stefania UgoliniThis book includes contributions about mathematics, physics, philosophy of science, economics and finance and resulted from the Summer School “Complexity and Emergence: Ideas, Methods, with a Special Attention to Economics and Finance” held in Lake Como School of Advanced Studies, on 22–27 July 2018.The aim of the book is to provide useful instruments from the theory of complex systems, both on the theoretical level and the methodological ones, profiting from knowledge and insights from leading experts of different communities. It moves from the volume editors' conviction that to achieve progress in understanding socio-economical as well as ecological problems of our complex word such preparation is needed, together with a critical reconsideration of our basic scientific and economical approach.The potential readers are primarily master and doctorate students of mathematics, information sciences, theoretical physics and economics, as well as research workers in those areas, who want to enlarge their spectrum of knowledge towards the area of complexity and emergence. Since ideas and methods of the theory of complex systems also apply to other areas (from engineering and architecture to biology and medicine, e.g.), students and research workers from those areas will also profit from this book.
Metodi e Modelli Matematici per le Dinamiche Urbane (UNITEXT #128)
by Sergio Albeverio Paolo Giordano Alberto VancheriIl testo presenta metodi e modelli per lo studio delle città viste come sistemi evolutivi che interagiscono con il territorio circostante. Gli aspetti morfologici, strutturali e dinamici sono sottolineati e analizzati con metodi qualitativi e quantitativi originati dalla matematica e dalla fisica, ma anche ispirati da altre scienze naturali e dallo studio dei sistemi socio-economici. Il libro usa la matematica in vari modi: i concetti e i metodi che vanno oltre quelli della matematica elementare vengono introdotti ed esposti brevemente, con particolare attenzione a quelli attinenti a probabilità e statistica che, non facendo parte dell'educazione di base, vengono presentati sistematicamente tramite capitoli appositi. Contributi più specializzati includono argomenti come la dinamica urbana, l'analisi di progetti architettonici per il territorio, l'uso di automi cellulari stocastici, la sintassi dello spazio urbano, l'influenza del paesaggio e della geografia, e i modelli per la mobilità urbana. Il libro è rivolto agli studenti di corsi avanzati di architettura, urbanistica e ingegneria, e a tutte le persone che studiano il territorio o vi operano.
Schrödinger Operators, Spectral Analysis and Number Theory: In Memory of Erik Balslev (Springer Proceedings in Mathematics & Statistics #348)
by Sergio Albeverio Anindita Balslev Ricardo WederThis book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential. Erik Balslev has made original and important contributions to several areas of Mathematics and its applications. He belongs to the founders of complex scaling, one of the most important methods in the mathematical and physical study of eigenvalues and resonances of Schrödinger operators, which has been very essential in advancing the solution of fundamental problems in Quantum Mechanics and related areas. He was also a pioneer in making available and developing spectral methods in the study of important problems in Analytic Number Theory.
Exact Solutions in Three-Dimensional Gravity (Cambridge Monographs on Mathematical Physics)
by Alberto A. García-DíazA self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravities, and therefore providing graduates and researchers with an invaluable resource on this important topic in gravitational physics. The first book in the field of 2+1 gravity to examine solutions of physical interest. All the physical and mathematical concepts required are explained in the text, enabling readers to gain a complete understanding of the complexities of the field. Includes a complete review of vacuum solutions of topologically massive gravity with a cosmological constant, which shows the algebraic classification of space times at work.
Measuring the User Experience: Collecting, Analyzing, and Presenting Usability Metrics (Second Edition)
by William Albert Thomas TullisMeasuring the User Experience was the first book that focused on how to quantify the user experience. Now in the second edition, the authors include new material on how recent technologies have made it easier and more effective to collect a broader range of data about the user experience. As more UX and web professionals need to justify their design decisions with solid, reliable data, Measuring the User Experience provides the quantitative analysis training that these professionals need. The second edition presents new metrics such as emotional engagement, personas, keystroke analysis, and net promoter score. It also examines how new technologies coming from neuro-marketing and online market research can refine user experience measurement, helping usability and user experience practitioners make business cases to stakeholders. The book also contains new research and updated examples, including tips on writing online survey questions, six new case studies, and examples using the most recent version of Excel. Learn which metrics to select for every case, including behavioral, physiological, emotional, aesthetic, gestural, verbal, and physical, as well as more specialized metrics such as eye-tracking and clickstream data. Find a vendor-neutral examination of how to measure the user experience with web sites, digital products, and virtually any other type of product or system. Discover in-depth global case studies showing how organizations have successfully used metrics and the information they revealed. Companion site, www. measuringux. com, includes articles, tools, spreadsheets, presentations, and other resources to help you effectively measure the user experience
Rhetorical Ways of Thinking
by Lillie R. Albert Danielle Corea Vittoria MacadinoRhetorical Ways of Thinking focuses on how the co-construction of learning models the interpretation of a mathematical situation. It is a comprehensive examination of the role of sociocultural-historical theory developed by Vygotsky. This book puts forward the supposition that the major assumptions of sociocultural-historic theory are essential to understanding the theory's application to mathematical pedagogy, which explores issues relevant to learning and teaching mathematics-in-context, thus providing a valuable practical tool for general mathematics education research. The most important goal, then, is to exemplify the merging of the theory with practice and the subsequent applications to mathematics teaching and learning. This monograph contains five chapters, including a primer to Vygotsky's sociocultural historic theory, three comprehensive empirical studies examining: prospective teachers' perception of mathematics teaching and learning and the practice of scaffolded instruction to assist practicing teachers in developing their understanding of pedagogical content knowledge. Finally, the book concludes with a contextualization of the theory, linking it to best practices in the classroom.
Probability and Bayesian Modeling (Chapman & Hall/CRC Texts in Statistical Science)
by Jim Albert Jingchen HuProbability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.
Handbook of Statistical Methods and Analyses in Sports (Chapman & Hall/CRC Handbooks of Modern Statistical Methods)
by Jim Albert Mark E. Glickman Ruud H. Koning Tim B. SwartzThis handbook will provide both overviews of statistical methods in sports and in-depth treatment of critical problems and challenges confronting statistical research in sports. The material in the handbook will be organized by major sport (baseball, football, hockey, basketball, and soccer) followed by a section on other sports and general statistical design and analysis issues that are common to all sports. This handbook has the potential to become the standard reference for obtaining the necessary background to conduct serious statistical analyses for sports applications and to appreciate scholarly work in this expanding area.
Visualizing Baseball (ASA-CRC Series on Statistical Reasoning in Science and Society)
by Jim AlbertVisualizing Baseball provides a visual exploration of the game of baseball. Graphical displays are used to show how measures of performance, at the team level and the individual level, have changed over the history of baseball. Graphs of career trajectories are helpful for understanding the rise and fall of individual performances of hitters and pitchers over time. One can measure the contribution of plays by the notion of runs expectancy. Graphs of runs expectancy are useful for understanding the importance of the game situation defined by the runners on base and number of outs. Also the runs measure can be used to quantify hitter and pitch counts and the win probabilities can be used to define the exciting plays during a baseball game. Special graphs are used to describe pitch data from the PitchFX system and batted ball data from the Statcast system. One can explore patterns of streaky performance and clutch play by the use of graphs, and special plots are used to predict final season batting averages based on data from the middle of the season. This book was written for several types of readers. Many baseball fans should be interested in the topics of the chapters, especially those who are interested in learning more about the quantitative side of baseball. Many statistical ideas are illustrated and so the graphs and accompanying insights can help in promoting statistical literacy at many levels. From a practitioner’s perspective, the chapters offer many illustrations of the use of a modern graphics system and R scripts are available on an accompanying website to reproduce and potentially improve the graphs in this book.
Mathematical Modeling and Applications in Nonlinear Dynamics
by Albert C.J. Luo Hüseyin MerdanThe book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.