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Rasch Meta-Metres of Growth for Some Intelligence and Attainment Tests
by David Andrich Ida Marais Sonia SapplThis book adapts Rasch’s approach for quantifying growth on physiological variables, where growth decelerates, to intellectual variables. To apply this approach, it is necessary to construct measurements in a constant unit over the relevant range of the variable. With such measurements, the book illustrates the approach to quantifying growth on six intellectual variables - two intelligences tests and two each of tests of proficiencies in reading comprehension and mathematics. The book discusses how it is not immediately obvious that deceleration on a quantitative scale should also hold for the growth in intellectual variables. It goes on to show that this is indeed the case with all six tests analysed and considers some implications of this feature for understanding intellectual development, in particular the centrality of the growth trajectory set in early life.
A Course in Rasch Measurement Theory: Measuring in the Educational, Social and Health Sciences (Springer Texts in Education)
by David Andrich Ida MaraisThis book applies Rasch measurement theory to the fields of education, psychology, sociology, marketing and health outcomes in order to measure various social constructs. The chief focus is on first principles of both the theory and its applications. Because software is readily available to carry out analyses of real data, numerous small examples are provided in the book. The software used in these examples, and which is helpful in working through the text, is RUMM2030 (Rasch unidimensional models for measurement).The book’s main goals are to equip researchers with the confidence they need in order to be in control of the analysis and interpretation of data, and to make professional rather than primarily statistical decisions mechanically. Because statistical principles are necessarily involved, reviews of the requisite statistics are provided in the Appendix.The content is based on courses that have been taught both online and in intensive form for over two decades. Although first principles are emphasised, much of the book is based on research conducted by the two authors and their colleagues.
Differential and Integral Inequalities (Springer Optimization and Its Applications #151)
by Dorin Andrica Themistocles M. RassiasTheories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.
Recurrent Sequences: Key Results, Applications, and Problems (Problem Books in Mathematics)
by Dorin Andrica Ovidiu BagdasarThis self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is designed to appeal to a wide readership, ranging from scholars and academics, to undergraduate students, or advanced high school and college students training for competitions. The content of the book is very recent, and focuses on areas where significant research is currently taking place. Among the new approaches promoted in this book, the authors highlight the visualization of some recurrences in the complex plane, the concurrent use of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and links to many applications. It contains techniques which are fundamental in other areas of math and encourages further research on the topic. The introductory chapters only require good understanding of college algebra, complex numbers, analysis and basic combinatorics. For Chapters 3, 4 and 6 the prerequisites include number theory, linear algebra and complex analysis. The first part of the book presents key theoretical elements required for a good understanding of the topic. The exposition moves on to to fundamental results and key examples of recurrences and their properties. The geometry of linear recurrences in the complex plane is presented in detail through numerous diagrams, which lead to often unexpected connections to combinatorics, number theory, integer sequences, and random number generation. The second part of the book presents a collection of 123 problems with full solutions, illustrating the wide range of topics where recurrent sequences can be found. This material is ideal for consolidating the theoretical knowledge and for preparing students for Olympiads.
Asymptotic Methods for Engineers
by Igor V. Andrianov Jan AwrejcewiczAsymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems.This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation.The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).
Introduction to Siegel Modular Forms and Dirichlet Series
by Anatoli AndrianovThis is intended for a graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The author's aim is to present a concise and self-contained introduction to an important and developing area of number theory that will serve to attract young researchers to this beautiful field. Topics include: * analytical properties of radial Dirichlet series attached to modular forms of genuses 1 and 2; * the abstract theory of Hecke-Shimura rings for symplectic and related groups; * action of Hecke operators on Siegel modular forms; * applications of Hecke operators to a study of multiplicative properties of Fourier coefficients of modular forms; * Hecke zeta functions of modular forms in one variable and to spinor (or Andrianov) zeta functions of Siegel modular forms of genus two; * the proof of analytical continuation and functional equation (under certain assumptions) for Euler products associated with modular forms of genus two. This text contains a number of exercises and the only prerequisites are standard courses in Algebra and Calculus (one and several variables).
Light and Waves: A Conceptual Exploration of Physics
by Steven S. AndrewsThis book explores light and other types of waves, using this as a window into other aspects of physics. It emphasizes a conceptual understanding, using examples chosen from everyday life and the natural environment. For example, it explains how hummingbird feathers create shimmering colors, how musical instruments produce sound, and how atoms stick together to form molecules. It provides a unique perspective on physics by emphasizing commonalities among different types of waves, including string waves, water waves, sound waves, light waves, the matter waves of quantum mechanics, and the gravitational waves of general relativity. This book is targeted toward college non-science majors, advanced high school students, and adults who are curious about our physical world. It assumes familiarity with algebra but no further mathematics and is classroom-ready with many worked examples, exercises, exploratory puzzles, and appendices to support students from a variety of backgrounds.
Doing Data Science in R: An Introduction for Social Scientists
by Mark AndrewsThis approachable introduction to doing data science in R provides step-by-step advice on using the tools and statistical methods to carry out data analysis. Introducing the fundamentals of data science and R before moving into more advanced topics like Multilevel Models and Probabilistic Modelling with Stan, it builds knowledge and skills gradually. This book: Focuses on providing practical guidance for all aspects, helping readers get to grips with the tools, software, and statistical methods needed to provide the right type and level of analysis their data requires Explores the foundations of data science and breaks down the processes involved, focusing on the link between data science and practical social science skills Introduces R at the outset and includes extensive worked examples and R code every step of the way, ensuring students see the value of R and its connection to methods while providing hands-on practice in the software Provides examples and datasets from different disciplines and locations demonstrate the widespread relevance, possible applications, and impact of data science across the social sciences.
Doing Data Science in R: An Introduction for Social Scientists
by Mark AndrewsThis approachable introduction to doing data science in R provides step-by-step advice on using the tools and statistical methods to carry out data analysis. Introducing the fundamentals of data science and R before moving into more advanced topics like Multilevel Models and Probabilistic Modelling with Stan, it builds knowledge and skills gradually. This book: Focuses on providing practical guidance for all aspects, helping readers get to grips with the tools, software, and statistical methods needed to provide the right type and level of analysis their data requires Explores the foundations of data science and breaks down the processes involved, focusing on the link between data science and practical social science skills Introduces R at the outset and includes extensive worked examples and R code every step of the way, ensuring students see the value of R and its connection to methods while providing hands-on practice in the software Provides examples and datasets from different disciplines and locations demonstrate the widespread relevance, possible applications, and impact of data science across the social sciences.
Aufgaben und Lösungen der Fürther Mathematik-Olympiade 2017–2022: Für Begabtenförderung, AGs und zur Vorbereitung auf Wettbewerbe
by Lutz Andrews Alfred Faulhaber Bertram Hell Paul Jainta Christine StreibDer vorliegende Band enthält alle Probleme der 26. bis 30. Fürther Mathematik-Olympiade, getrennt nach Jahrgangsstufen und Lösungsstrategien. Die Aufgaben belegen, dass sich Problemlösen vermitteln und erlernen lässt. Zum erfolgreichen Lösen von Aufgaben gehört gar nicht so viel: Zuversicht, Konzentration und Mut. Zielloses Probieren und strenges Vorgehen sind ebenso legitime Maßnahmen. Als Zugewinn winkt ein Mix aus Strategien und taktischen Tricks. Das hat nicht selten den erfreulichen Nebeneffekt, dass Skeptiker („Wie bringe ich da Mathematik hinein?“) zu ihrer eigenen Verblüffung in manchen Alltagssituationen mathematische Zusammenhänge erkennen. Problemlösen kann durch viel Übung und Tun erlernt werden. Daher soll das Buch neugierig machen auf Knobeln, auf verschiedene Zugänge zu den Problemen – und auf Mathematik! Es richtet sich an eine breite Leserschaft, angefangen bei Schülern ab Klasse 5 bis 8, die wissbegierig sind und Neues lernen wollen, an Lehrkräfte, Eltern sowie an alle Liebhaber der Mathematik. Die Aufgaben sind erfolgreich einsetzbar in der mathematischen Förderung begabter SchülerInnen in Arbeitsgemeinschaften oder Pluskursen, können eine willkommene Abwechslung im Unterricht sein und eignen sich zum Selbststudium. Die zahlreichen Aufgaben stellen reichhaltiges Übungsmaterial für weiterführende Wettbewerbe bereit. Die Aufgabenstellungen sind in der Regel kurz und griffig wie eine Werbebotschaft, um vor allem auch jüngere SchülerInnen anzulocken.
An Introduction to Cellular Network Analysis Using Stochastic Geometry (Synthesis Lectures on Learning, Networks, and Algorithms)
by Jeffrey G. Andrews Abhishek K. Gupta Ahmad Alammouri Harpreet S. DhillonThis book provides an accessible yet rigorous first reference for readers interested in learning how to model and analyze cellular network performance using stochastic geometry. In addition to the canonical downlink and uplink settings, analyses of heterogeneous cellular networks and dense cellular networks are also included. For each of these settings, the focus is on the calculation of coverage probability, which gives the complementary cumulative distribution function (ccdf) of signal-to-interference-and-noise ratio (SINR) and is the complement of the outage probability. Using this, other key performance metrics, such as the area spectral efficiency, are also derived. These metrics are especially useful in understanding the effect of densification on network performance. In order to make this a truly self-contained reference, all the required background material from stochastic geometry is introduced in a coherent and digestible manner.This Book:Provides an approachable introduction to the analysis of cellular networks and illuminates key system dependenciesFeatures an approach based on stochastic geometry as applied to cellular networks including both downlink and uplinkFocuses on the statistical distribution of signal-to-interference-and-noise ratio (SINR) and related metrics
Comptia A+ Guide To Information Technology Technical Support
by Jean Andrews Joy Shelton Nicholas PierceUsing a step-by-step, highly visual approach, Andrews/Dark Shelton/Pierce's bestselling COMPTIA A+ GUIDE TO IT TECHNICAL SUPPORT, 11th edition, teaches you how to work with users as well as install, maintain, troubleshoot and network computer hardware and software. Ensuring you are well prepared for 220-1101 and 220-1102 certification exams, each module covers core and advanced topics while emphasizing practical application of the most current technology, techniques and industry standards. You will study the latest hardware, security, Active Directory, operational procedures, basics of scripting, virtualization, cloud computing, mobile devices, Windows 10, macOS and Linux. Digital lab manuals, live virtual machine labs, simulations, auto-graded quizzes and interactive activities provide additional preparation for the certification exam -- and your role as an IT support technician or administrator.
Analytic Number Theory, Modular Forms and q-Hypergeometric Series: In Honor of Krishna Alladi's 60th Birthday, University of Florida, Gainesville, March 2016 (Springer Proceedings in Mathematics & Statistics #221)
by George E. Andrews Frank GarvanGathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. <P><P> Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
Integer Partitions
by George E. Andrews Kimmo ErikssonThe theory of integer partitions is a subject of enduring interest as well as a major research area. It has found numerous applications, including celebrated results such as the Rogers-Ramanujan identities. The aim of this introductory textbook is to provide an accessible and wide-ranging introduction to partitions, without requiring anything more than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints.
Ramanujan's Lost Notebook, Part IV
by George E. Andrews Bruce C. BerndtIn the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.<P><P> This volume is the fourth of five volumes that the authors plan to write on Ramanujan's lost notebook. In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series. Most of the entries examined in this volume fall under the purviews of number theory and classical analysis. Several incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed. Three of the partial manuscripts are on diophantine approximation, and others are in classical Fourier analysis and prime number theory. Most of the entries in number theory fall under the umbrella of classical analytic number theory. Perhaps the most intriguing entries are connected with the classical, unsolved circle and divisor problems.
Number Theory: The Theory Of Partitions (Dover Books on Mathematics #Vol. 2)
by George E. AndrewsAlthough mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..
A Missing Link in Cybernetics: Logic and Continuity (IFSR International Series in Systems Science and Systems Engineering #26)
by Alex M. AndrewThe text begins by reviewing the origins and aims of cybernetics with particular reference to Warren McCulloch's declared lifetime quest of "understanding man's understanding". It is shown that continuous systems can undergo complex self-organization, but a need for classification of situations becomes apparent and can be seen as the evolutionary beginning of concept-based processing. Possibilities for complex self-organization are emphasized by discussion of a general principle that has been termed significance feedback, of which backpropagation of errors in neural nets is a special case. It is also noted that continuous measures come to be associated with processing that is essentially concept-based, as acknowledged in Marvin Minsky's reference to heuristic connection between problems, and the associated basic learning heuristic of Minsky and Selfridge. This reappearance of continuity, along with observations on the multi-layer structure of intelligent systems, supports a potentially valuable view of intelligence as having a fractal nature. This is such that structures at a complex level, interpreted in terms of these emergent measures, reflect others at a simpler level. Implications for neuroscience and Artificial Intelligence are also examined. The book presents unconventional and challenging viewpoints that will be of interest to researchers in AI, psychology, cybernetics and systems science, and should help promote further research.
Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems (Computational Methods in Applied Sciences #49)
by Esther Andrés-Pérez Leo M. González Jacques Periaux Nicolas Gauger Domenico Quagliarella Kyriakos GiannakoglouThis book contains thirty-five selected papers presented at the International Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2017). This was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Topics treated in the various chapters reflect the state of the art in theoretical and numerical methods and tools for optimization, and engineering design and societal applications. The volume focuses particularly on intelligent systems for multidisciplinary design optimization (mdo) problems based on multi-hybridized software, adjoint-based and one-shot methods, uncertainty quantification and optimization, multidisciplinary design optimization, applications of game theory to industrial optimization problems, applications in structural and civil engineering optimum design and surrogate models based optimization methods in aerodynamic design.
Preparing For The Regents Examination: Geometry
by Richard J. Andres Joyce BernsteinTo prepare students for the New York State Regents Examination, Geometry.
Kinetic Simulations of Ion Transport in Fusion Devices
by Andrés de Bustos MolinaThis thesis deals with the problem of ion confinement in thermonuclear fusion devices. It is a topic of general interest, as it helps to understand via numerical simulations the ion confinement properties in complex geometries, in order to predict their behavior and maximize the performance of future fusion reactors. The main work carried out in this thesis is the improvement and exploitation of an existing simulation code called ISDEP. This code solves the so-called ion collisional transport in arbitrary plasma geometry, improving in this sense other existing codes. Additionally, it presents outstanding portability and scalability in distributed computing architectures, such as Grid or Volunteer Computing. The main physical results can be divided into two blocks. First, the study of 3D ion transport in ITER is presented. ITER is the largest fusion reactor (under construction) and most of the simulations so far assume the axis-symmetry of the device. Unfortunately, this symmetry is only an approximation because of the discrete number of magnetic coils used. ISDEP has shown, using a simple model of the 3D magnetic field, how the ion confinement is affected by this symmetry breaking. Secondly, ISDEP has been applied successfully to the study of fast ion dynamics in fusion plasmas. The fast ions, with energies much larger than the thermal energy, are a product of the device's heating system. Thus, a numerical predictive tool can be used to improve the heating efficiency. ISDEP has been combined with the FAFNER2 code to study such ions in stellarator (TJ-II, LHD) and tokamak (ITER) geometries. It has also been validated by experimental results. In particular, comparisons with the CNPA diagnostic in the TJ-II stellarator are remarkable.
Digital Health Technology for Better Aging: A multidisciplinary approach (Research for Development)
by Giuseppe Andreoni Cinzia MambrettiThis book describes the multidisciplinary approach needed to tackle better aging. Aging populations are one of the 21st century’s biggest challenges. National health systems are forced to adapt in order to provide adequate and affordable care. Innovation, driven by digital technology, is a key to improving quality of life and encouraging healthy living. Well-designed technology keeps people empowered, independent, and mobile; however, despite widespread adoption of ICT in day-to-day life, digital health technologies have yet to catch on. To this end, technology needs to be effective, usable, cheap, and designed to ensure the security of the managed data. In the era of mHealth, mobile technology, and social design, this book describes, in six sections, the collaboration of polytechnic know-how and social science and health sectors in the creation of a system for encouraging people to engage in healthy behavior and achieve a better quality of life.
Bayesian Methods for the Physical Sciences: Learning from Examples in Astronomy and Physics (Springer Series in Astrostatistics #4)
by Stefano Andreon Brian WeaverStatistical literacy is critical for the modern researcher in Physics and Astronomy. This book empowers researchers in these disciplines by providing the tools they will need to analyze their own data. Chapters in this book provide a statistical base from which to approach new problems, including numerical advice and a profusion of examples. The examples are engaging analyses of real-world problems taken from modern astronomical research. The examples are intended to be starting points for readers as they learn to approach their own data and research questions. Acknowledging that scientific progress now hinges on the availability of data and the possibility to improve previous analyses, data and code are distributed throughout the book. The JAGS symbolic language used throughout the book makes it easy to perform Bayesian analysis and is particularly valuable as readers may use it in a myriad of scenarios through slight modifications. This book is comprehensive, well written, and will surely be regarded as a standard text in both astrostatistics and physical statistics. Joseph M. Hilbe, President, International Astrostatistics Association, Professor Emeritus, University of Hawaii, and Adjunct Professor of Statistics, Arizona State University
Infoglut: How Too Much Information Is Changing the Way We Think and Know
by Mark AndrejevicToday, more mediated information is available to more people than at any other time in human history. New and revitalized sense-making strategies multiply in response to the challenges of "cutting through the clutter" of competing narratives and taming the avalanche of information. Data miners, "sentiment analysts," and decision markets offer to help bodies of data "speak for themselves"—making sense of their own patterns so we don’t have to. Neuromarketers and body language experts promise to peer behind people’s words to see what their brains are really thinking and feeling. New forms of information processing promise to displace the need for expertise and even comprehension—at least for those with access to the data. Infoglut explores the connections between these wide-ranging sense-making strategies for an era of information overload and "big data," and the new forms of control they enable. Andrejevic critiques the popular embrace of deconstructive debunkery, calling into question the post-truth, post-narrative, and post-comprehension politics it underwrites, and tracing a way beyond them.
Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology (Springer Optimization and Its Applications #121)
by Neculai AndreiThis book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.