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The Role of the History of Mathematics in the Teaching/Learning Process: A CIEAEM Sourcebook (Advances in Mathematics Education)

by Gilles Aldon Peter Appelbaum Sixto Romero Sanchez Ana Serradó Bayés

This volume presents multiple perspectives on the uses of the history of mathematics for teaching and learning, including the value of historical topics in challenging mathematics tasks, for provoking teachers’ reflection on the nature of mathematics, curriculum development questions that mirror earlier pedagogical choices in the history of mathematics education, and the history of technological innovations in the teaching and learning of mathematics. An ethnomathematical perspective on the history of mathematics challenges readers to appreciate the role of mathematics in perpetuating consequences of colonialism. Histories of the textbook and its uses offer interesting insights into how technology has changed the fundamental role of curriculum materials and classroom pedagogies. History is explored as a source for the training of teachers, for good puzzles and problems, and for a broad understanding of mathematics education policy. Third in a series of sourcebooks from the International Commission for the Study and Improvement of Mathematics Teaching, this collection of cutting-edge research, stories from the field, and policy implications is a contemporary and global perspective on current possibilities for the history of mathematics for mathematics education. This latest volume integrates discussions regarding history of mathematics, history of mathematics education and history of technology for education that have taken place at the Commission's recent annual conferences.

The Routledge Handbook of African Demography

by Clifford O. Odimegwu Yemi Adewoyin

This handbook provides an authoritative and comprehensive overview of African population dynamics, variations, causes and consequences, demonstrating the real-world applications of research in policies and programmes.African demography has come of age. Over 50 years, the discipline has grown exponentially in the number of training and research institutions, specialist experts and academic output, all with an aim of addressing the enormous demographic challenges faced by the continent. The book draws on old and emerging analytical tools to explore the relationships between population dynamics and social, economic, cultural and political environments from African perspectives. Key topics include fertility, sexual behaviours, healthcare, ageing, mortality, migration, displacement, the causes and consequences of demographic changes and teaching and research developments in African demography.The Routledge Handbook of African Demography will be an essential resource for students and researchers of African demography, sociology, development and cultural studies.

The Routledge Handbook of the Economics of Ageing (Routledge International Handbooks)

by David E. Bloom Alfonso Sousa-Poza Uwe Sunde

Ageing populations pose some of the foremost global challenges of this century. Drawing on an international pool of scholars, this cutting-edge Handbook surveys the micro, macro and institutional aspects of the economics of ageing. Structured in seven parts, the volume addresses a broad range of themes, including health economics, labour economics, pensions and social security, generational accounting, wealth inequality and regional perspectives. Each chapter combines a succinct overview of the state of current research with a sketch of a promising future research agenda. This Handbook will be an essential resource for advanced students, researchers and policymakers looking at the economics of ageing across the disciplines of economics, demography, public policy, public health and beyond.

The Rules of Contagion: Why Things Spread--And Why They Stop

by Adam Kucharski

From ideas and infections to financial crises and fake news, an "utterly timely" look at why the science of outbreaks is the science of modern lifeThese days, whenever anything spreads, whether it's a YouTube fad or a political rumor, we say it went viral. But how does virality actually work? In The Rules of Contagion, epidemiologist Adam Kucharski explores topics including gun violence, online manipulation, and, of course, outbreaks of disease to show how much we get wrong about contagion, and how astonishing the real science is. Why did the president retweet a Mussolini quote as his own? Why do financial bubbles take off so quickly? Why are disinformation campaigns so effective? And what makes the emergence of new illnesses -- such as MERS, SARS, or the coronavirus disease COVID-19 -- so challenging? By uncovering the crucial factors driving outbreaks, we can see how things really spread -- and what we can do about it.Whether you are an author seeking an audience, a defender of truth, or simply someone interested in human social behavior, The Rules of Contagion is an essential guide to modern life.

The Run to the Pennant: A Multiple Equilibria Approach to Professional Sports Leagues

by Stephen T Easton Duane W Rockerbie

A number of clubs in professional sports leagues exhibit winning streaks over a number of consecutive seasons that do not conform to the standard economic model of a professional sports league developed by El Hodiri and Quirk (1994) and Fort and Quirk (1995). These clubs appear to display what we term "unsustainable runs", defined as a period of two to four seasons where the club acquires expensive talent and attempts to win a league championship despite not having the market size to sustain such a competitive position in the long run. The standard model predicts that clubs that locate in large economic markets will tend to acquire more talent, achieve more success on the field and at the box office than clubs that are located in small markets. This book builds a model that can allow unsustainable runs yet retains most of the features of the standard model. The model is then subjected to empirical verification. The new model we develop in the book has as its central feature the possibility of generating two equilibria for a club. In the empirical sections of the book, we use time-series analysis to attempt to test for the presence of unsustainable runs using historical data from National Football League (NFL), National Basketball Association (NBA), National Hockey League (NHL) and Major League Baseball (MLB). The multiple equilibria model retains all of the features of the standard model of a professional sports league that is accepted quite universally by economists, yet it offers a much richer approach by including an exploration of the effects of revenues that are earned at the league level (television, apparel, naming rights, etc.) that are then shared by all of the member clubs, making this book unique and of great interest to scholars in a variety of fields in economics.

The Runmakers: A New Way to Rate Baseball Players

by Frederick E. Taylor

Statistics are the lifeblood of baseball. Managers pore over batting averages to determine game day lineups and batting orders; high number of runs batted in and low earned run averages receive praise from the press, higher salaries from the front office, and love from fans; and the fate of fantasy baseball players rises and falls with each statistical change. The prominence of the RC/27 and other more complex, formula-driven stats has made numbers even more important to understanding and appreciating the game. For all these baseball buffs and more, Frederick E. Taylor provides a new measure of hitting prowess that just might be a game changer. Taylor's potential runs per game (PRG) measure accounts for batters getting on base, advancing runners, and driving in runs, and it separates leadoff and second batters from those in the middle of the order. Taylor introduces the measure, explains how it works, and applies it to players past and present. He breaks the history of major league baseball into eight eras based on differences in runs scored per game. He systematically—player-by-player and position-by-position—compares the results of the PRG measure to those drawn from other statistics, such as on-base percentage and slugging average. Taylor shows that PRG is more accurate and that career clutch hitting is a myth.Sabermetricians, baseball fans of all stripes, and anyone who earns a living from the sport will find a wealth of information and a whole new set of stats to obsess over in The Runmakers. Measuring baseball will never be the same.

The SAGE Dictionary of Quantitative Management Research

by Luiz Moutinho Graeme Hutcheson

A must-have reference resource for quantitative management researchers, the Dictionary contains over 100 entries covering the fundamentals of quantitative methodologies; covering both analysis and implementation and examples of use, as well as detailed graphics to aid understanding. Every entry features: -An introduction to the topic, -Key relevant features, -A worked example, -A concise summary and a selection of further reading suggestions -Cross-references to associated concepts within the dictionary

The SAGE Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences

by Robert Burke Johnson W. (William) Vogt

Written in a clear, readable style with a wide range of explanations and examples, this must-have dictionary reflects recent changes in the fields of statistics and methodology. Packed with new definitions, terms, and graphics, this invaluable resource is an ideal reference for researchers and professionals in the field and provides everything students need to read and understand a research report, including elementary terms, concepts, methodology, and design definitions, as well as concepts from qualitative research methods and terms from theory and philosophy.

The SAGE Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences

by Robert Burke Johnson W. (William) Vogt

Written in a clear, readable style with a wide range of explanations and examples, this must-have dictionary reflects recent changes in the fields of statistics and methodology. Packed with new definitions, terms, and graphics, this invaluable resource is an ideal reference for researchers and professionals in the field and provides everything students need to read and understand a research report, including elementary terms, concepts, methodology, and design definitions, as well as concepts from qualitative research methods and terms from theory and philosophy.

The SIML Filtering Method for Noisy Non-stationary Economic Time Series (SpringerBriefs in Statistics)

by Naoto Kunitomo Seisho Sato

In this book, we explain the development of a new filtering method to estimate the hidden states of random variables for multiple non-stationary time series data. This method is particularly helpful in analyzing small-sample non-stationary macro-economic time series. The method is based on the frequency-domain application of the separating information maximum likelihood (SIML) method, which was proposed by Kunitomo, Sato, and Kurisu (Springer, 2018) for financial high-frequency time series. We solve the filtering problem of hidden random variables of trend-cycle, seasonal, and measurement-error components and propose a method to handle macro-economic time series. The asymptotic theory based on the frequency-domain analysis for non-stationary time series is developed with illustrative applications, including properties of the method of Muller and Watson (2018), and analyses of macro-economic data in Japan. Vast research has been carried out on the use of statistical time series analysis for macro-economic time series. One important feature of the series, which is different from standard statistical time series analysis, is that the observed time series is an apparent mixture of non-stationary and stationary components. We apply the SIML method for estimating the non-stationary errors-in-variables models. As well, we discuss the asymptotic and finite sample properties of the estimation of unknown parameters in the statistical models. Finally, we utilize their results to solve the filtering problem of hidden random variables and to show that they lead to new a way to handle macro-economic time series.

The Scaling of Relaxation Processes (Advances in Dielectrics)

by Friedrich Kremer Alois Loidl

The dielectric properties especially of glassy materials are nowadays explored at widely varying temperatures and pressures without any gap in the spectral range from µHz up to the Infrared, thus covering typically 20 decades or more. This extraordinary span enables to trace the scaling and the mutual interactions of relaxation processes in detail, e.g. the dynamic glass transition and secondary relaxations, but as well far infrared vibrations, like the Boson peak. Additionally the evolution of intra-molecular interactions in the course of the dynamic glass transition is also well explored by (Fourier Transform) Infrared Spectroscopy. This volume within 'Advances in Dielectrics' summarizes this knowledge and discusses it with respect to the existing and often competing theoretical concepts.

The Schrödinger-Virasoro Algebra

by Claude Roger Jérémie Unterberger

This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure--the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key rôle in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrödinger operators.

The Schwarz Lemma (Dover Books on Mathematics)

by Sean Dineen

The Schwarz lemma is among the simplest results in complex analysis that capture the rigidity of holomorphic functions. This self-contained volume provides a thorough overview of the subject; it assumes no knowledge of intrinsic metrics and aims for the main results, introducing notation, secondary concepts, and techniques as necessary. Suitable for advanced undergraduates and graduate students of mathematics, the two-part treatment covers basic theory and applications. Starting with an exploration of the subject in terms of holomorphic and subharmonic functions, the treatment proves a Schwarz lemma for plurisubharmonic functions and discusses the basic properties of the Poincaré distance and the Schwarz-Pick systems of pseudodistances. Additional topics include hyperbolic manifolds, special domains, pseudometrics defined using the (complex) Green function, holomorphic curvature, and the algebraic metric of Harris. The second part explores fixed point theorems and the analytic Radon-Nikodym property.

The Science Girls

by Aki

Grab your goggles and join the Science Girls! We’re science girls! We love to learn.We gather, test, assess, discern!From the lab to the meadow to the greenhouse—the science girls have lots to see, lots to do, and lots to explore. Follow this troupe of busy girls as they have fun hypothesizing and analyzing in a day full of curiosity and excitement.

The Science and Art of Simulation: Trust in Science

by Michael M. Resch Andreas Kaminski Nico Formánek Ammu Joshy

Trust is a central pillar of the scientific enterprise. Much work in the philosophy of science can be seen as coping with the problem of establishing trust in a certain theory, a certain model, or even science as a whole. However, trust in science is threatened by various developments. With the advent of more complex models and the increasing usage of computer methods such as machine learning and computer simulation, it seems increasingly challenging to establish trust in science. How and on what basis can an appropriate trust in science be built? We are interested in how trust is established in such cases of increasing complexity (of models and communication) and what could be appropriate measures to alleviate doubt.

The Science of Cities and Regions: Lectures on Mathematical Model Design

by Alan Wilson

A 'science of cities and regions' is critical for meeting future challenges. The world is urbanising: huge cities are being created and are continuing to grow rapidly. There are many planning and development issues arising in different manifestations in countries across the globe. These developments can, in principle, be simulated through mathematical computer models which provide tools for forecasting and testing future scenarios and plans. These models can represent the functioning of cities and regions, predicting the spatial demography and the economy, the main flows such as journey to work or to services, and the mechanisms of future evolution. In this book, the main principles involved in the design of this range of models are articulated, providing an account of the current state of the art as well as future research challenges. Alan Wilson has over forty years working with urban and regional models and has contributed important discoveries. He has distilled this experience into what serves as both an introduction and a review of the research frontier. Topics covered include the Lowry model, the retail model, principles of account-based models and the methods rooted in Boltzmann-style statistical modelling and the Lotka-Volterra approach to system evolution. Applications range from urban and regional planning to wars and epidemics.

The Science of Conjecture: Evidence and Probability before Pascal

by James Franklin

How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates.The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk.

The Science of Influencers and Superspreaders: Using Networks and Artificial Intelligence to Understand Fake News, Pandemics, Markets, and the Brain (Understanding Complex Systems)

by Hernán A. Makse Marta Zava

This book explores the identification of influencers in complex networks, bridging theoretical approaches with practical applications across diverse fields. It examines interdisciplinary complex systems, including online social media, biological networks, brain networks, socioeconomic and financial systems, and ecosystems. The research presented aims to benefit scientists in relevant areas and inspire new scientific inquiries, potentially advancing the field of influencer identification. In this context, 'influencer' serves as an umbrella term for essential, core, or central nodes within any complex network. The book investigates various manifestations of influencers, such as key figures in social media, critical nodes in genetic and brain networks, keystone species in ecosystems, systemically important banks in financial markets, and disease superspreaders. These diverse scenarios are approached by mapping the influencer identification problem to challenges in physics or computer science. The book caters to readers at three distinct levels: 1. Those seeking mathematically rigorous theories of influencers will find Chapter 2 particularly valuable, as it delves into the mathematical foundations of influencer identification algorithms. Subsequent chapters explore the application of these theories across various disciplines. 2. Data scientists interested in implementing these algorithms in their research and practical work will find relevant information throughout the book. 3. Professionals in finance, marketing, politics, and social media, as well as readers curious about the intersection of big data, influencers, and AI, will gain insights into how these tools can enhance decision-making processes. These readers are encouraged to focus on the introduction and chapters most relevant to their fields, while briefly reviewing the more technical sections. By offering this multi-layered approach, the book aims to provide a comprehensive understanding of influencer identification in complex networks, from theoretical foundations to real-world applications across various domains.

The Science of Measurement: A Historical Survey

by Herbert Arthur Klein

"Klein is both a skilled reporter and a wide-ranging humanistic scholar. The book is popular and learned, witty and serious, literary and mathematical -- always solid and entertaining." -- Los Angeles Times.Although the topic of measurement might seem to lend itself to a dry-as-dust treatment, this book is just the opposite: an engrossing, easy-to-read study that treats a multifaceted topic with wit, imagination, and wide-ranging scholarship.Metrology, the science of measurement, usually concerns itself with length, weight, volume, temperature, and time, but in this comprehensive work the topic also encompasses nuclear radiation, thermal power, light, pressure, sound, and many other areas. Representing nearly ten years of research effort, The Science of Measurement is considered a definitive book on the concepts and units by which we measure everything in our universe. Nontechnical in its approach, it is not only completely accessible to the general reader but as entertaining and fun to read as it is informative and comprehensive. " . . . not concerned only with problems of measuring the limits of space or the size of the proton. It is filled with interesting digressions. Not a book for daydreaming, but a book for the curious. Klein's survey of the units and concepts by which we measure everything in the universe helps us understand that universe much better." -- Boston Herald Advertiser

The Science of Sci-Fi Music (Science and Fiction)

by Andrew May

The 20th century saw radical changes in the way serious music is composed and produced, including the advent of electronic instruments and novel compositional methods such as serialism and stochastic music. Unlike previous artistic revolutions, this one took its cues from the world of science. Creating electronic sounds, in the early days, required a well-equipped laboratory and an understanding of acoustic theory. Composition became increasingly “algorithmic”, with many composers embracing the mathematics of set theory. The result was some of the most intellectually challenging music ever written – yet also some of the best known, thanks to its rapid assimilation into sci-fi movies and TV shows, from the electronic scores of Forbidden Planet and Dr Who to the other-worldly sounds of 2001: A Space Odyssey.This book takes a close look at the science behind "science fiction" music, as well as exploring the way sci-fi imagery found its way into the work of musicians like Sun Ra and David Bowie, and how music influenced the science fiction writings of Philip K. Dick and others.

The Science of Soccer

by John Wesson

Updated and revised throughout, this new edition of The Science of Soccer applies scientific analysis to football, giving us the answers to questions like "what's the chance of a team that wins the Premiership also winning the Cup? Can you predict how many goals will be scored? What's the best height for footballers? Is the team that wins the league the best team?" Starting with a qualitative description of the basic physics that relate to the ball and its bounce, the author then moves through kicks and throws, to a simple account of the more complex physics of a ball in flight. Fulfilling your scientific curiosity, this book uncovers aspects of the game that are not normally discussed. It includes a look at game theory, how the rules affect the flow and enjoyment of the game, unusual statistics about players, and an insight into the economics of the game. For those with a more mathematical interest in the physics, the final chapter provides a readable account of the theory behind the beautiful game. Features: Accessible to anyone interested in understanding more about the science behind the sport Updated throughout, with new content on transfer fees, wages, and the top goal-scorers Discusses topics not explored in current literature, including rudimentary game theory

The Science of State Power in the Habsburg Monarchy, 1790-1880 (New Perspectives on Central and Eastern European Studies #5)

by Borbala Zsuzsanna Török

The formation of modern European states during the long 19th century was a complicated process, challenged by the integration of widely different territories and populations. The Science of State Power in the Habsburg Monarchy, 1790-1880 builds on recent research to investigate the history of statistics as an overlooked part of the sciences of the state in Habsburg legal education as well as within the broader public sphere. By exploring the practices and social spaces of statistics, author Borbála Zsuzsanna Török uncovers its central role in imagining the composite Habsburg Monarchy as a modern and unified administrative space.

The Scottish Book

by R. Daniel Mauldin

The second edition of this book updates and expands upon a historically important collection of mathematical problems first published in the United States by Birkhäuser in 1981. These problems serve as a record of the informal discussions held by a group of mathematicians at the Scottish Café in Lwów, Poland, between the two world wars. Many of them were leaders in the development of such areas as functional and real analysis, group theory, measure and set theory, probability, and topology. Finding solutions to the problems they proposed has been ongoing since World War II, with prizes offered in many cases to those who are successful. In the 35 years since the first edition published, several more problems have been fully or partially solved, but even today many still remain unsolved and several prizes remain unclaimed. In view of this, the editor has gathered new and updated commentaries on the original 193 problems. Some problems are solved for the first time in this edition. Included again in full are transcripts of lectures given by Stanislaw Ulam, Mark Kac, Antoni Zygmund, Paul Erdös, and Andrzej Granas that provide amazing insights into the mathematical environment of Lwów before World War II and the development of The Scottish Book. Also new in this edition are a brief history of the University of WrocÅ,aw's New Scottish Book, created to revive the tradition of the original, and some selected problems from it. The Scottish Book offers a unique opportunity to communicate with the people and ideas of a time and place that had an enormous influence on the development of mathematics and try their hand on the unsolved problems. Anyone in the general mathematical community with an interest in the history of modern mathematics will find this to be an insightful and fascinating read.

The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel

by I. Grattan-Guinness

While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.

The Search for Method in STEAM Education

by Jaime E. Martinez

This book explores various approaches to building a positive interdisciplinary STEAM (science, technology, engineering, arts and math) learning environment, as described by educators across the K-20 educational ladder. Crucial to their success, Martinez finds, is the playful and performatory approach they employ in their teaching. Their practices are creative, improvisational, and inclusive, and are shared in detail through illustrations and interviews. Throughout the book, the author explores a Vygotskian cultural performatory approach to creating interdisciplinary STEAM learning environments, drawing out the history of this approach and its success in fostering collaboration, creativity, leadership, and communication skills, as well as its effect on social, emotional, and cognitive growth in both formal and informal educational settings.

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