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The Lefschetz Properties
by Junzo Watanabe Yasuhide Numata Toshiaki Maeno Hideaki Morita Akihito Wachi Tadahito HarimaThis is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically.
The Legacy of Alladi Ramakrishnan in the Mathematical Sciences
by Krishnaswami Alladi John R. Klauder Calyampudi R. RaoIn the spirit of Alladi Ramakrishnan's profound interest and contributions to three fields of science -- Mathematics, Statistics, and Physics -- this volume contains invited surveys and research articles from prominent members of these communities who also knew Ramakrishnan personally and greatly respected his influence in these areas of science. Historical photos, telegrams, and biographical narratives of Alladi Ramakrishnan's illustrious career of special interest are included as well.
The Legacy of Felix Klein (ICME-13 Monographs)
by Michael Neubrand Hans-Georg Weigand Gert Schubring William McCallum Marta MenghiniThis open access book provides an overview of Felix Klein’s ideas, highlighting developments in university teaching and school mathematics related to Klein’s thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein’s ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein’s ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint.
The Legacy of Tatjana Afanassjewa: Philosophical Insights from the Work of an Original Physicist and Mathematician (Women in the History of Philosophy and Sciences #7)
by Jos Uffink Giovanni Valente Charlotte Werndl Lena ZuchowskiThis book presents a collection of essays that explore the life and works of Tatjana Afanassjewa (1876–1964), a Russian–Dutch physicist–mathematician. Readers will discover a scientist whose work on the foundations of thermodynamics significantly influenced the field itself as well as the philosophy of physics. This book highlights the philosophical consequences of her work in physics and mathematics and discusses historical aspects of her writings on the foundations of physics. In addition, it features English translations and critical reviews of key selections from her texts.First and foremost, the book highlights the numerous contributions that Afanassjewa made to the field. In particular, the authors examine her work on the foundations of thermodynamics and statistical physics, starting in the 1920s and extending to 1956, well after the untimely death of her husband in 1933. They also explore her almost entirely forgotten work on the didactics of mathematics. In addition, they discuss her influential collaboration with her husband, the Austrian physicist Paul Ehrenfest (1880–1933).The portrait that emerges is that of a highly original physicist and mathematician, whose legacy continues to influence scientists and philosophers today and whose lesser-known works deserve more attention than they have received. Readers will find a rich body of work that continues to this day to yield insights into the foundations of physics and mathematics.
The Lemonade War (Into Reading, Trade Book #2)
by Jacqueline DaviesNIMAC-sourced textbook <p><p> Fourth-grader Evan Treski is people-smart. He’s good at talking with people, even grownups. His younger sister, Jessie, on the other hand, is math-smart, but not especially good with people. So when the siblings’ lemonade stand war begins, there really is no telling who will win—or even if their fight will ever end. Brimming with savvy marketing tips for making money at any business, definitions of business terms, charts, diagrams, and even math problems, this fresh, funny, emotionally charged novel subtly explores how arguments can escalate beyond anyone’s intent.
The Life-Changing Magic of Numbers
by Bobby SeagullIf you found maths lessons at school irrelevant and boring, that’s because you didn’t have a teacher like Bobby Seagull.***As seen on Monkman & Seagull's Genius Guide to Britain*** Long before his rise to cult fandom on University Challenge, Bobby Seagull was obsessed with numbers. They were the keys that unlocked the randomness of football results, the beauty of art and the best way to get things done. In his absorbing book, Bobby tells the story of his life through numbers and shows the incredible ways maths can make sense of the world around us. From magic shows to rap lyrics, from hobbies to outer space, from fitness to food – Bobby’s infectious enthusiasm for numbers will change how you think about almost everything. Told through fascinating stories and insights from Bobby’s life, and with head-scratching puzzles in every chapter, you’ll never look at numbers the same way again.
The Limits of Resolution (Series in Optics and Optoelectronics)
by Geoffrey de Villiers E. Roy Pike"This beautiful book can be read as a novel presenting carefully our quest to get more and more information from our observations and measurements. Its authors are particularly good at relating it." --Pierre C. Sabatier "This is a unique text - a labor of love pulling together for the first time the remarkably large array of mathematical and statistical techniques used for analysis of resolution in many systems of importance today – optical, acoustical, radar, etc…. I believe it will find widespread use and value." --Dr. Robert G.W. Brown, Chief Executive Officer, American Institute of Physics "The mix of physics and mathematics is a unique feature of this book which can be basic not only for PhD students but also for researchers in the area of computational imaging." --Mario Bertero, Professor, University of Geneva "a tour-de-force covering aspects of history, mathematical theory and practical applications. The authors provide a penetrating insight into the often confused topic of resolution and in doing offer a unifying approach to the subject that is applicable not only to traditional optical systems but also modern day, computer-based systems such as radar and RF communications." --Prof. Ian Proudler, Loughborough University "a ‘must have’ for anyone interested in imaging and the spatial resolution of images. This book provides detailed and very readable account of resolution in imaging and organizes the recent history of the subject in excellent fashion.… I strongly recommend it." --Michael A. Fiddy, Professor, University of North Carolina at Charlotte This book brings together the concept of resolution, which limits what we can determine about our physical world, with the theory of linear inverse problems, emphasizing practical applications. The book focuses on methods for solving illposed problems that do not have unique stable solutions. After introducing basic concepts, the contents address problems with "continuous" data in detail before turning to cases of discrete data sets. As one of the unifying principles of the text, the authors explain how non-uniqueness is a feature of measurement problems in science where precision and resolution is essentially always limited by some kind of noise.
The Limits to Growth: A Report for the Club of Rome's Project on the Predicament of Mankind
by Donella H. Meadows Dennis L. Meadows Jorgen Randers William W. Behrens IIIA report from The Club of Rome, an informal organization that has been aptly described as an "invisible college." Its purposes are to foster understanding of the varied but interdependent components-- economic, political, natural, and social-- that make up the global system in which we all live; to bring that new understanding to the attention of policy-makers and the public worldwide; and in this way to promote new policy initiatives and action. This report caused much controversy when it was published.
The Lineaments of Population Policy in India: Women and Family Planning
by Mohan RaoIndia is the first country in the world to have an official programme for family planning that commenced in 1952. It has also seen a strong women’s movement to assert reproductive and contraceptive rights. This book brings to the fore several contestations and negotiations between public policy and the women’s movement in India. The comprehensive volume puts together key documents from archival records and authoritative sources, and traces the contours that have marked and defined the population policy in India as well as rights issues for women. <P><P>A major intervention in the field, this book will be indispensable for scholars and researchers in public policy, public health, demography, gender studies, social policy, development studies, sociology, social justice, human rights, politics and those interested in the study of modern India.
The Linear Algebra a Beginning Graduate Student Ought to Know
by Jonathan S. GolanLinear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate course is insufficient for graduate study. This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader. In the latest edition, new major theorems have been added, as well as many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.
The Linear Model and Hypothesis
by George SeberThis book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The approach used is a geometrical one based on the concept of projections and their associated idempotent matrices, thus largely avoiding the need to involvematrix ranks. It is shown that all the hypotheses encountered are either linear or asymptotically linear, and that all the underlying models used are either exactly or asymptotically linear normal models. This equivalence can be used, for example, to extend the concept of orthogonality to other models in the analysis of variance, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.
The Literature and Study of Urban and Regional Planning (Routledge Revivals)
by Brenda WhiteFirst published in 1974, The Literature and Study of Urban and Regional Planning discusses the processes of spatial planning and the range of subject knowledge which is required to contribute to it. It describes the physical forms in which the literature relating to spatial planning is usually presented and the ways in which this literature is made available in different types of organization. The author gives details of the most useful libraries whose facilities are available to students, and of the research which is being undertaken into the principal problems of planning information. The second part of the book consists of a subject bibliography, divided for ease of reference into twenty-six sections each concerned with a component part of spatial planning and containing annotated references to books, official publications, developmental plans, legislation, and other material. This book will be of interest to students of sociology and urban studies.
The Little Book of Data: Understanding the Powerful Analytics that Fuel AI, Make or Break Careers, and Could Just End Up Saving the World
by Justin EvansData is not about number crunching. It&’s about ideas. And when used properly (read: ethically), it is the problem solver of our time.Yet many savvy people seem to be in data denial: they don&’t think they need to understand data, or it&’s too complicated, or worse, using it is somehow unethical. Yet as data and AI (just an accelerated way to put data to work) move to the center of professional and civic life, every professional and citizen needs to harness this power.In The Little Book of Data, each chapter illustrates one of the core principles of solving problems with data by featuring an expert who has solved a big problem with data—from the entrepreneur creating a &“loneliness score&” to the epidemiologist trying to save lives by finding disease &“hotspots.&”The stories are told in a fast-moving, vivid, sometimes comic style, and cover a wide frame of reference from adtech to climate tech, the bubonic plague, tiny submarines, genomics, railroads, bond ratings, and meat grading. (That&’s right. Meat.)Along the way Evans injects lessons from his own career journey and offers practical thought-starters for readers to apply to their own organizations.By reading The Little Book of Data, you will achieve the fluency to apply your data superpowers to your own mission and challenges—and you will have fun along the way.You will be, in other words, a data person.
The Little Book of Mathematical Principles, Theories & Things
by Robert SolomonThis little book makes serious math simple—with more than 120 laws, theorems, paradoxes, and more explained in jargon-free terms.The Little Book of Mathematical Principles provides simple, clear explanations for the principles, equations, paradoxes, laws, and theorems that form the basis of modern mathematics. It is a refreshingly engaging tour of Fibonacci numbers, Euclid's Elements, and Zeno's paradoxes, as well as other fundamental principles such as chaos theory, game theory, and the game of life.Renowned mathematics author Dr. Robert Solomon simplifies the ancient discipline of mathematics and provides fascinating answers to intriguing questions, such as: What is the greatest pyramid?, What is a perfect number?, and Is there a theory for stacking oranges?
The Little Data Book on Gender in Africa 2012/13
by World BankThe Little Data Book on Gender in Africa 2012/13 provides a summary collection of gender statistics on Africa available in one volume. It contains 60 indicators, covering 53 African countries. Additional data may be found on the companion CD-ROM or online, covering about 1,700 indicators from 1961 to 2011. Key themes are : - Basic demographic indicators- Education- Health- Labor force and wages- Women's empowermentDesigned to provide all those interested in Africa with quick reference and a reliable set of data to monitor development programs and aid flows in the region, this is an invaluable pocket edition reference tool for analysts and policy makers who want a better understanding of the economic and social developments occurring in Africa. For free access to Africa Development Indicators online, please visit http://data. worldbank. org/data-catalog.
The Little Green Math Book: 30 Powerful Principles for Building Math and Numeracy Skills
by Brandon Royal<p>The Little Green Math Book reads like a collection of math recipes to help us blend problems, principles, and approaches in creating our own lineup of splendid math cuisine. The book's four chapters include: (1) Basic Numeracy Ingredients, (2) Wonderful Math Recipes, (3) Favorite Numeracy Dishes, and (4) Special Math Garnishments. Along with 30 of the most fundamental, recurring math principles and rules, readers will find a three-tier system to rate the difficulty level of all 100 problems – one chili (“mild”), two chilies (“hot”), and three chilies (“very hot”). <p>Fine-tune your numerical mindset with a quantitative review that serves as a refresher course and as a tool for perceiving math in a new way. Whether you’re a high school or college student, test-prep candidate, or working professional, this book’s wealth of explanations and insights makes it a perfect learning companion.</p>
The Logic Of Infinity
by Barnaby SheppardFew mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.
The Logic of Chance: An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Logical Bearings And Its Ap (Dover Books on Mathematics)
by John VennNo mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity, readability, and sheer charm. Its author, British logician John Venn (1834-1923), popularized the famous Venn Diagrams that are commonly used for teaching elementary mathematics. In The Logic of Chance, he employs the same directness that makes his diagrams so effective.The three-part treatment commences with an overview of the physical foundations of the science of probability, including surveys of the arrangement and formation of the series of probability; the origin or process of causation of the series; how to discover and prove the series; and the conception of randomness. The second part examines the logical superstructure on the basis of physical foundations, encompassing the measurement of belief; the rules of inference in probability; the rule of succession; induction; chance, causation, and design; material and formal logic; modality; and fallacies. The final section explores various applications of the theory of probability, including such intriguing aspects as insurance and gambling, the credibility of extraordinary stories, and approximating the truth by means of the theory of averages.
The Logic of Miracles: Making Sense of Rare, Really Rare, and Impossibly Rare Events
by Laszlo Mero&“Consistently surprising…The Logic of Miracles breaks new ground in the relationship of probability, fate, and the ability of human beings to behold them."—Douglas Rushkoff, author of Team Human We live in a more turbulent world than we like to think. Yet the science we use to analyze economic, financial, and statistical events mostly disregards the world&’s essentially chaotic nature. We need to get used to the idea that wildly improbable events are actually part of the natural order. Here, a renowned mathematician and psychologist explains how the wild and mild worlds (which he names Wildovia and Mildovia) coexist, and that different laws apply to each. Even if we live in an ultimately wild universe, he argues, we&’re better off pretending that it obeys Mildovian laws. Doing so may amount to a self-fulfilling prophecy and create an island of predictability in a very rough sea. Perched on the ragged border between economics and complexity theory, the author proposes to extend the reach of science to subjects previously considered outside its grasp: the unpredictable, unrepeatable, highly improbable events we commonly call &“miracles.&” &“It's hard to see how miracles and math fit together. But if you accept László Mérö's invitation, you will enter a world where miracles are normal and the predictable sits side-by-side with the unpredictable. Along the way, he unveils the mathematics of the stock market and explains, in a playful yet mathematically accurate way, the roots of market crashes and earthquakes, and why &‘black swans&’ are not just calamities but opportunities.&”—Albert-László Barabási, author of Linked
The Logic of Poverty: The Case of the Brazilian Northeast (Routledge Revivals)
by Simon MitchellFirst published in 1981, The Logic of Poverty consists of eight essays that share at least one assumption: that Northeast Brazil provides a startling example of inhumane economic development. The contributors have all worked in the area, and know it at first hand. They look at rural structure and the role of the unemployed ‘reserve army’, the state of the sugar industry, the ineffectiveness of the irrigation schemes, the stagnation in the fishing sector, the lack of credit available to peasants and the role of SUDENE, the first development agency in the region. Together they paint a picture of poverty and of the factors that allow it to continue, and they place that poverty in the context of the wider economy of Brazil, relating it to the extraordinary transformation that has been called ‘the Brazilian miracle’. This book will be of interest to students of geography, anthropology, economics and sociology.
The Logic, Philosophy, and History of the Lambda-Calculus: Theory and Applications (History of Analytic Philosophy)
by Levis ZerpaThis is the first book focused on the logico-philosophical aspects of the lambda-calculus since the inception of the field in 1932 in the pioneering work of Alonzo Church. The book starts a new field called “lambda-philosophy”: a branch of logic-based analytic philosophy in the tradition of Frege and Russell, directly constructed from the lambda-calculus. Another innovation of the book is a new graphical and intuitive logico-mathematical notation for the lambda-calculus called “the container notation”. The book covers in detail some episodes of the history of the subject, including three comparative studies of the lambda-calculus with Viète's algebra, Descartes' analytic geometry, and Wittgenstein’s Tractatus. A didactic approach to the logico-mathematical aspects of the lambda-calculus, partially based on cognitive science, provides the technical basis for the analysis. In this way, the book provides a systematic and coherent treatment of diverse logico-philosophical aspects and applications of the lambda-calculus as part of the platform offered by lambda-philosophy. The book includes the following: a detailed treatment of the ambiguities of the concept of function (under the traditional or Euler’s notation); an elucidation of the notion of transformative philosophical analysis; an account of Church’s methodology which shows that the lambda-calculus is an adequate solution to the problem of a philosophical analysis of functions as rules of computation; a didactic treatment of the formal aspects of the lambda-calculus through the container notation; and diverse arithmetical and logical examples of the container notation. The book questions a dogma of algorithmic thinking by arguing that the lambda-calculus is more intuitive and natural than Turing machines. The Logic, Philosophy, and History of the Lambda-Calculus is essential reading for all scholars and researchers of the history of analytic philosophy and especially those focussing on logic-based analytic philosophy.
The Logical Foundations of Scientific Theories: Languages, Structures, and Models (Routledge Studies in the Philosophy of Mathematics and Physics)
by Decio Krause Jonas R.B. ArenhartThis book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science.
The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age
by Paul J. NahinHow two pioneers of math and technology ushered in the computer revolutionBoolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use—from our computers and cars, to home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer, Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras—mathematician and philosopher George Boole and electrical engineer and pioneering information theorist Claude Shannon—advanced Boolean logic and became founding fathers of the electronic communications age. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of modern digital machines, in order to explore computing and its possible limitations in the twenty-first century and beyond.
The Long Baby Boom: An Optimistic Vision for a Graying Generation
by Jeff Goldsmith“Important, timely . . . should be the basis for a national debate about how we each want to grow older and what kind of society we want to do it in.” —John Rother, Group Executive Officer of Policy and Strategy, AARPThe aging of the boomer generation has unleashed a veritable tidal wave of gloomy punditry, advertising for financial services, and forecasts of impending national bankruptcy. In The Long Baby Boom, Jeff Goldsmith counters the catastrophic predictions with a far more optimistic scenario.Drawing on evidence that most baby boomers plan on working long past age sixty-five, Goldsmith argues that they will have a constructive impact on society. By assuming a much larger portion of the financial burden of their own retirement and health costs, they will help preserve Social Security and Medicare for the less fortunate—and for successive generations.The Long Baby Boom is the first comprehensive forecast of baby boomers’ career plans, health trends, and cultural and political values. Goldsmith’s pro-work, pro-savings, pro-health social policy emphasizes personal responsibility without ripping the social safety net. Constructive and innovative, The Long Baby Boom doesn’t promise a cloud-free future, but it does reassure us that the sky isn’t falling.
The Longevity Dividend: Later Life, Lifelong Learning and Productive Societies (International Perspectives on Aging #39)
by Satya BrinkThis book offers global evidence about the increasing longevity, its consequences and its potential for societal benefits. Based on statistics, academic literature, policy initiatives and numerous country experiences, it explains the interconnected effects of a longer later life, lifelong learning and more productive societies. This larger picture shows how the future can be managed by making strategic choices today. Choosing the right policies allows gaining the maximum benefits from the longevity dividend for current and future generations. This book explains how investing in lifelong learning can enrich the longevity dividend. It gives valuable insights for policy advisors, decision makers, researchers, health professionals, practitioners, students of aging and late life educators.