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The Seven Pillars of Statistical Wisdom
by Stephen M. StiglerWhat gives statistics its unity as a science? Stephen Stigler sets forth the seven foundational ideas of statistics--a scientific discipline related to but distinct from mathematics and computer science and one which often seems counterintuitive. His original account will fascinate the interested layperson and engage the professional statistician.
Seventeenth-Century Indivisibles Revisited
by Vincent JullienThe tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign. These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods and highlights the rich relationships between them and integral calculus. The present book aims to be exhaustive since it analyzes the works of all major inventors of methods of indivisibles during the seventeenth century, from Kepler to Leibniz. It takes into account the rich existing literature usually devoted to a single author. This book results from the joint work of a team of specialists able to browse through this entire important episode in the history of mathematics and to comment it. The list of authors involved in indivisibles´ field is probably sufficient to realize the richness of this attempt; one meets Kepler, Cavalieri, Galileo, Torricelli, Gregoire de Saint Vincent, Descartes, Roberval, Pascal, Tacquet, Lalouvère, Guldin, Barrow, Mengoli, Wallis, Leibniz, Newton.
Several Complex Variables and the Geometry of Real Hypersurfaces
by John P. D'AngeloSeveral Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.
Several Real Variables
by Shmuel KantorovitzThis undergraduate textbook is based on lectures given bythe author on the differential and integral calculus of functions of severalreal variables. The book has a modern approach and includes topics such as: *The p-norms on vector space and theirequivalence *The Weierstrass and Stone-Weierstrassapproximation theorems *The differential as a linear functional;Jacobians, Hessians, and Taylor's theorem in several variables *The Implicit Function Theorem for a system ofequations, proved via Banach's Fixed Point Theorem *Applications to Ordinary Differential Equations *Line integrals and an introduction to surfaceintegrals This book features numerous examples, detailed proofs, aswell as exercises at the end of sections. Many of the exercises have detailedsolutions, making the book suitable for self-study. Several Real Variables will be useful for undergraduatestudents in mathematics who have completed first courses in linear algebra andanalysis of one real variable.
Severe Storms: Anatomy, Early Warning Systems and Aftermath in Changing Climate Scenarios
by Someshwar Das Wei-Kuo TaoThe book provides information on the observational aspects of the severe storms through satellite, radar, aircraft, and ground based network of stations and these issues are discussed in the first part of the book consisting of 8 chapters. The numerical modelling and data assimilation techniques are discussed in the second part of the book aimed at development of Early Warning Systems (12 chapters) and finally the outlook of the severe storms in a changing climate scenario, their socio-economic impacts and policies for disaster mitigation are discussed in the third part of the book consisting of 6 chapters. This book is of great interest to atmospheric scientists and other researchers, practitioners, policy and decision makers, international institutions, governmental and non-governmental organizations, educators, as well as students.
Sex, Drugs, and Body Counts: The Politics of Numbers in Global Crime and Conflict
by Peter Andreas Kelly M. GreenhillAt least 200,000-250,000 people died in the war in Bosnia. "There are three million child soldiers in Africa." "More than 650,000 civilians have been killed as a result of the U.S. occupation of Iraq." "Between 600,000 and 800,000 women are trafficked across borders every year." "Money laundering represents as much as 10 percent of global GDP." "Internet child porn is a $20 billion-a-year industry." These are big, attention-grabbing numbers, frequently used in policy debates and media reporting. Peter Andreas and Kelly M. Greenhill see only one problem: these numbers are probably false. Their continued use and abuse reflect a much larger and troubling pattern: policymakers and the media naively or deliberately accept highly politicized and questionable statistical claims about activities that are extremely difficult to measure. As a result, we too often become trapped by these mythical numbers, with perverse and counterproductive consequences.This problem exists in myriad policy realms. But it is particularly pronounced in statistics related to the politically charged realms of global crime and conflict-numbers of people killed in massacres and during genocides, the size of refugee flows, the magnitude of the illicit global trade in drugs and human beings, and so on. In Sex, Drugs, and Body Counts, political scientists, anthropologists, sociologists, and policy analysts critically examine the murky origins of some of these statistics and trace their remarkable proliferation. They also assess the standard metrics used to evaluate policy effectiveness in combating problems such as terrorist financing, sex trafficking, and the drug trade.
The Sexuality-Reproduction Nexus and the Three Demographic Transitions: An Integrative Framework (SpringerBriefs in Population Studies)
by Nikolai BotevThis monograph outlines an integrative framework that conceptualizes the role of relations of control in human reproduction and long-term population dynamics. It thereby draws on the demographic transition theory, sexuality studies, Foucault’s concept of bio-power and sexuality as key to social control, cognate concepts and theories, and on findings from demography, anthropology, archaeology and other disciplines. The framework is based on the premise that four demographic regimes can be identified over the course of human history. They are defined by the primary locus and modus of control over reproduction. The framework questions some of the basic postulates in population studies, including how demographic transitions are interpreted. As such this book contributes to the debate on the longer-term trends in population dynamics and the relations of power and control in human reproduction.
Shadow Algorithms Data Miner
by Andrew Woo Pierre PoulinShadow Algorithms Data Miner provides a high-level understanding of the complete set of shadow concepts and algorithms, addressing their usefulness from a larger graphics system perspective. It discusses the applicability and limitations of all the direct illumination approaches for shadow generation.With an emphasis on shadow fundamentals, the boo
Shallow and Deep Learning Principles: Scientific, Philosophical, and Logical Perspectives
by Zekâi ŞenThis book discusses Artificial Neural Networks (ANN) and their ability to predict outcomes using deep and shallow learning principles. The author first describes ANN implementation, consisting of at least three layers that must be established together with cells, one of which is input, the other is output, and the third is a hidden (intermediate) layer. For this, the author states, it is necessary to develop an architecture that will not model mathematical rules but only the action and response variables that control the event and the reactions that may occur within it. The book explains the reasons and necessity of each ANN model, considering the similarity to the previous methods and the philosophical - logical rules.
Shallow Learning vs. Deep Learning: A Practical Guide for Machine Learning Solutions (The Springer Series in Applied Machine Learning)
by Ömer Faruk Ertuğrul Josep M. Guerrero Musa YilmazThis book explores the ongoing debate between shallow and deep learning in the field of machine learning. It provides a comprehensive survey of machine learning methods, from shallow learning to deep learning, and examines their applications across various domains. Shallow Learning vs Deep Learning: A Practical Guide for Machine Learning Solutions emphasizes that the choice of a machine learning approach should be informed by the specific characteristics of the dataset, the operational environment, and the unique requirements of each application, rather than being influenced by prevailing trends. In each chapter, the book delves into different application areas, such as engineering, real-world scenarios, social applications, image processing, biomedical applications, anomaly detection, natural language processing, speech recognition, recommendation systems, autonomous systems, and smart grid applications. By comparing and contrasting the effectiveness of shallow and deep learning in these areas, the book provides a framework for thoughtful selection and application of machine learning strategies. This guide is designed for researchers, practitioners, and students who seek to deepen their understanding of when and how to apply different machine learning techniques effectively. Through comparative studies and detailed analyses, readers will gain valuable insights to make informed decisions in their respective fields.
Shallow Water Hydraulics
by Oscar Castro-Orgaz Willi H. HagerThis book presents the theory and computation of open channel flows, using detailed analytical, numerical and experimental results. The fundamental equations of open channel flows are derived by means of a rigorous vertical integration of the RANS equations for turbulent flow. In turn, the hydrostatic pressure hypothesis, which forms the core of many shallow water hydraulic models, is scrutinized by analyzing its underlying assumptions. The book’s main focus is on one-dimensional models, including detailed treatments of unsteady and steady flows. The use of modern shock capturing finite difference and finite volume methods is described in detail, and the quality of solutions is carefully assessed on the basis of analytical and experimental results.The book’s unique features include:• Rigorous derivation of the hydrostatic-based shallow water hydraulic models• Detailed treatment of steady open channel flows, including the computation of transcritical flow profiles• General analysis of gate maneuvers as the solution of a Riemann problem• Presents modern shock capturing finite volume methods for the computation of unsteady free surface flows• Introduces readers to movable bed and sediment transport in shallow water models• Includes numerical solutions of shallow water hydraulic models for non-hydrostatic steady and unsteady free surface flowsThis book is suitable for both undergraduate and graduate level students, given that the theory and numerical methods are progressively introduced starting with the basics. As supporting material, a collection of source codes written in Visual Basic and inserted as macros in Microsoft Excel® is available. The theory is implemented step-by-step in the codes, and the resulting programs are used throughout the book to produce the respective solutions.
Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
by Jordan EllenbergFrom the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. <P><P>How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. <P><P>If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. <P><P>Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry," from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how. <P><P><b>A New York Times Bestseller</b>
Shape (Math Counts: Updated Editions)
by Henry PluckroseAn introduction to capacity for the youngest readers!Math Counts series introduces young readers (grades K-3) to early math concepts. Real-world examples and corresponding photos make math concepts easy to grasp.Squares, triangles, circles... Shapes are all around us.
The Shape and Size of the Earth: A Historical Journey from Homer to Artificial Satellites
by Dino BoccalettiThis book describes in detail the various theories on the shape of the Earth from classical antiquity to the present day and examines how measurements of its form and dimensions have evolved throughout this period. The origins of the notion of the sphericity of the Earth are explained, dating back to Eratosthenes and beyond, and detailed attention is paid to the struggle to establish key discoveries as part of the cultural heritage of humanity. In this context, the roles played by the Catholic Church and the philosophers of the Middle Ages are scrutinized. Later contributions by such luminaries as Richer, Newton, Clairaut, Maupertuis, and Delambre are thoroughly reviewed, with exploration of the importance of mathematics in their geodetic enterprises. The culmination of progress in scientific research is the recognition that the reference figure is not a sphere but rather a geoid and that the earth’s shape is oblate. Today, satellite geodesy permits the solution of geodetic problems by means of precise measurements. Narrating this fascinating story from the very beginning not only casts light on our emerging understanding of the figure of the Earth but also offers profound insights into the broader evolution of human thought.
Shape and Space: Activities for Children with Mathematical Learning Difficulties
by Mel LeverFirst Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.
Shape in Medical Imaging: International Workshop, ShapeMI 2024, Held in Conjunction with MICCAI 2024, Marrakesh, Morocco, October 6, 2024, Proceedings (Lecture Notes in Computer Science #15275)
by Christian Wachinger Beatriz Paniagua Shireen Elhabian Gijs Luijten Jan EggerThis book constitutes the proceedings of the International Workshop on Shape in Medical Imaging, ShapeMI 2024, which took place in Marrakesh, Morocco, on October 6, 2024, held in conjunction with MICCAI 2024. The 16 full papers included in this book were carefully reviewed and selected from 24 submissions. They focus on shape and spectral analysis, geometric learning and modeling algorithms, and application-driven research.
The Shape of a Life: One Mathematician's Search for the Universe's Hidden Geometry
by Shing-Tung Yau Steve NadisA Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe.Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems.With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.“The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe“An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe“Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist
The Shape of Content: Creative Writing in Mathematics and Science
by Chandler Davis Marjorie Wikler Senechal Jan ZwickyThis book is a collection of creative pieces-poems, short stories, essays, play excerpts-that give shape to mathematical and scientific content. This book portrays by example how various people work creatively with ideas from mathematics and other sciences. Creative writing about the content of mathematics and science is rare, and creative writing
The Shape of Data: Geometry-Based Machine Learning and Data Analysis in R
by Colleen M. Farrelly Yaé Ulrich GabaThis advanced machine learning book highlights many algorithms from a geometric perspective and introduces tools in network science, metric geometry, and topological data analysis through practical application.Whether you&’re a mathematician, seasoned data scientist, or marketing professional, you&’ll find The Shape of Data to be the perfect introduction to the critical interplay between the geometry of data structures and machine learning.This book&’s extensive collection of case studies (drawn from medicine, education, sociology, linguistics, and more) and gentle explanations of the math behind dozens of algorithms provide a comprehensive yet accessible look at how geometry shapes the algorithms that drive data analysis.In addition to gaining a deeper understanding of how to implement geometry-based algorithms with code, you&’ll explore:Supervised and unsupervised learning algorithms and their application to network data analysisThe way distance metrics and dimensionality reduction impact machine learningHow to visualize, embed, and analyze survey and text data with topology-based algorithmsNew approaches to computational solutions, including distributed computing and quantum algorithms
The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions
by Shing-Tung Yau Steve NadisString theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau's penetrating thinking on where we've been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.
The Shape of Space (Chapman & Hall/CRC Pure and Applied Mathematics #249)
by Jeffrey R. WeeksMaintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
The Shape of Space: How To Visualize Surfaces And Three-dimensional Manifolds (Textbooks in Mathematics #Vol. 249)
by Jeffrey R. WeeksThe Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spaces—stretching students’ minds as they learn to visualize new possibilities for the shape of our universe. Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space. Features of the Third Edition: Full-color figures throughout "Picture proofs" have replaced algebraic proofs Simpler handles-and-crosscaps approach to surfaces Updated discussion of cosmological applications Intuitive examples missing from many college and graduate school curricula About the Author: Jeffrey R. Weeks is a freelance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology and—closest to his heart—exposition for the general public.
Shape Optimization And Optimal Design
by John Cagnol Michael P. Polis Jean-Paul ZolésioThis volume presents developments and advances in modelling passive and active control systems governed by partial differential equations. It emphasizes shape analysis, optimal shape design, controllability, nonlinear boundary control, and stabilization. The authors include essential data on exact boundary controllability of thermoelastic plates with variable transmission coefficients.
Shape Optimization, Homogenization and Optimal Control: DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 (International Series of Numerical Mathematics #169)
by Volker Schulz Diaraf SeckThe contributions in this volume give an insight into current research activities in Shape Optimization, Homogenization and Optimal Control performed in Africa, Germany and internationally. Seeds for collaboration can be found in the first four papers in the field of homogenization. Modelling and optimal control in partial differential equations is the topic of the next six papers, again mixed from Africa and Germany. Finally, new results in the field of shape optimization are discussed in the final international three papers.This workshop, held at the AIMS Center Senegal, March 13-16, 2017, has been supported by the Deutsche Forschungsgemeinschaft (DFG) and by the African Institute for Mathematical Sciences (AIMS) in Senegal, which is one of six centres of a pan-African network of centres of excellence for postgraduate education, research and outreach in mathematical sciences.
Shape Optimization Problems (Springer Optimization and Its Applications #164)
by Hideyuki AzegamiThis book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations.The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.