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| five equations that changed the world chapter summary: Seventeen Equations that Changed the World Ian Stewart, 2012-02-02 From Newton's Law of Gravity to the Black-Scholes model used by bankers to predict the markets, equations, are everywhere -- and they are fundamental to everyday life.Seventeen Equations that Changed the World examines seventeen ground-breaking equations that have altered the course of human history. He explores how Pythagoras's Theorem led to GPS and Satnav; how logarithms are applied in architecture; why imaginary numbers were important in the development of the digital camera, and what is really going on with Schrödinger's cat. Entertaining, surprising and vastly informative, Seventeen Equations that Changed the World is a highly original exploration -- and explanation -- of life on earth. |
| five equations that changed the world chapter summary: The Ten Equations That Rule the World David Sumpter, 2021-08-24 Is there a secret formula for getting rich? For going viral? For deciding how long to stick with your current job, Netflix series, or even relationship? This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthfully, and see through scaremongering. They are known by only the privileged few - until now. With wit and clarity, mathematician David Sumpter shows that it isn't the technical details that make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone can learn. Empowering and illuminating, The Ten Equations shows how math really can change your life. |
| five equations that changed the world chapter summary: The Great Equations: Breakthroughs in Science from Pythagoras to Heisenberg Robert P. Crease, 2010-01-18 Any reader who aspires to be scientifically literate will find this a good starting place. —Publishers Weekly While we may be familiar with some of science’s greatest equations, we may not know that each and every equation emerged not in Eureka! moments but in years of cultural developments and scientific knowledge. With vignettes full of humor, drama, and eccentricity, philosopher and science historian Robert P. Crease shares the stories behind ten of history’s greatest equations, from the first equation, 1 + 1 = 2, which promises a rational, well-ordered world, to Heisenberg’s uncertainty principle, which reveals the limitations of human knowledge. For every equation, Crease provides a brief account of who discovered it, what dissatisfactions lay behind its discovery, and what the equation says about the nature of our world. |
| five equations that changed the world chapter summary: Bridges to Infinity Michael Guillen, 1983 This book is an endlessly fascinating journey through a mathematician's looking glass. |
| five equations that changed the world chapter summary: From ER to E.T. Rajeev Bansal, 2017-01-04 This book covers the study of electromagnetic wave theory and describes how electromagnetic technologies affect our daily lives. From ER to ET: How Electromagnetic Technologies Are Changing Our Lives explores electromagnetic wave theory including its founders, scientific underpinnings, ethical issues, and applications through history. Utilizing a format of short essays, this book explains in a balanced, and direct style how electromagnetic technologies are changing the world we live in and the future they may create for us. Quizzes at the end of each chapter provide the reader with a deeper understanding of the material. This book is a valuable resource for microwave engineers of varying levels of experience, and for instructors to motivate their students and add depth to their assignments. In addition, this book: Presents topics that investigate all aspects of electromagnetic technology throughout history Explores societal and global issues that relate to the field of electrical engineering (emphasized in current ABET accreditation criteria) Includes quizzes relevant to every essay and answers which explain technical perspectives Rajeev Bansal, PhD, is a professor of Electrical and Computer Engineering at the University of Connecticut. He is a member of IEEE and the Connecticut Academy of Science and Engineering. He is a Fellow of the Electromagnetics Academy. His editing credits include Fundamentals of Engineering Electromagnetics and Engineering Electromagnetics: Applications. Dr. Bansal contributes regular columns to IEEE Antennas and Propagation Magazine and IEEE Microwave Magazine. |
| five equations that changed the world chapter summary: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning. |
| five equations that changed the world chapter summary: An Introduction to Difference Equations Saber N. Elaydi, 2013-06-29 This book grew out of lecture notes I used in a course on difference equations that I taught at Trinity University for the past five years. The classes were largely pop ulated by juniors and seniors majoring in Mathematics, Engineering, Chemistry, Computer Science, and Physics. This book is intended to be used as a textbook for a course on difference equations at the level of both advanced undergraduate and beginning graduate. It may also be used as a supplement for engineering courses on discrete systems and control theory. The main prerequisites for most of the material in this book are calculus and linear algebra. However, some topics in later chapters may require some rudiments of advanced calculus. Since many of the chapters in the book are independent, the instructor has great flexibility in choosing topics for the first one-semester course. A diagram showing the interdependence of the chapters in the book appears following the preface. This book presents the current state of affairs in many areas such as stability, Z-transform, asymptoticity, oscillations and control theory. However, this book is by no means encyclopedic and does not contain many important topics, such as Numerical Analysis, Combinatorics, Special functions and orthogonal polyno mials, boundary value problems, partial difference equations, chaos theory, and fractals. The nonselection of these topics is dictated not only by the limitations imposed by the elementary nature of this book, but also by the research interest (or lack thereof) of the author. |
| five equations that changed the world chapter summary: Instant Physics Tony Rothman, 1995-02-21 For everyone who breaks out in a sweat at the thought of thermodynamics or quantum mechanics, now there's a concise and comprehensive text that's the ideal remedial remedy--guaranteed to produce advanced results. Filled with features such as chapter summaries, a who's who list, and biographical and historical tidbits, plus illustrations, photos, equations, and diagrams. |
| five equations that changed the world chapter summary: Evolution on Planet Earth Lynn Rothschild, Adrian Lister, 2003-06-19 Driving evolution forward, the Earth's physical environment has challenged the very survival of organisms and ecosystems throughout the ages. With a fresh new perspective, Evolution on Planet Earth shows how these physical realities and hurdles shaped the primary phases of life on the planet. The book's thorough coverage also includes chapters on more proximate factors and paleoenvironmental events that influenced the diversity of life. A team of notable ecologists, evolutionary biologists, and paleontologists join forces to describe drifting continents, extinction events, and climate change -- important topics that continue to shape Earth's inhabitants to this very day. In a world where global change has become an international issue, this book provides a several billion-year evolutionary perspective on what the environment and environmental change means to life.* Provides thorough background information on each topic while introducing cutting-edge research* Features original material solicited from the leading minds in evolutionary biology and geology today* Emphasizes the influence of massive geological forces - continental drift, volcanic activity, sea and tides |
| five equations that changed the world chapter summary: When We Cease to Understand the World Benjamín Labatut, 2020-09-03 SELECTED FOR BARACK OBAMA'S SUMMER READING LIST 'A monstrous and brilliant book' Philip Pullman'Wholly mesmerising and revelatory... Completely fascinating' William Boyd Sometimes discovery brings destruction When We Cease to Understand the World shows us great minds striking out into dangerous, uncharted terrain. Fritz Haber, Alexander Grothendieck, Werner Heisenberg, Erwin Schrödinger: these are among the luminaries into whose troubled lives we are thrust as they grapple with the most profound questions of existence. They have strokes of unparalleled genius, they alienate friends and lovers, they descend into isolated states of madness. Some of their discoveries revolutionise our world for the better; others pave the way to chaos and unimaginable suffering. The lines are never clear. With breakneck pace and wondrous detail, Benjamín Labatut uses the imaginative resources of fiction to break open the stories of scientists and mathematicians who expanded our notions of the possible. |
| five equations that changed the world chapter summary: A Book of Abstract Algebra Charles C Pinter, 2010-01-14 Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition. |
| five equations that changed the world chapter summary: The Goal Eliyahu M. Goldratt, Jeff Cox, 2016-08-12 Alex Rogo is a harried plant manager working ever more desperately to try and improve performance. His factory is rapidly heading for disaster. So is his marriage. He has ninety days to save his plant - or it will be closed by corporate HQ, with hundreds of job losses. It takes a chance meeting with a colleague from student days - Jonah - to help him break out of conventional ways of thinking to see what needs to be done. Described by Fortune as a 'guru to industry' and by Businessweek as a 'genius', Eliyahu M. Goldratt was an internationally recognized leader in the development of new business management concepts and systems. This 20th anniversary edition includes a series of detailed case study interviews by David Whitford, Editor at Large, Fortune Small Business, which explore how organizations around the world have been transformed by Eli Goldratt's ideas. The story of Alex's fight to save his plant contains a serious message for all managers in industry and explains the ideas which underline the Theory of Constraints (TOC) developed by Eli Goldratt. Written in a fast-paced thriller style, The Goal is the gripping novel which is transforming management thinking throughout the Western world. It is a book to recommend to your friends in industry - even to your bosses - but not to your competitors! |
| five equations that changed the world chapter summary: Mathematics and Climate Hans Kaper, Hans Engler, 2013-10-18 Mathematics and Climate is a timely textbook aimed at students and researchers in mathematics and statistics who are interested in current issues of climate science, as well as at climate scientists who wish to become familiar with qualitative and quantitative methods of mathematics and statistics. The authors emphasize conceptual models that capture important aspects of Earth's climate system and present the mathematical and statistical techniques that can be applied to their analysis. Topics from climate science include the Earth?s energy balance, temperature distribution, ocean circulation patterns such as El Ni?o?Southern Oscillation, ice caps and glaciation periods, the carbon cycle, and the biological pump. Among the mathematical and statistical techniques presented in the text are dynamical systems and bifurcation theory, Fourier analysis, conservation laws, regression analysis, and extreme value theory. The following features make Mathematics and Climate a valuable teaching resource: issues of current interest in climate science and sustainability are used to introduce the student to the methods of mathematics and statistics; the mathematical sophistication increases as the book progresses and topics can thus be selected according to interest and level of knowledge; each chapter ends with a set of exercises that reinforce or enhance the material presented in the chapter and stimulate critical thinking and communication skills; and the book contains an extensive list of references to the literature, a glossary of terms for the nontechnical reader, and a detailed index. |
| five equations that changed the world chapter summary: Mapping Reality Willie Maartens, 2006-06 We must clearly distinguish between reality (the territory), and what we perceive to be reality (the map of the territory)! In our journey through life, we need something to guide us, to give us reassurance that we are on the right track. Modern science has done its best to take that reassurance away from us, telling us that there is no destination, no purpose, in life, and that in effect our lives are an accident of 'Nature'. Religion, too, has become equally unhelpful: it has become dogmatic, sectarian, and self-serving. We have lost the core, the real message, of religion, but we still need true spirituality. Indeed, we need a map to the Truth. |
| five equations that changed the world chapter summary: Book Review Digest , 2001 |
| five equations that changed the world chapter summary: Physical Chemistry Kenneth S Schmitz, 2016-11-11 Physical Chemistry: Concepts and Theory provides a comprehensive overview of physical and theoretical chemistry while focusing on the basic principles that unite the sub-disciplines of the field. With an emphasis on multidisciplinary, as well as interdisciplinary applications, the book extensively reviews fundamental principles and presents recent research to help the reader make logical connections between the theory and application of physical chemistry concepts. Also available from the author: Physical Chemistry: Multidisciplinary Applications (ISBN 9780128005132). - Describes how materials behave and chemical reactions occur at the molecular and atomic levels - Uses theoretical constructs and mathematical computations to explain chemical properties and describe behavior of molecular and condensed matter - Demonstrates the connection between math and chemistry and how to use math as a powerful tool to predict the properties of chemicals - Emphasizes the intersection of chemistry, math, and physics and the resulting applications across many disciplines of science |
| five equations that changed the world chapter summary: Algorithms from THE BOOK Kenneth Lange, 2020-05-04 Algorithms are a dominant force in modern culture, and every indication is that they will become more pervasive, not less. The best algorithms are undergirded by beautiful mathematics. This text cuts across discipline boundaries to highlight some of the most famous and successful algorithms. Readers are exposed to the principles behind these examples and guided in assembling complex algorithms from simpler building blocks. Written in clear, instructive language within the constraints of mathematical rigor, Algorithms from THE BOOK includes a large number of classroom-tested exercises at the end of each chapter. The appendices cover background material often omitted from undergraduate courses. Most of the algorithm descriptions are accompanied by Julia code, an ideal language for scientific computing. This code is immediately available for experimentation. Algorithms from THE BOOK is aimed at first-year graduate and advanced undergraduate students. It will also serve as a convenient reference for professionals throughout the mathematical sciences, physical sciences, engineering, and the quantitative sectors of the biological and social sciences. |
| five equations that changed the world chapter summary: Equations of Life Simon Morden, 2011-04-01 Winner of the 2012 Philip K. Dick Award Samuil Petrovitch is a survivor. He survived the nuclear fallout in St. Petersburg and hid in the London Metrozone -- the last city in England. He's lived this long because he's a man of rules and logic. For example, getting involved = a bad idea. But when he stumbles into a kidnapping in progress, he acts without even thinking. Before he can stop himself, he's saved the daughter of the most dangerous man in London. And clearly saving the girl = getting involved. Now, the equation of Petrovitch's life is looking increasingly complex. Russian mobsters + Yakuza + something called the New Machine Jihad = one dead Petrovitch. But Petrovitch has a plan -- he always has a plan -- he's just not sure it's a good one. |
| five equations that changed the world chapter summary: Introduction to Smooth Manifolds John M. Lee, 2013-03-09 Manifolds are everywhere. These generalizations of curves and surfaces to arbitrarily many dimensions provide the mathematical context for under standing space in all of its manifestations. Today, the tools of manifold theory are indispensable in most major subfields of pure mathematics, and outside of pure mathematics they are becoming increasingly important to scientists in such diverse fields as genetics, robotics, econometrics, com puter graphics, biomedical imaging, and, of course, the undisputed leader among consumers (and inspirers) of mathematics-theoretical physics. No longer a specialized subject that is studied only by differential geometers, manifold theory is now one of the basic skills that all mathematics students should acquire as early as possible. Over the past few centuries, mathematicians have developed a wondrous collection of conceptual machines designed to enable us to peer ever more deeply into the invisible world of geometry in higher dimensions. Once their operation is mastered, these powerful machines enable us to think geometrically about the 6-dimensional zero set of a polynomial in four complex variables, or the lO-dimensional manifold of 5 x 5 orthogonal ma trices, as easily as we think about the familiar 2-dimensional sphere in ]R3. |
| five equations that changed the world chapter summary: Hyperfocus Chris Bailey, 2018-08-28 Canada's productivity expert returns with a totally fresh angle on how to do more with less. Throughout his experiments and research, Chris Bailey came across many little-known insights into how we focus (a key element of productivity), including the surprising idea that focus isn't so much a state of heightened awareness (as we'd assume), but a balance between two frames of mind. The most recent neuroscientific research on attention reveals that our brain has two powerful modes that can be unlocked when we use our attention well: a focused mode (hyperfocus), which is the foundation for being highly productive, and a creative mode (scatterfocus), which enables us to connect ideas in novel ways. Hyperfocus helps readers unlock both, so they can concentrate more deeply, think more clearly, and work and live more deliberately. Diving deep into the science and theories about how and why we bring our attention to bear on life's big goals and everyday tasks, Chris Bailey takes his unique approach to productivity to the next level in Hyperfocus, while retaining the approachable voice and perspective that made him a fast favourite. |
| five equations that changed the world chapter summary: Finite Difference Methods for Ordinary and Partial Differential Equations Randall J. LeVeque, 2007-01-01 This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. |
| five equations that changed the world chapter summary: Until the End of Time Brian Greene, 2021-04-06 NEW YORK TIMES BESTSELLER • A captivating exploration of deep time and humanity's search for purpose, from the world-renowned physicist and best-selling author of The Elegant Universe. Few humans share Greene’s mastery of both the latest cosmological science and English prose. —The New York Times Until the End of Time is Brian Greene's breathtaking new exploration of the cosmos and our quest to find meaning in the face of this vast expanse. Greene takes us on a journey from the big bang to the end of time, exploring how lasting structures formed, how life and mind emerged, and how we grapple with our existence through narrative, myth, religion, creative expression, science, the quest for truth, and a deep longing for the eternal. From particles to planets, consciousness to creativity, matter to meaning—Brian Greene allows us all to grasp and appreciate our fleeting but utterly exquisite moment in the cosmos. |
| five equations that changed the world chapter summary: My Remarkable Journey Katherine Johnson, Joylette Hylick, Katherine Moore, 2021-05-25 The remarkable woman at heart of the smash New York Times bestseller and Oscar-winning film Hidden Figures tells the full story of her life, including what it took to work at NASA, help land the first man on the moon, and live through a century of turmoil and change. In 2015, at the age of 97, Katherine Johnson became a global celebrity. President Barack Obama awarded her the prestigious Presidential Medal of Freedom—the nation’s highest civilian honor—for her pioneering work as a mathematician on NASA’s first flights into space. Her contributions to America’s space program were celebrated in a blockbuster and Academy-award nominated movie. In this memoir, Katherine shares her personal journey from child prodigy in the Allegheny Mountains of West Virginia to NASA human computer. In her life after retirement, she served as a beacon of light for her family and community alike. Her story is centered around the basic tenets of her life—no one is better than you, education is paramount, and asking questions can break barriers. The memoir captures the many facets of this unique woman: the curious “daddy’s girl,” pioneering professional, and sage elder. This multidimensional portrait is also the record of a century of racial history that reveals the influential role educators at segregated schools and Historically Black Colleges and Universities played in nurturing the dreams of trailblazers like Katherine. The author pays homage to her mentor—the African American professor who inspired her to become a research mathematician despite having his own dream crushed by racism. Infused with the uplifting wisdom of a woman who handled great fame with genuine humility and great tragedy with enduring hope, My Remarkable Journey ultimately brings into focus a determined woman who navigated tough racial terrain with soft-spoken grace—and the unrelenting grit required to make history and inspire future generations. |
| five equations that changed the world chapter summary: The CahnHilliard Equation: Recent Advances and Applications Alain Miranville, 2019-09-09 This is the first book to present a detailed discussion of both classical and recent results on the popular CahnHilliard equation and some of its variants. The focus is on mathematical analysis of CahnHilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the CahnHilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest. |
| five equations that changed the world chapter summary: The Age of AI Henry A Kissinger, Eric Schmidt, Daniel Huttenlocher, 2021-11-02 Three of the world’s most accomplished and deep thinkers come together to explore Artificial Intelligence (AI) and the way it is transforming human society—and what this technology means for us all. Generative AI is filling the internet with false information. Artists, writers, and many other professionals are in fear of their jobs. AI is discovering new medicines, running military drones, and transforming the world around us—yet we do not understand the decisions it makes, and we don’t know how to control them. In The Age of AI, three leading thinkers have come together to consider how AI will change our relationships with knowledge, politics, and the societies in which we live. The Age of AI is an essential roadmap to our present and our future, an era unlike any that has come before. |
| five equations that changed the world chapter summary: Functional Analysis, Sobolev Spaces and Partial Differential Equations Haim Brezis, 2010-11-10 This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list. |
| five equations that changed the world chapter summary: Archimedes to Hawking Clifford Pickover, 2008-04-16 Archimedes to Hawking takes the reader on a journey across the centuries as it explores the eponymous physical laws--from Archimedes' Law of Buoyancy and Kepler's Laws of Planetary Motion to Heisenberg's Uncertainty Principle and Hubble's Law of Cosmic Expansion--whose ramifications have profoundly altered our everyday lives and our understanding of the universe. Throughout this fascinating book, Clifford Pickover invites us to share in the amazing adventures of brilliant, quirky, and passionate people after whom these laws are named. These lawgivers turn out to be a fascinating, diverse, and sometimes eccentric group of people. Many were extremely versatile polymaths--human dynamos with a seemingly infinite supply of curiosity and energy and who worked in many different areas in science. Others had non-conventional educations and displayed their unusual talents from an early age. Some experienced resistance to their ideas, causing significant personal anguish. Pickover examines more than 40 great laws, providing brief and cogent introductions to the science behind the laws as well as engaging biographies of such scientists as Newton, Faraday, Ohm, Curie, and Planck. Throughout, he includes fascinating, little-known tidbits relating to the law or lawgiver, and he provides cross-references to other laws or equations mentioned in the book. For several entries, he includes simple numerical examples and solved problems so that readers can have a hands-on understanding of the application of the law. A sweeping survey of scientific discovery as well as an intriguing portrait gallery of some of the greatest minds in history, this superb volume will engage everyone interested in science and the physical world or in the dazzling creativity of these brilliant thinkers. |
| five equations that changed the world chapter summary: Introduction to Probability Joseph K. Blitzstein, Jessica Hwang, 2014-07-24 Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment. |
| five equations that changed the world chapter summary: A Student's Guide to Maxwell's Equations Daniel Fleisch, 2008-01-10 Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter. |
| five equations that changed the world chapter summary: Thinking in Systems Donella H. Meadows, 2009 Thinking in Systems is a concise and crucial book offering insight for problem-solving on scales ranging from the personal to the global. This essential primer brings systems thinking out of the realm of computers and equations and into the tangible world, showing readers how to develop the systems-thinking skills that thought leaders across the globe consider critical for 21st-century life.While readers will learn the conceptual tools and methods of systems thinking, the heart of the book is grander than methodology. Donella Meadows was known as much for nurturing positive outcomes as she was for delving into the science behind global dilemmas. She reminds readers to pay attention to what is important, not just what is quantifiable, to stay humble and to continue to learn.In a world growing ever more complicated, crowded, and interdependent, Thinking in Systems helps readers avoid confusion and helplessness, the first step toward finding proactive and effective solutions. A vital read for students, professionals and all those concerned with economics, business, sustainability and the environment |
| five equations that changed the world chapter summary: The Scottish Book R. Daniel Mauldin, 2015-11-26 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 Wrocław’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. |
| five equations that changed the world chapter summary: Charlie Thorne and the Last Equation Stuart Gibbs, 2020-09-01 “Fast-paced, smart, and action-packed...a real page-burner.” —Chris Grabenstein, #1 New York Times bestselling author of the Mr. Lemoncello’s Library series From New York Times bestselling author Stuart Gibbs comes the first novel in a thrilling new series about the world’s youngest and smartest genius who’s forced to use her unbelievable code-breaking skills to outsmart Einstein. Charlie Thorne is a genius. Charlie Thorne is a thief. Charlie Thorne isn’t old enough to drive. And now it’s up to her to save the world… Decades ago, Albert Einstein devised an equation that could benefit all life on earth—or destroy it. Fearing what would happen if the equation fell into the wrong hands, he hid it. But now, a diabolical group known as the Furies are closing in on its location. In desperation, a team of CIA agents drags Charlie into the hunt, needing her brilliance to find it first—even though this means placing her life in grave danger. In a breakneck adventure that spans the globe, Charlie must crack a complex code created by Einstein himself, struggle to survive in a world where no one can be trusted, and fight to keep the last equation safe once and for all. |
| five equations that changed the world chapter summary: The Curious Incident of the Dog in the Night-Time Mark Haddon, 2009-02-24 A bestselling modern classic—both poignant and funny—narrated by a fifteen year old autistic savant obsessed with Sherlock Holmes, this dazzling novel weaves together an old-fashioned mystery, a contemporary coming-of-age story, and a fascinating excursion into a mind incapable of processing emotions. Christopher John Francis Boone knows all the countries of the world and their capitals and every prime number up to 7,057. Although gifted with a superbly logical brain, Christopher is autistic. Everyday interactions and admonishments have little meaning for him. At fifteen, Christopher’s carefully constructed world falls apart when he finds his neighbour’s dog Wellington impaled on a garden fork, and he is initially blamed for the killing. Christopher decides that he will track down the real killer, and turns to his favourite fictional character, the impeccably logical Sherlock Holmes, for inspiration. But the investigation leads him down some unexpected paths and ultimately brings him face to face with the dissolution of his parents’ marriage. As Christopher tries to deal with the crisis within his own family, the narrative draws readers into the workings of Christopher’s mind. And herein lies the key to the brilliance of Mark Haddon’s choice of narrator: The most wrenching of emotional moments are chronicled by a boy who cannot fathom emotions. The effect is dazzling, making for one of the freshest debut in years: a comedy, a tearjerker, a mystery story, a novel of exceptional literary merit that is great fun to read. |
| five equations that changed the world chapter summary: Air University Library Index to Military Periodicals , 1997 |
| five equations that changed the world chapter summary: Mathematics Of Life Ian Stewart, 2011-04-07 A new partnership of biologists and mathematicians is picking apart the hidden complexity of animals and plants to throw fresh light on the behaviour of entire organisms, how they interact and how changes in biological diversity affect the planet's ecological balance. Mathematics offers new and sometimes startling perspectives on evolution and how patterns of inheritance and population work out over time-scales ranging from millions to hundreds of years - as well as what's going on to change us right now. Ian Stewart, in characteristically clear and entertaining fashion, explores these and a whole range of pertinent issues, including how far genes control behaviour and the nature of life itself. He shows how far mathematicians and biologists are succeeding in tackling some of the most difficult scientific problems the human race has ever confronted and where their research is currently taking us. |
| five equations that changed the world chapter summary: The Origin of Consciousness in the Breakdown of the Bicameral Mind Julian Jaynes, 2000-08-15 National Book Award Finalist: “This man’s ideas may be the most influential, not to say controversial, of the second half of the twentieth century.”—Columbus Dispatch At the heart of this classic, seminal book is Julian Jaynes's still-controversial thesis that human consciousness did not begin far back in animal evolution but instead is a learned process that came about only three thousand years ago and is still developing. The implications of this revolutionary scientific paradigm extend into virtually every aspect of our psychology, our history and culture, our religion—and indeed our future. “Don’t be put off by the academic title of Julian Jaynes’s The Origin of Consciousness in the Breakdown of the Bicameral Mind. Its prose is always lucid and often lyrical…he unfolds his case with the utmost intellectual rigor.”—The New York Times “When Julian Jaynes . . . speculates that until late in the twentieth millennium BC men had no consciousness but were automatically obeying the voices of the gods, we are astounded but compelled to follow this remarkable thesis.”—John Updike, The New Yorker “He is as startling as Freud was in The Interpretation of Dreams, and Jaynes is equally as adept at forcing a new view of known human behavior.”—American Journal of Psychiatry |
| five equations that changed the world chapter summary: Handbook of Mathematical Functions Milton Abramowitz, Irene A. Stegun, 1965-01-01 An extensive summary of mathematical functions that occur in physical and engineering problems |
| five equations that changed the world chapter summary: Bayesian Data Analysis, Third Edition Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin, 2013-11-01 Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page. |
| five equations that changed the world chapter summary: Nonlinear Waves in Integrable and Non-integrable Systems Jianke Yang, 2010-12-02 Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics). |
| five equations that changed the world chapter summary: The Molecular Switch Rob Phillips, 2020-09 A signature feature of living organisms is their ability to carry out purposeful actions by taking stock of the world around them. To that end, cells have an arsenal of signaling molecules linked together in signaling pathways, which switch between inactive and active conformations. The Molecular Switch articulates a biophysical perspective on signaling, showing how allostery—a powerful explanation of how molecules function across all biological domains—can be reformulated using equilibrium statistical mechanics, applied to diverse biological systems exhibiting switching behaviors, and successfully unify seemingly unrelated phenomena. Rob Phillips weaves together allostery and statistical mechanics via a series of biological vignettes, each of which showcases an important biological question and accompanying physical analysis. Beginning with the study of ligand-gated ion channels and their role in problems ranging from muscle action to vision, Phillips then undertakes increasingly sophisticated case studies, from bacterial chemotaxis and quorum sensing to hemoglobin and its role in mammalian physiology. He looks at G-protein coupled receptors as well as the role of allosteric molecules in gene regulation. Phillips concludes by surveying problems in biological fidelity and offering a speculative chapter on the relationship between allostery and biological Maxwell demons. Appropriate for graduate students and researchers in biophysics, physics, engineering, biology, and neuroscience, The Molecular Switch presents a unified, quantitative model for describing biological signaling phenomena. |
FiveM - the GTA V multiplayer modification you have dreamt of
Building upon years of development on the Cfx.re framework, which has existed in various forms since 2014, FiveM is the original community-driven and source-available GTA V multiplayer …
Setting up a server - Cfx.re Docs - FiveM
A step-by-step guide on setting up FXServer. Setting up a server. This page shows you how to run the Cfx.re platform server (also often named 'FXServer') on Windows, Linux, txAdmin, or a …
Home - Cfx.re Docs - FiveM
👋🏼 Home. Welcome to the documentation for the FiveM modification framework. Use the links below to find the information you're looking for. Server owners. 🤩 Find out how to start a server on …
Server hosting - FiveM
Host your server. Set up your server in under 5 minutes via one of our authorized hosting partners. Run your favorite gamemode, create your own scripts, and get creative!
Client manual - Cfx.re Docs - FiveM
Client manual Basics. Installing FiveM; CFX articles; Console commands; FiveM shortcut; CitizenFX.ini; FiveM singleplayer. FiveM also ships with a customized singleplayer mode.
Client FAQ - Cfx.re Docs - FiveM
Client FAQ Will FiveM run on Xbox or Playstation? No. FiveM is developed exclusively for the PC version of GTA V. There are no plans to support consoles.
/artifacts/fivem/build_server_windows/master/ / FiveM Artifacts
Download essential FiveM server artifacts to host and customize your multiplayer gaming experience on GTA V.
Setting up a server using txAdmin - Cfx.re Docs - FiveM
Setting up a server using txAdmin Ultimate easy setup guide. Windows Download the server. Go to the Windows server build listing ('artifacts' listing, as in 'build artifacts').; Download the latest …
Scripting introduction - Cfx.re Docs - FiveM
API Set: all; server; client; Language:
Cfx.re Server List
Browse thousands of servers for FiveM and RedM. "role play" for full string match, tag: to match tags, locale: to match locale,
FiveM - the GTA V multiplayer modification you have dreamt of
Building upon years of development on the Cfx.re framework, which has existed in various forms since 2014, FiveM is the original community-driven and source-available GTA V multiplayer …
Setting up a server - Cfx.re Docs - FiveM
A step-by-step guide on setting up FXServer. Setting up a server. This page shows you how to run the Cfx.re platform server (also often named 'FXServer') on Windows, Linux, txAdmin, or a …
Home - Cfx.re Docs - FiveM
👋🏼 Home. Welcome to the documentation for the FiveM modification framework. Use the links below to find the information you're looking for. Server owners. 🤩 Find out how to start a server on …
Server hosting - FiveM
Host your server. Set up your server in under 5 minutes via one of our authorized hosting partners. Run your favorite gamemode, create your own scripts, and get creative!
Client manual - Cfx.re Docs - FiveM
Client manual Basics. Installing FiveM; CFX articles; Console commands; FiveM shortcut; CitizenFX.ini; FiveM singleplayer. FiveM also ships with a customized singleplayer mode.
Client FAQ - Cfx.re Docs - FiveM
Client FAQ Will FiveM run on Xbox or Playstation? No. FiveM is developed exclusively for the PC version of GTA V. There are no plans to support consoles.
/artifacts/fivem/build_server_windows/master/ / FiveM Artifacts
Download essential FiveM server artifacts to host and customize your multiplayer gaming experience on GTA V.
Setting up a server using txAdmin - Cfx.re Docs - FiveM
Setting up a server using txAdmin Ultimate easy setup guide. Windows Download the server. Go to the Windows server build listing ('artifacts' listing, as in 'build artifacts').; Download the latest …
Scripting introduction - Cfx.re Docs - FiveM
API Set: all; server; client; Language:
Cfx.re Server List
Browse thousands of servers for FiveM and RedM. "role play" for full string match, tag: to match tags, locale: to match locale,
