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The Monge-Ampère Equation
by Cristian E. GutiérrezThis updated and revised monograph continues to follow the latest advances in the study of the Monge-Ampère equation and its applications. These advances are reflected in an essentially self-contained systematic exposition of the theory of weak solutions, including recent regularity results by L. A. Caffarelli. This volume can be used for a graduate level topics course in differential equations, and features bibliographic notes at the end of each chapter for further exploration. Additions to the second edition include: A new proof of the theorem that viscosity solutions are Aleksandrov solutions without using deep regularity results A new chapter on the Harnack inequality for the linearized Monge-Ampère equation. A new chapter on interior Hölder estimates for second derivatives Note sections expanded to include new developments since 2001
The Monte Carlo Simulation Method for System Reliability and Risk Analysis
by Enrico ZioMonte Carlo simulation is one of the best tools for performing realistic analysis of complex systems as it allows most of the limiting assumptions on system behavior to be relaxed. The Monte Carlo Simulation Method for System Reliability and Risk Analysis comprehensively illustrates the Monte Carlo simulation method and its application to reliability and system engineering. Readers are given a sound understanding of the fundamentals of Monte Carlo sampling and simulation and its application for realistic system modeling. Whilst many of the topics rely on a high-level understanding of calculus, probability and statistics, simple academic examples will be provided in support to the explanation of the theoretical foundations to facilitate comprehension of the subject matter. Case studies will be introduced to provide the practical value of the most advanced techniques. This detailed approach makes The Monte Carlo Simulation Method for System Reliability and Risk Analysis a key reference for senior undergraduate and graduate students as well as researchers and practitioners. It provides a powerful tool for all those involved in system analysis for reliability, maintenance and risk evaluations.
The Montessori Method: My First Book of Numbers
by The Montessori MethodLearn about numbers the Montessori way with this line of board books following the world-leading educational approach, THE MONTESSORI METHOD!Montessori education values the development of the whole child-physically, socially, emotionally, cognitively. These books tap into the Montessori Method at home, allowing children to discover and engage with concepts in a holistic way that promotes a drive for knowledge and self-motivation. In NUMBERS, children are invited to imagine, touch, mimic, and learn about numbers and how they function in the world around us. Infused with humor and math concepts that both engage and challenge children, this book is sure to inspire a generation of mathematicians!Learn more with THE MONTESSORI METHOD: FEELINGS!
The Moral Imagination of Patricia Werhane: A Festschrift (Issues in Business Ethics #47)
by R. Edward Freeman Andrew C. Wicks Sergiy DmytriyevThis book celebrates the work of Patricia Werhane, an iconic figure in business ethics. This festschrift is a collection of articles that build on Werhane’s contributions to business ethics in such areas as Employee Rights, the Legacy of Adam Smith, Moral Imagination, Women in Business, the development of the field of business ethics, and her contributions to such fields as Health Care, Education, Teaching, and Philosophy.All papers are new contributions to the management literature written by well-known business ethicists, such as Norman Bowie, Richard De George, Ronald Duska, Edwin Hartman, Michael Hoffman, Mollie Painter-Morland, Mark Schwartz, Andrew Wicks, and others. The volume is comprised of articles that reflect on Werhane’s work as well as build on it as a way to advance further research. At the end of the festschrift, Pat Werhane provides responses to each chapter. The first chapter of the book also includes the overview of Patricia Werhane’s work and her academic career.The book is written to appeal to management scholars and graduate students interested in the areas of Business Ethics, Modern Capitalism, and Human Rights. Patricia Werhane is one of the most distinguished figures in the field of business ethics. She was a founder of the field, she is one of its leading scholars, and she has had a profound impact on the world of business practice. Among her many accomplishments, Pat is known for her original work on moral imagination, she is an acclaimed authority on employee rights in the workplace, and she is one of the leading scholars on Adam Smith. Having been active in Academia for over 50 years, Werhane is a prolific author of over a hundred articles and book chapters, and the author or editor of twenty-seven books, including Adam Smith and his Legacy for Modern Capitalism, Moral Imagination and Management Decision-Making, and co-authored books Organization Ethics in Health Care, Alleviating Poverty Through Profitable Partnerships, Obstacles to Ethical Decision-Making, Corporate Responsibility: The American Experience, and Research Approaches to Business Ethics and Corporate Responsibility.
The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)
by Boris A. KordemskyThis is, quite simply, the best and most popular puzzle book ever published in the Soviet Union. Since its first appearance in 1956 there have been eight editions as well as translations from the original Russian into Ukrainian, Estonian, Lettish, and Lithuanian. Almost a million copies of the Russian version alone have been sold.Part of the reason for the book's success is its marvelously varied assortment of brainteasers ranging from simple "catch" riddles to difficult problems (none, however, requiring advanced mathematics). Many of the puzzles will be new to Western readers, while some familiar problems have been clothed in new forms. Often the puzzles are presented in the form of charming stories that provide non-Russian readers with valuable insights into contemporary Russian life and customs. In addition, Martin Gardner, former editor of the Mathematical Games Department, Scientific American, has clarified and simplified the book to make it as easy as possible for an English-reading public to understand and enjoy. He has been careful, moreover, to retain nearly all the freshness, warmth, and humor of the original.Lavishly illustrated with over 400 clear diagrams and amusing sketches, this inexpensive edition of the first English translation will offer weeks or even months of stimulating entertainment. It belongs in the library of every puzzlist or lover of recreational mathematics.
The Motion Paradox
by Joseph MazurThe epic tale of an ancient, unsolved puzzle and how it relates to all scientific attempts to explain the basic structure of the universe At the dawn of science the ancient Greek philosopher Zeno formulated his paradox of motion, and amazingly, it is still on the cutting edge of all investigations into the fabric of reality. Zeno used logic to argue that motion is impossible, and at the heart of his maddening puzzle is the nature of space and time. Is space-time continuous or broken up like a string of beads? Over the past two millennia, many of our greatest minds-including Aristotle, Galileo, Newton, Einstein, Stephen Hawking, and other current theoreticians-have been gripped by the mystery this puzzle represents. Joseph Mazur, acclaimed author of Euclid in the Rainforest, shows how historic breakthroughs in our understanding of motion shed light on Zeno's paradox. The orbits of the planets were explained, the laws of motion were revealed, the theory of relativity was discovered-but the basic structure of time and space remained elusive. In the tradition of Fermat's Enigma and Zero, The Motion Paradox is a lively history of this apparently simple puzzle whose solution-if indeed it can be solved-will reveal nothing less than the fundamental nature of reality.
The Multiple Facets of Partial Least Squares and Related Methods
by Vincenzo Esposito Vinzi Giorgio Russolillo Laura Trinchera Hervé Abdi Gilbert SaportaThis volume presents state of the art theories, new developments, and important applications of Partial Least Square (PLS) methods. The text begins with the invited communications of current leaders in the field who cover the history of PLS, an overview of methodological issues, and recent advances in regression and multi-block approaches. The rest of the volume comprises selected, reviewed contributions from the 8th International Conference on Partial Least Squares and Related Methods held in Paris, France, on 26-28 May, 2014. They are organized in four coherent sections: 1) new developments in genomics and brain imaging, 2) new and alternative methods for multi-table and path analysis, 3) advances in partial least square regression (PLSR), and 4) partial least square path modeling (PLS-PM) breakthroughs and applications. PLS methods are very versatile methods that are now used in areas as diverse as engineering, life science, sociology, psychology, brain imaging, genomics, and business among both academics and practitioners. The selected chapters here highlight this diversity with applied examples as well as the most recent advances.
The Music of Pythagoras: How an Ancient Brotherhood Cracked the Code of the Universe and Lit the Path from Antiquity to Outer Space
by Kitty FergusonFerguson, a musician and author of several books on the history of science, presents an entertaining, erudite history of the work of Pythagoras, from its murky origins in the sixth century B.C.E. to the present. She explores the use of Pythagorean mathematics in Greek, Roman, Arabic and Western European intellectual tradition in a clear, unbiased manner, with many diagrams and explanations to aid those for who haven't kept up their high school math.
The Mutual Construction of Statistics and Society (Routledge Advances in Research Methods)
by Ann Rudinow SætnanStatistics are often seen as simple, straightforward, and objective descriptions of society. However, what we choose to count, what we choose not to count, who does the counting, and the categories and values we choose to apply when counting, matter. This volume addresses the ways in which statistics and numbers are gathered and applied in social science research. The contributors argue that we must become more aware of the power and the limitations of statistics. Learning statistics needs to be about more than simply mastering the techniques of using the tool; it needs to also be about learning the dangers of that tool and learning to control it within social and ethical bounds. These dangers lie in the routines through which statistics are applied; the discourses from which they emerge and into which they are deployed; the power relations created by those discourses; and the assumptions, meanings, and categories statistics carry with them in those discourses. This volume will be necessary reading for students and scholars using quantitative data within the social sciences.
The Mystery of Rationality: Mind, Beliefs and the Social Sciences (Lecture Notes in Morphogenesis)
by Gérald Bronner Francesco Di IorioThis book contributes to the developing dialogue between cognitive science and social sciences. It focuses on a central issue in both fields, i.e. the nature and the limitations of the rationality of beliefs and action. The development of cognitive science is one of the most important and fascinating intellectual advances of recent decades, and social scientists are paying increasing attention to the findings of this new branch of science that forces us to consider many classical issues related to epistemology and philosophy of action in a new light. Analysis of the concept of rationality is a leitmotiv in the history of the social sciences and has involved endless disputes. Since it is difficult to give a precise definition of this concept, and there is a lack of agreement about its meaning, it is possible to say that there is a ‘mystery of rationality’. What is it to be rational? Is rationality merely instrumental or does it also involve the endorsement of values, i.e. the choice of goals? Should we consider rationality to be a normative principle or a descriptive one? Can rationality be only Cartesian or can it also be argumentative? Is rationality a conscious skill or a partly tacit one? This book, which has been written by an outstanding collection of authors, including both philosophers and social scientists, tries to make a useful contribution to the debates on these problems and shed some light on the mystery of rationality. The target audience primarily comprises researchers and experts in the field.
The Mystery of the Aleph
by Amir D. AczelThe history of infinity emphasizing the people who were interested in the concept. Stresses philosophical and religious importance of mathematical ideas throughout history. Fascinating even if math is not your strong suit.
The Mystery of the Ultimatum Game: Why We Are Predictably Irrational
by Kayoko KobayashiThis ambitious book is the first to present a theoretical framework for a unified analysis of both behavioral and traditional economics. It explores the ultimate factors from an evolutionary perspective in addressing why humans are predictably irrational and proposes "adaptive rationality," a new direction for understanding human behavior. Taking anomalies in ultimatum game experiments as a starting point, this book presents findings from hundreds of experiments. The interdisciplinary nature of the book, which encompasses the latest research across an astonishingly wide range of fields—including game theory, psychology, neuroscience, cognitive science, cultural anthropology, biology, and ethology—provides boundless intellectual excitement. While this is an academic book discussing human rationality, it can also be seen as a popular science book that delves deeply into questions such as "What underlies human decision making?" The book stands out for its unique approach, making it an unparalleled reading experience. The original Japanese edition won the Nikkei Prize for Economics Books (the 64th Nikkei-Keizai Tosho Bunka award) in 2021, an accolade bestowed upon an outstanding economics book published in a given year. Furthermore, this edition also received the Takashima Kunio Jiyu Prize Encouragement Award in 2024.
The Myth of Ability: Nurturing Mathematical Talent in Every Child
by John MightonJohn Mighton’s revolutionary bestselling guide to how every child can learn math through his groundbreaking JUMP program.A student in a remedial class who couldn't count by twos is now in an academic program a year ahead of her grade level. An entire Grade 3 class, including so-called slow learners, scores over 90% on a Grade 6-7 math test. These are just two of mathematician John Mighton's many success stories since he started JUMP (Junior Undiscovered Math Prodigies), a not-for-profit organization providing free math tutoring for elementary-level students from low income homes.In The Myth of Ability John Mighton tells JUMP's fascinating story and explains its teaching method with lots of simple examples.
The Naked Android: Synthetic Socialness and the Human Gaze (Chapman & Hall/CRC Artificial Intelligence and Robotics Series)
by Julie CarpenterThe Naked Android: Synthetic Socialness and the Human Gaze illuminates the connection between the stories people tell, their expectations of what a robot is, and how these beliefs and values manifest in how real robots are designed and used.The introduction of the “human gaze” articulates how peoples’ expectations and perceptions about robots are ultimately based on deeply personal cultural interpretations of what is artificial or human and what problems social robots should –or should not –solve. The Naked Android clarifies how human qualities like understanding and desire are designed into robots as mediums as well as projected onto them by the people who live with them.By investigating the fluidity of identities across human culture and social robotics, this book unpacks the contextual complexities of their interactions and mutual influences. Using ethnographic methods including in-depth interviews with a variety of stakeholders, each chapter explores how people are designing social robots, the experience of living with robots, and people whose jobs it is to dream about a future integrated with robots.Key Features: Introduces the concept of the “human gaze” (and the “robot gaze”) as means of understanding how people live with robots. Each chapter includes in-depth interviews with people who make, live with, or create art about robots. Using ethnographic methods, paints a vivid description of the interconnecting influences of science fiction, human imagination, and real technology.
The Naked Future
by Patrick TuckerIn the past, the future was opaque--the territory of fortune-tellers, gurus, and dubious local TV weathermen. But thanks to recent advances in computing and the reams of data we create through smartphone and Internet use, prediction models for individual behavior grow smarter and more sophisticated by the day. Whom you should marry, whether you'll commit a crime or fall victim to one, if you'll contract a specific strain of flu--even your precise location at any given moment years into the future--are becoming easily accessible facts. the naked future is upon us, and the implications are staggering. Patrick Tucker draws on stories from health care to urban planning to online dating to reveal the shape of a future that's ever more certain. In these pages you'll meet scientists and inventors who can predict your behavior based on your friends' Twitter updates. They are also hacking the New York City sewer system to predict environmental conditions, anticipating how much the weather a year from now will cost an individual farmer, figuring out the time of day you're most likely to slip back into a bad habit, and guessing how well you'll do on a test before you take it. You'll learn how social networks like Facebook are using your data to turn you into an advertisement and why the winning formula for a blockbuster movie is more predictable than ever. The rise of big data and predictive analytics means that governments and corporations are becoming much more effective at accomplishing their goals and at much less cost. Tucker knows that's not always a good thing. But he also shows how we've gained tremendous benefits that we have yet to fully realize. Thanks to the increased power of predictive science, we'll be better able to stay healthy, invest our savings more wisely, learn faster and more efficiently, buy a house in the right neighborhood at the right time, avoid crime, thwart terrorists, and mitigate the consequences of natural disasters. What happens in a future that anticipates your every move? the surprising answer: we'll live better as a result. 'Where I saw a thrilling and historic transformation in the world's oldest idea--the future--other people saw only Target, Facebook, Google, and the government using their data to surveil, track, and trick them . . . But in fact, your data is your best defense against coercive marketing and intrusive government practices. Your data is nothing less than a superpower waiting to be harnessed. ' from the Introduction
The Naked Future
by Patrick Tucker"A thorough yet thoroughly digestible book on the ubiquity of data gathering and the unraveling of personal privacy." --Daniel Pink, author of DriveThanks to recent advances in technology, prediction models for individual behavior grow more sophisticated by the day. Whether you'll marry, commit a crime or fall victim to one, or contract a disease are becoming easily accessible facts. The naked future is upon us, and the implications are staggering.Patrick Tucker draws on fascinating stories from health care to urban planning to online dating. He shows how scientists can predict your behavior based on your friends' Twitter updates, anticipate the weather a year from now, figure out the time of day you're most likely to slip back into a bad habit, and guess how well you'll do on a test before you take it.Tucker knows that the rise of Big Data is not always a good thing. But he also shows how we've gained tremendous benefits that we have yet to fully realize.g. Patrick Tucker draws on stories from health care to urban planning to online dating to reveal the shape of a future that's ever more certain. In these pages you'll meet scientists and inventors who can predict your behavior based on your friends' Twitter updates. They are also hacking the New York City sewer system to predict environmental conditions, anticipating how much the weather a year from now will cost an individual farmer, figuring out the time of day you're most likely to slip back into a bad habit, and guessing how well you'll do on a test before you take it. You'll learn how social networks like Facebook are using your data to turn you into an advertisement and why the winning formula for a blockbuster movie is more predictable than ever. The rise of big data and predictive analytics means that governments and corporations are becoming much more effective at accomplishing their goals and at much less cost. Tucker knows that's not always a good thing. But he also shows how we've gained tremendous benefits that we have yet to fully realize. Thanks to the increased power of predictive science, we'll be better able to stay healthy, invest our savings more wisely, learn faster and more efficiently, buy a house in the right neighborhood at the right time, avoid crime, thwart terrorists, and mitigate the consequences of natural disasters. What happens in a future that anticipates your every move? The surprising answer: we'll live better as a result.
The Narrative Gym for Science Graduate Students and Postdocs: Using the ABT Framework for Proposals, Papers, Presentations, and Life in General
by Randy Olson Marlis Douglas Keisha BahrIt’s ABT Time: Science consists of equal parts research and communication, AND if you do a good job with communication then your research will reach its full impact, BUT communication can’t be mastered in a day, THEREFORE get thee to the Narrative Gym with this book! <p><p> What is the ABT? Only the most important communications tool you’ll ever need. It provides the core of narrative structure, which is what makes the difference between whether you bore or confuse an audience versus interest and engage them. The ABT is about the three forces of narrative (agreement, contradiction, consequence) which are embodied in the three words of the ABT (and, but, therefore). <P><P> In this short, simple, practical book three scientists present what they have learned about the use of the ABT with science graduate students and postdocs. It provides an introduction to the ABT with an explanation of how to apply it to everything from proposals, papers and presentations to your life in general.
The Natural Law of Cycles: Governing the Mobile Symmetries of Animals and Machines
by James H. BunnThe Natural Law of Cycles assembles scientific work from different disciplines to show how research on angular momentum and rotational symmetry can be used to develop a law of energy cycles as a local and global influence. Angular momentum regulates small-scale rotational cycles such as the swimming of fish in water, the running of animals on land, and the flight of birds in air. Also, it regulates large-scale rotation cycles such as global currents of wind and water.James H. Bunn introduces concepts of symmetry, balance, and angular momentum, showing how together they shape the mobile symmetries of animals. Chapter 1 studies the configurations of animals as they move in a head-first direction. Chapter 2 shows how sea animals follow currents and tides generated by the rotational cycles of the earth. In chapter 3, Bunn explores the biomechanical pace of walking as a partial cycle of rotating limbs. On a large scale, angular momentum governs balanced shifts in plate tectonics.Chapter 4 begins with an examination of rotational wind patterns in terms of the counter-balancing forces of angular momentum. The author shows how these winds augment the flights of birds during migrations. A final chapter centres on the conservation of energy as the most basic principle of science. Bunn argues that in the nineteenth century the unity of nature was seen in the emergent concept of energy, not matter, as the source of power, including the movements of animals and machines. In each chapter Bunn features environmental writers who celebrate mobile symmetries. This book will interest students, naturalists, and advocates of the environmental movement.
The Nature and Power of Mathematics
by Donald M. DavisThis captivating book explains some of mathematics' most fascinating ideas to nonspecialists. It explores items of philosophical and historical interest, discusses the often-surprising applicability of mathematics, and reveals the subject's intrinsic beauty. Author Donald M. Davis focuses on three main areas: non-Euclidean geometry, a basis for relativity theory; number theory, a major component of cryptography; and fractals, the key elements of computer-generated art. He also discusses related topics, such as the relevance of Greek mathematics to Kepler's laws of planetary motion, and the theoretical work that led to the development of computers.Only a background in basic algebra and geometry is necessary to appreciate this volume, which features exercises that further develop some of its important concepts. Graded according to difficulty, these exercises are designed to improve readers' skills in logic, and to enable them to experience mathematics at increasingly advanced levels.Supplementary materials at the end of each chapter include intriguing examples of the subjects' applications, as well as biographical sketches of Archimedes, Einstein, Newton, and other luminaries of mathematics.
The Nature of Mathematical Thinking (Studies in Mathematical Thinking and Learning Series)
by Robert J. Sternberg Talia Ben-ZeevWhy do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject. The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat.
The Nature of Mathematics
by Karl SmithWritten for liberal arts students and based on the belief that learning to solve problems is the principal reason for studying mathematics, Karl Smith introduces students to Polya’s problem-solving techniques and shows them how to use these techniques to solve unfamiliar problems that they encounter in their own lives. Through the emphasis on problem solving and estimation, along with numerous in-text study aids, students are assisted in understanding the concepts and mastering the techniques. In addition to the problem-solving emphasis, THE NATURE OF MATHEMATICS is renowned for its clear writing, coverage of historical topics, selection of topics, level, and excellent applications problems. Smith includes material on such practical real-world topics as finances (e.g. amortization, installment buying, annuities) and voting and apportionment. With the help of this text, thousands of students have experienced mathematics rather than just do problems--and benefited from a writing style that boosts their confidence and fosters their ability to use mathematics effectively in their everyday lives.
The Nature of Mathematics
by Philip E. JourdainAnyone with an interest in mathematics will welcome the republication of this little volume by a remarkable mathematician who was also a logician, a philosopher, and an occasional writer of fiction and poetry. Originally published in 1913, and later included in the acclaimed anthology The World of Mathematics, Jourdain's survey shows how and why the methods of mathematics were developed, traces the development of mathematical science from the earliest to modern times, and chronicles the application of mathematics to natural science.Starting with the ancient Egyptians and Greeks, the author profiles mathematics' rise and progress with the development of analytical methods by Descartes, Galileo, Newton, Leibnitz, and others. The text focuses on principles rather than techniques, exploring the foundations of algebra, analytical geometry, and the method of indivisibles. It discusses the beginnings of the correlation of mathematics and natural science in the study of dynamics as well as the emergence of modern mathematics with the infinitesimal calculus. Additional topics include contemporary views of limits and numbers and a brief summation of the nature of mathematics.
The Nature of Statistics
by Prof. Harry V. Roberts W. Allen Wallis George P ShultzFocusing on everyday applications as well as those of scientific research, this classic of modern statistical methods requires little to no mathematical background. Readers develop basic skills for evaluating and using statistical data. Lively, relevant examples include applications to business, government, social and physical sciences, genetics, medicine, and public health. "W. Allen Wallis and Harry V. Roberts have made statistics fascinating." -- The New York Times "The authors have set out with considerable success, to write a text which would be of interest and value to the student who, not concerned primarily with statistical technics, must understand the nature and methodology of the subject in order to make proper use of its results." -- American Journal of Public Health and the Nation's Health "This book is a distinct and important contribution to the text literature in statistics for social scientists and should be given careful consideration by sociologists." -- American Sociological Review.
The Navier-Stokes Equations: Theory and Numerical Methods (Lecture Notes in Pure and Applied Mathematics)
by Rodolfo Salvi"Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."
The Navier-Stokes Problem in the 21st Century
by Pierre Gilles Lemarie-RieussetPraise for the first edition “The author is an outstanding expert in harmonic analysis who has made important contributions. The book contains rigorous proofs of a number of the latest results in the field. I strongly recommend the book to postgraduate students and researchers working on challenging problems of harmonic analysis and mathematical theory of Navier-Stokes equations." —Gregory Seregin, St Hildas College, Oxford University “"This is a great book on the mathematical aspects of the fundamental equations of hydrodynamics, the incompressible Navier-Stokes equations. It covers many important topics and recent results and gives the reader a very good idea about where the theory stands at present.” —Vladimir Sverak, University of Minnesota The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century, Second Edition continues to provide a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics, now revised to include fresh examples, theorems, results, and references that have become relevant since the first edition published in 2016.