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Thermodynamics of Information Processing in Small Systems
by Takahiro SagawaThis thesis presents a general theory of nonequilibrium thermodynamics for information processing. Ever since Maxwell's demon was proposed in the nineteenth century, the relationship between thermodynamics and information has attracted much attention because it concerns the foundation of the second law of thermodynamics. From the modern point of view, Maxwell's demon is formulated as an information processing device that performs measurement and feedback at the level of thermal fluctuations. By unifying information theory, measurement theory, and the recently developed theory of nonequilibrium statistical mechanics, the author has constructed a theory of "information thermodynamics," in which information contents and thermodynamic variables are treated on an equal footing. In particular, the maximum work that can be extracted by the demon and the minimum work that is needed for measurement and information erasure by the demon has been determined. Additionally, generalizations of nonequilibrium relations such as a Jarzynski equality for classical stochastic systems in the presence of feedback control have been derived. One of the generalized equalities has recently been verified experimentally by using sub-micron colloidal particles. The results obtained serve as fundamental principles for information processing in small thermodynamic systems, and are applicable to nanomachines and nanodevices.
Thermodynamik für das Bachelorstudium
by Klaus StierstadtDas Verständnis der Thermodynamik ist nicht nur Voraussetzung für die moderne Physik, Chemie, Biologie und Technik, sondern auch für die Frage der Energieversorgung der Zukunft. Der Autor führt in die Prinzipien, Methoden und Ergebnisse der Thermodynamik ein, indem er die Größen Temperatur, Wärme und Entropie auf die Eigenschaften der Atome und auf ihr Zusammenwirken zurückgeführt. Basierend auf den vier Hauptsätzen der Thermodynamik werden die wichtigsten Anwendungen, z. B. Energieumwandlung und Nanotechnologie, ausführlich besprochen.
Thermodynamik für das Bachelorstudium
by Klaus StierstadtDas Verständnis der Thermodynamik ist nicht nur Voraussetzung für die moderne Physik, Chemie, Biologie und Technik, sondern auch für die Frage der Energieversorgung der Zukunft. Der Autor führt in die Prinzipien, Methoden und Ergebnisse der Thermodynamik ein, indem er die Größen Temperatur, Wärme und Entropie auf die Eigenschaften der Atome und auf ihr Zusammenwirken zurückgeführt. Basierend auf den vier Hauptsätzen der Thermodynamik werden die wichtigsten Anwendungen, z. B. Energieumwandlung und Nanotechnologie, ausführlich besprochen.
Thermodynamische Potenziale und Zustandssumme: Ein Überblick über die Definitionen in der Thermodynamik (essentials)
by Klaus StierstadtDieses essential gibt einen Überblick über die Definitionen und die Bedeutung thermodynamischer Potenziale und ermöglicht auch Einsteigern ein Verständnis der Thematik, welche eine Voraussetzung für die moderne Physik, die Chemie, Biologie und Technik ist. Der Schwerpunkt liegt auf den Grundlagen und aktuellen Fragestellungen. Es schlägt eine Brücke zwischen den beiden Thermodynamik-Vorlesungen: der einfachen Wärmelehre im 1. oder 2. Semester und der anspruchsvollen Statistischen Physik im 5. Semester. Das essential ist Teil einer dreiteiligen Reihe zur Thermodynamik zusammen mit Temperatur und Wärme – was ist das wirklich? und Die Eigenschaften der Stoffe: Suszeptibilitäten und Transportkoeffizienten.
Thermofluid Dynamics of Turbulent Flows: Fundamentals and Modelling (UNIPA Springer Series)
by Michele CiofaloThe book provides the theoretical fundamentals on turbulence and a complete overview of turbulence models, from the simplest to the most advanced ones including Direct and Large Eddy Simulation. It mainly focuses on problems of modeling and computation, and provides information regarding the theory of dynamical systems and their bifurcations. It also examines turbulence aspects which are not treated in most existing books on this subject, such as turbulence in free and mixed convection, transient turbulence and transition to turbulence. The book adopts the tensor notation, which is the most appropriate to deal with intrinsically tensor quantities such as stresses and strain rates, and for those who are not familiar with it an Appendix on tensor algebra and tensor notation are provided.
Thermomechanical Industrial Processes: Modeling and Numerical Simulation (Wiley-iste Ser.)
by Jean Michel BergheauThe numerical simulation of manufacturing processes and of their mechanical consequences is of growing interest in industry. However, such simulations need the modeling of couplings between several physical phenomena such as heat transfer, material transformations and solid or fluid mechanics, as well as to be adapted to numerical methodologies. This book gathers a state of the art on how to simulate industrial processes, what data are needed and what numerical simulation can bring. Assembling processes such as welding and friction stir welding, material removal processes, elaboration processes of composite structures, sintering processes, surface-finishing techniques, and thermo-chemical treatments are investigated.This book is the work of a group of researchers who have been working together in this field for more than 12 years. It should prove useful for both those working in industry and those studying the numerical methods applied to multiphysics problems encountered in manufacturing processes.
Thicker Than Blood: How Racial Statistics Lie
by Tukufu ZuberiTukufu Zuberi offers a concise account of the historical connections between the development of the idea of race and the birth of social statistics. Zuberi describes the ways race-differentiated data is misinterpreted in the social sciences and asks searching questions about the ways racial statistics are used. He argues that statistical analysis can and must be deracialized, and that this deracialization is essential to the goal of achieving social justice for all.
Thin Liquid Films
by Ralf BlosseyThis book is a treatise on the thermodynamic and dynamic properties of thin liquid films at solid surfaces and, in particular, their rupture instabilities. For the quantitative study of these phenomena, polymer thin films (sometimes referred to as "ultrathin") have proven to be an invaluable experimental model system. What is it that makes thin film instabilities special and interesting? First, thin polymeric films have an important range of applications. An understanding of their instabilities is therefore of practical relevance for the design of such films. The first chapter of the book intends to give a snapshot of current applications, and an outlook on promising future ones. Second, thin liquid films are an interdisciplinary research topic, which leads to a fairly heterogeneous community working on the topic. It justifies attempting to write a text which gives a coherent presentation of the field which researchers across their specialized communities might be interested in. Finally, thin liquid films are an interesting laboratory for a theorist to confront a well-established theory, hydrodynamics, with its limits. Thin films are therefore a field in which a highly fruitful exchange and collaboration exists between experimentalists and theorists. The book stretches from the more concrete to more abstract levels of study: we roughly progress from applications via theory and experiment to rigorous mathematical theory. For an experimental scientist, the book should serve as a reference and guide to what is the current consensus of the theoretical underpinnings of the field of thin film dynamics. Controversial problems on which such a consensus has not yet been reached are clearly indicated in the text, as well as discussed in a final chapter. From a theoretical point of view, the field of dewetting has mainly been treated in a mathematically 'light' yet elegant fashion, often making use of scaling arguments. For the untrained researcher, this approach is not always easy to follow. The present book attempts to bridge between the 'light' and the 'rigorous', always with the ambition to enhance insight and understanding - and to not let go the elegance of the theory.
Thin Plates and Shells: Theory: Analysis, and Applications
by Eduard Ventsel Theodor KrauthammerPresenting recent principles of thin plate and shell theories, this book emphasizes novel analytical and numerical methods for solving linear and nonlinear plate and shell dilemmas, new theories for the design and analysis of thin plate-shell structures, and real-world numerical solutions, mechanics, and plate and shell models for engineering applications. It includes computer processes for finite difference, finite element, boundary element, and boundary collocation methods as well as other variational and numerical methods. It also contains end-of-chapter examples and problem/solution sets, a catalog of solutions for cylindrical and spherical shells, and tables of the most commonly used plates and shells.
Things to Make and Do in the Fourth Dimension
by Matthew ParkerMathematics made mouth-watering. Things to Make and Do in the Fourth Dimension is an alternative math class. How can math help you choose a second-hand car? Why is a text message like a Sudoku? How much fun can you have with a barcode? Matt Parker explains that math is difficult because it's one of the few subjects that requires us to train our brains to think in an entirely new way, and to confront things with no direct analogy in everyday life--imaginary numbers, snowflakes that only exist in 196884 dimensions, and objects beyond infinity--and shows us why it's worth the effort. Starting with basic arithmetic and geometry, Things To Make and Do teaches us the math we never got to enjoy at school. Each chapter is structured around activities and thought experiments: we are invited to make a calculator out of dominoes, find out why wrapping oranges in plastic wrap is a good way to learn about higher dimensions, and discover what soap bubbles have to teach us about calculus. A series of incremental and hugely entertaining steps take us all the way from simple algebra to the most exotic and fascinating ideas in mathematics: Klein bottles, higher dimensional topology and the many different species of infinity, via unimaginably small pizza slices, Mobius strips and a thorough examination of The Sausage Conjecture. This lively, funny, and deeply intelligent book teaches math in a fun, interactive manner rather than by rote learning and exercises. You'll not look at the number 37 the same way again. And you just might take part in Mobius strip craftwork.
Think Bayes
by Allen B. DowneyIf you know how to program with Python and also know a little about probability, you're ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you'll begin to apply these techniques to real-world problems.Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book's computational approach helps you get a solid start.Use your existing programming skills to learn and understand Bayesian statisticsWork with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testingGet started with simple examples, using coins, M&Ms, Dungeons & Dragons dice, paintball, and hockeyLearn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome.<P><P> Advisory: Bookshare has learned that this book offers only partial accessibility. We have kept it in the collection because it is useful for some of our members. To explore further access options with us, please contact us through the Book Quality link on the right sidebar. Benetech is actively working on projects to improve accessibility issues such as these.
Think Bayes: Bayesian Statistics In Python
by Allen B. DowneyIf you know how to program, you're ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical formulas, using discrete probability distributions rather than continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer and you'll begin to apply these techniques to real-world problems.Bayesian statistical methods are becoming more common and more important, but there aren't many resources available to help beginners. Based on undergraduate classes taught by author Allen B. Downey, this book's computational approach helps you get a solid start.Use your programming skills to learn and understand Bayesian statisticsWork with problems involving estimation, prediction, decision analysis, evidence, and Bayesian hypothesis testingGet started with simple examples, using coins, dice, and a bowl of cookiesLearn computational methods for solving real-world problems
Think Positive, Pippa! (Math Matters)
by Catherine DalyDiscover Math Matters! With over 15 million books sold worldwide, this award-winning series of easy-to-read books will help young readers ages 5-8 approach math with enthusiasm. Great for fans of MathStart or Step into Reading Math.A day at a Renaissance fair? Pippa isn&’t so sure. First she gets stuck with the jester costume, then the fair runs out of turkey legs. But after she becomes a game piece in a living board game, positive and negative take on all new meanings. Steps forward could take her to Unicorn Falls. Steps backward to Stinky Swamp. Think positive, Pippa! With engaging stories that connect math to kids&’ everyday lives, each book in the Teachers&’ Choice Award-winning Math Matters series focuses on a single concept and reinforces math vocabulary and skills. Bonus activities in the back of each book feature math and reading comprehension questions, and even more free activities online add to the fun! (Math topic: Positive and negative numbers).
Think Twice
by Michael J. MauboussinNo matter your field, industry, or specialty, as a leader you make a series of crucial decisions every single day. And the harsh truth is that the majority of decisions--no matter how good the intentions behind them--are mismanaged, resulting in a huge toll on organizations, the people they employ, and even the people they serve.So why is it so hard to make sound decisions? In Think Twice, now in paperback, Michael Mauboussin argues that we often fall victim to simplified mental routines that prevent us from coping with the complex realities inherent in important judgment calls. Yet these cognitive errors are preventable.In this engaging book, Mauboussin shows us how to recognize and avoid common mental missteps. These include misunderstanding cause-and-effect linkages, not considering enough alternative possibilities in making a decision, and relying too much on experts.Through vivid stories, the author presents memorable rules for avoiding each error and explains how to recognize when you should "think twice"--questioning your reasoning and adopting decision-making strategies that are far more effective, even if they seem counterintuitive. Armed with this awareness, you'll soon begin making sounder judgment calls that benefit (rather than hurt) your organization.
Thinking About Equations
by William A. Friedman Matt A. BernsteinAn accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineeringEquations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences.Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including:Approximation and estimationIsolating important variablesGeneralization and special casesDimensional analysis and scalingPictorial methods and graphical solutionsSymmetry to simplify equationsEach chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension.Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.
Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity (Einstein Studies #15)
by Claus Beisbart Tilman Sauer Christian WüthrichThis volume offers an integrated understanding of how the theory of general relativity gained momentum after Einstein had formulated it in 1915. Chapters focus on the early reception of the theory in physics and philosophy and on the systematic questions that emerged shortly after Einstein's momentous discovery. They are written by physicists, historians of science, and philosophers, and were originally presented at the conference titled Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity, held at the University of Bern from September 12-14, 2017. By establishing the historical context first, and then moving into more philosophical chapters, this volume will provide readers with a more complete understanding of early applications of general relativity (e.g., to cosmology) and of related philosophical issues. Because the chapters are often cross-disciplinary, they cover a wide variety of topics related to the general theory of relativity. These include:Heuristics used in the discovery of general relativityMach's PrincipleThe structure of Einstein's theoryCosmology and the Einstein worldStability of cosmological modelsThe metaphysical nature of spacetimeThe relationship between spacetime and dynamicsThe Geodesic PrincipleSymmetriesThinking About Space and Time will be a valuable resource for historians of science and philosophers who seek a deeper knowledge of the (early and later) uses of general relativity, as well as for physicists and mathematicians interested in exploring the wider historical and philosophical context of Einstein's theory.
Thinking and Reasoning with Data and Chance Sixty-eighth Yearbook
by Gail F. Burrill Portia C. ElliottThe 2006 NCTM Sixty-eighth Yearbook focuses on students' and teachers' learning in statistics centered on a set of activities. Topics include the relation between mathematics and statistics, the development and enrichment of mathematical concepts through the use of statistics, and a discussion of the research related to teaching and learning statistics. The yearbook articles cover a variety of broad areas, including sections on Learning about Data and Chance, Reasoning with Data and Chance, and Reflecting on Issues Related to Data and Chance. Articles focus on such topics as examining children's beliefs about what is fair and using simulation techniques in the classroom. NCTM yearbooks focus concerted attention on timely issues by viewing them in depth, from multiple perspectives, through interdisciplinary lenses, and across different grade bands. The year 2006 marks the sixty-eighth yearbook in the NCTM yearbook series.
Thinking Better: The Art of the Shortcut in Math and Life
by Marcus du SautoyOne of the world's great mathematicians shows why math is the ultimate timesaver—and how everyone can make their lives easier with a few simple shortcuts.We are often told that hard work is the key to success. But success isn&’t about hard work – it&’s about shortcuts. Shortcuts allow us to solve one problem quickly so that we can tackle an even bigger one. They make us capable of doing great things. And according to Marcus du Sautoy, math is the very art of the shortcut.Thinking Better is a celebration of how math lets us do more with less. Du Sautoy explores how diagramming revolutionized therapy, why calculus is the greatest shortcut ever invented, whether you must really practice for ten thousand hours to become a concert violinist, and why shortcuts give us an advantage over even the most powerful AI. Throughout, we meet artists, scientists, and entrepreneurs who use mathematical shortcuts to change the world.Delightful, illuminating, and above all practical, Thinking Better is for anyone who has wondered why you should waste time climbing the mountain when you could go around it much faster.
Thinking Deeply About Primary Mathematics
by Kieran MackleThinking Deeply about Primary Mathematics is a comprehensive exploration of the ideas, theories and practices of most value to beginning teachers, as well as any teacher with the desire to improve their practice.Immediately applicable in the classroom and supported by robust analysis of research into mathematics teaching, this book is designed to provide inspiration for specialised teaching assignments with the power to enhance both the rate and quality of your professional development journey.Through the use of expertly crafted explanations, examples and tasks, each chapter will guide you step by step through the otherwise intimidating world of primary mathematics teaching.This book is perfect for teachers driven to become highly effective practitioners. It also serves as a blueprint for school leaders looking to develop the abilities of their teachers and ensure the highest quality mathematics education for all children.Teacher proficiency is a vast uneven continuum but in taking time to think deeply about primary mathematics we allow ourselves with the opportunity to build a solid base from which a successful, fulfilling career can be constructed.The insight and expertise provided by Thinking Deeply About Primary Mathematics is essential for anyone involved in the teaching of mathematics.
Thinking Deeply About Primary Mathematics
by Kieran MackleThinking Deeply about Primary Mathematics is a comprehensive exploration of the ideas, theories and practices of most value to beginning teachers, as well as any teacher with the desire to improve their practice.Immediately applicable in the classroom and supported by robust analysis of research into mathematics teaching, this book is designed to provide inspiration for specialised teaching assignments with the power to enhance both the rate and quality of your professional development journey.Through the use of expertly crafted explanations, examples and tasks, each chapter will guide you step by step through the otherwise intimidating world of primary mathematics teaching.This book is perfect for teachers driven to become highly effective practitioners. It also serves as a blueprint for school leaders looking to develop the abilities of their teachers and ensure the highest quality mathematics education for all children.Teacher proficiency is a vast uneven continuum but in taking time to think deeply about primary mathematics we allow ourselves with the opportunity to build a solid base from which a successful, fulfilling career can be constructed.The insight and expertise provided by Thinking Deeply About Primary Mathematics is essential for anyone involved in the teaching of mathematics.
Thinking, Drawing, Modelling: GEOMETRIAS 2017, Coimbra, Portugal, June 16–18 (Springer Proceedings in Mathematics & Statistics #326)
by Vera Viana Vítor Murtinho João Pedro XavierThis book presents a selection of papers from the International Conference Geometrias’17, which was hosted by the Department of Architecture at the University of Coimbra from 16 to 18 June 2017. The Geometrias conferences, organized by Aproged (the Portuguese Geometry and Drawing Teachers’ Association), foster debate and exchange on practical and theoretical research in mathematics, architecture, the arts, engineering, and related fields.Geometrias’17, with the leitmotif “Thinking, Drawing, Modelling”, brought together a group of recognized experts to discuss the importance of geometric literacy and the science of representation for the development of scientific and technological research and professional practices. The 12 peer-reviewed papers gathered here show how geometry, drawing, stereotomy, and the science of representation are still at the core of every act leading to the conception and materialization of form, and highlight their continuing relevance for scholars and professionals in the fields of architecture, engineering, and applied mathematics.
Thinking Geometrically: A Survey of Geometries (Maa Textbooks #26)
by Thomas Q. SibleyThis is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. <P><P>Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. <P><P>The text is self-contained, including appendices with the material in Euclid s first book and a high school axiomatic system as well as Hilbert s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.
Thinking in Numbers: How Maths Illuminates Our Lives
by Daniel TammetThis is the book that Daniel Tammet, bestselling author and mathematical savant, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes and everyday examples, Tammet allows us to share his unique insights and delight in the way numbers, fractions and equations underpin all our lives.Inspired by the complexity of snowflakes, Anne Boleyn's sixth finger or his mother's unpredictable behaviour, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person and how we can make sense of those we love.Thinking in Numbers will change the way you think about maths and fire your imagination to see the world with fresh eyes.
Thinking In Numbers: On Life, Love, Meaning, and Math
by Daniel Tammet"Englarges one's wonder at Tammet's mind and his all-embracing vision of the world as grounded in numbers." --Oliver Sacks, MD THINKING IN NUMBERS is the book that Daniel Tammet, bestselling author and mathematical savant, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired by the complexity of snowflakes, Anne Boleyn's eleven fingers, or his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. THINKING IN NUMBERS will change the way you think about math and fire your imagination to see the world with fresh eyes.
Thinking in Numbers: How Maths Illuminates Our Lives
by Daniel TammetThis is the book that Daniel Tammet, bestselling author and mathematical savant, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes and everyday examples, Tammet allows us to share his unique insights and delight in the way numbers, fractions and equations underpin all our lives.Inspired by the complexity of snowflakes, Anne Boleyn's sixth finger or his mother's unpredictable behaviour, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person and how we can make sense of those we love.Thinking in Numbers will change the way you think about maths and fire your imagination to see the world with fresh eyes.(P)2013 Hodder & Stoughton