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An interdisciplinary approach of interest to scientists and engineers working in a number of areas.

The book combines recent results of quantum dot laser modeling with mathematical details and an analytic understanding of nonlinear phenomena in semiconductor lasers and points out possible applications of lasers in cryptography and chaos control. This interdisciplinary approach makes it a unique and powerful source of knowledge for anyone intending to contribute to this field of research.

By presenting both experimental and theoretical results, the distinguished authors consider solitary lasers with nano-structured material, as well as integrated devices with complex feedback sections. In so doing, they address such topics as the bifurcation theory of systems with time delay, analysis of chaotic dynamics, and the modeling of quantum transport. They also address chaos-based cryptography as an example of the technical application of highly nonlinear laser systems.

The authors explore the application of these concepts to nano- and biosystems by cross-linking key methods and ideas from nonequilibrium statistical physics, thermodynamics, stochastic theory, and dynamical systems. By providing an up-to-date survey of small systems physics, the text serves as both a valuable reference for experienced researchers and as an ideal starting point for graduate-level students entering this newly emerging research field.

For everybody working on the synthesis and integration of nanoscopic devices who sooner or later will have to learn how to deal with nonlinear effects.

task, the editor of the book invited experts in bio-engineering, chemistry, cardiology, neuroscience,

computer science, and applied mathematics, to provide their perspectives.

Each chapter is a window into the current state of the art in the areas of research discussed and the book is intended for advanced researchers interested in recent developments in these fields. While multiscale

analysis is the major integrating theme of the book, its subtitle does not call for bridging the

scales from genes to behavior, but rather stresses the unifying perspective offered by the concepts

referred to in the title.

It is believed that the interdisciplinary approach adopted here will be beneficial for all the above mentioned fields.

This book defines the field of complex interacting networks in its infancy and presents the dynamics of networks and their structure as a key concept across disciplines.

The contributions present common underlying principles of network dynamics and their theoretical description and are of interest to specialists as well as to the non-specialized reader looking for an introduction to this new exciting field.

Theoretical concepts include modeling networks as dynamical systems with numerical methods and new graph theoretical methods, but also focus on networks that change their topology as in morphogenesis and self-organization. The authors offer concepts to model network structures and dynamics, focussing on approaches applicable across disciplines.

criticality and brain function.

The book begins by summarizing experimental evidence for criticality and self-organized

criticality in the brain. Subsequently, important breakthroughs in modeling of critical neuronal circuits and how to establish self-organized criticality in the brain are described.

A milestone publication, defining upcoming directions of research in this new fi eld and set to become the primary source of information on the brain and criticality.

The editors provide both in-depth knowledge of the topic as well as vast experience in guiding an expert team of authors. The review style articles offer a coherent view of the micromixing methods, resulting in a much-needed synopsis of the theoretical models needed to direct experimental research and establish engineering principles for future applications.

Since these processes are governed by nonlinear phenomena, this book will appeal to readers from both communities: fluid mechanics and nonlinear dynamics.

What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.

In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.

Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before.

At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

Physicist Dave Goldberg speeds across space, time and everything in between showing that our elegant universe—from the Higgs boson to antimatter to the most massive group of galaxies—is shaped by hidden symmetries that have driven all our recent discoveries about the universe and all the ones to come.

Why is the sky dark at night? If there is anti-matter, can there be anti-people? Why are past, present, and future our only options? Saluting the brilliant but unsung female mathematician Emmy Noether as well as other giants of physics, Goldberg answers these questions and more, exuberantly demonstrating that symmetry is the big idea—and the key to what lies ahead.

From the Trade Paperback edition.

The Future of the Mind brings a topic that once belonged solely to the province of science fiction into a startling new reality. This scientific tour de force unveils the astonishing research being done in top laboratories around the world—all based on the latest advancements in neuroscience and physics—including recent experiments in telepathy, mind control, avatars, telekinesis, and recording memories and dreams. The Future of the Mind is an extraordinary, mind-boggling exploration of the frontiers of neuroscience. Dr. Kaku looks toward the day when we may achieve the ability to upload the human brain to a computer, neuron for neuron; project thoughts and emotions around the world on a brain-net; take a “smart pill” to enhance cognition; send our consciousness across the universe; and push the very limits of immortality.

Space and time form the very fabric of the cosmos. Yet they remain among the most mysterious of concepts. Is space an entity? Why does time have a direction? Could the universe exist without space and time? Can we travel to the past? Greene has set himself a daunting task: to explain non-intuitive, mathematical concepts like String Theory, the Heisenberg Uncertainty Principle, and Inflationary Cosmology with analogies drawn from common experience. From Newton’s unchanging realm in which space and time are absolute, to Einstein’s fluid conception of spacetime, to quantum mechanics’ entangled arena where vastly distant objects can instantaneously coordinate their behavior, Greene takes us all, regardless of our scientific backgrounds, on an irresistible and revelatory journey to the new layers of reality that modern physics has discovered lying just beneath the surface of our everyday world.

“Where did the universe come from? What was there before it? What will the future bring? And finally, why is there something rather than nothing?”

One of the few prominent scientists today to have crossed the chasm between science and popular culture, Krauss describes the staggeringly beautiful experimental observations and mind-bending new theories that demonstrate not only can something arise from nothing, something will always arise from nothing. With a new preface about the significance of the discovery of the Higgs particle, A Universe from Nothing uses Krauss’s characteristic wry humor and wonderfully clear explanations to take us back to the beginning of the beginning, presenting the most recent evidence for how our universe evolved—and the implications for how it’s going to end.

Provocative, challenging, and delightfully readable, this is a game-changing look at the most basic underpinning of existence and a powerful antidote to outmoded philosophical, religious, and scientific thinking.

After the economic meltdown of 2008, Warren Buffett famously warned, “beware of geeks bearing formulas.” But while many of the mathematicians and software engineers on Wall Street failed when their abstractions turned ugly in practice, a special breed of physicists has a much deeper history of revolutionizing finance. Taking us from fin-de-siècle Paris to Rat Pack–era Las Vegas, from wartime government labs to Yippie communes on the Pacific coast, James Owen Weatherall shows how physicists successfully brought their science to bear on some of the thorniest problems in economics, from options pricing to bubbles.

The crisis was partly a failure of mathematical modeling. But even more, it was a failure of some very sophisticated financial institutions to think like physicists. Models—whether in science or finance—have limitations; they break down under certain conditions. And in 2008, sophisticated models fell into the hands of people who didn’t understand their purpose, and didn’t care. It was a catastrophic misuse of science. The solution, however, is not to give up on models; it’s to make them better.

This book reveals the people and ideas on the cusp of a new era in finance, from a geophysicist using a model designed for earthquakes to predict a massive stock market crash to a physicist-run hedge fund earning 2,478.6% over the course of the 1990s. Weatherall shows how an obscure idea from quantum theory might soon be used to create a far more accurate Consumer Price Index. The Physics of Wall Street will change how we think about our economic future.

“Fascinating history . . . Happily, the author has a gift for making complex concepts clear to lay readers.” —Booklist

"Such a richness of topics and amazing splendor of illustrations!" — Mathematics Magazine

"An inviting exposition for a literate but not highly scientific audience." — American Mathematical Monthly

This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. Author Manfred Schroeder — hailed by Publishers Weekly as a modern Lewis Carroll — conveys memorable insights in the form of puns and puzzles that relate abstract mathematics to everyday experience.

Excellent entertainment for readers with a grasp of algebra and some calculus, this book forms a fine university-level introduction to fractal math. Eight pages of color images clarify the text, along with numerous black-and-white illustrations.

Richard Feynman, winner of the Nobel Prize in physics, thrived on outrageous adventures. Here he recounts in his inimitable voice his experience trading ideas on atomic physics with Einstein and Bohr and ideas on gambling with Nick the Greek; cracking the uncrackable safes guarding the most deeply held nuclear secrets; accompanying a ballet on his bongo drums; painting a naked female toreador. In short, here is Feynman's life in all its eccentric—a combustible mixture of high intelligence, unlimited curiosity, and raging chutzpah.

In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems--some three dozen in all--that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end.

Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class--and anyone who enjoys popular math books.

From the Trade Paperback edition.

The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book.

Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.

- Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis.

This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.

Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure.

The book is arranged in four sections, devoted to realizing the universal principle force equals curvature:

Part I: The Euclidean Manifold as a Paradigm

Part II: Ariadne's Thread in Gauge Theory

Part III: Einstein's Theory of Special Relativity

Part IV: Ariadne's Thread in Cohomology

For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum.

Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.

- Fully searchable CD that puts information at your

fingertips included with text

- Most up to date listing of integrals, series and

products

- Provides accuracy and efficiency in work

It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived.

As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.

http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html

- Compact modal logic reference

- Computational approaches fully discussed

- Contemporary applications of modal logic covered in depth

Starting with a survey of basic statistical mechanics, the treatment proceeds to examinations of the one-dimensional Ising model, the mean field model, the Ising model on the Bethe lattice, and the spherical model. Subsequent chapters address duality and star-triangle transforms of planar Ising models, the square-lattice Ising model, ice-type models, and the square lattice eight-vertex model. Additional topics include the Kagomé lattice eight-vertex model, Potts and Ashkin-Teller models, Corner transfer matrices, hard hexagon and related models, and elliptic functions. Seventy-six figures illuminate the text.

The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.

This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.

Over 36,000 copies sold worldwideAccessible, practical yet rigorous approach to a complex topic--also suitable for self-studyExtensive update of appendices on Mathematica and Maple software packagesThorough streamlining of second edition's numbering systemFuller information on solutions to odd-numbered problemsAdditional exercises and hints guide students in using the latest computer modeling toolsFor more than thirty years as a beloved professor at the Massachusetts Institute of Technology, Lewin honed his singular craft of making physics not only accessible but truly fun, whether putting his head in the path of a wrecking ball, supercharging himself with three hundred thousand volts of electricity, or demonstrating why the sky is blue and why clouds are white. Now, as Carl Sagan did for astronomy and Brian Green did for cosmology, Lewin takes readers on a marvelous journey in For the Love of Physics, opening our eyes as never before to the amazing beauty and power with which physics can reveal the hidden workings of the world all around us. “I introduce people to their own world,” writes Lewin, “the world they live in and are familiar with but don’t approach like a physicist—yet.”

Could it be true that we are shorter standing up than lying down? Why can we snorkel no deeper than about one foot below the surface? Why are the colors of a rainbow always in the same order, and would it be possible to put our hand out and touch one? Whether introducing why the air smells so fresh after a lightning storm, why we briefly lose (and gain) weight when we ride in an elevator, or what the big bang would have sounded like had anyone existed to hear it, Lewin never ceases to surprise and delight with the extraordinary ability of physics to answer even the most elusive questions.

Recounting his own exciting discoveries as a pioneer in the field of X-ray astronomy—arriving at MIT right at the start of an astonishing revolution in astronomy—he also brings to life the power of physics to reach into the vastness of space and unveil exotic uncharted territories, from the marvels of a supernova explosion in the Large Magellanic Cloud to the unseeable depths of black holes.

“For me,” Lewin writes, “physics is a way of seeing—the spectacular and the mundane, the immense and the minute—as a beautiful, thrillingly interwoven whole.” His wonderfully inventive and vivid ways of introducing us to the revelations of physics impart to us a new appreciation of the remarkable beauty and intricate harmonies of the forces that govern our lives.

Kaku skillfully guides us through the latest innovations in string theory and its latest iteration, M-theory, which posits that our universe may be just one in an endless multiverse, a singular bubble floating in a sea of infinite bubble universes. If M-theory is proven correct, we may perhaps finally find answer to the question, “What happened before the big bang?” This is an exciting and unforgettable introduction into the new cutting-edge theories of physics and cosmology from one of the pre-eminent voices in the field.

From the Trade Paperback edition.

In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study.

While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicists who would like to see a more mathematical approach to the ideas.

Every now and then a simple yet radical idea shakes the very foundations of knowledge. The startling discovery that the world was not flat challenged and ultimately changed the way people perceived themselves and their relationship with the world. For most humans of the 15th century, the notion of Earth as ball of rock was nonsense. The whole of Western, natural philosophy is undergoing a sea change again, increasingly being forced upon us by the experimental findings of quantum theory, and at the same time, towards doubt and uncertainty in the physical explanations of the universe’s genesis and structure. Biocentrism completes this shift in worldview, turning the planet upside down again with the revolutionary view that life creates the universe instead of the other way around.

In this paradigm, life is not an accidental byproduct of the laws of physics. Biocentrism takes the reader on a seemingly improbable but ultimately inescapable journey through a foreign universe—our own—from the viewpoints of an acclaimed biologist and a leading astronomer. Switching perspective from physics to biology unlocks the cages in which Western science has unwittingly managed to confine itself. Biocentrism will shatter the reader’s ideas of life—time and space, and even death. At the same time it will release us from the dull worldview of life being merely the activity of an admixture of carbon and a few other elements; it suggests the exhilarating possibility that life is fundamentally immortal.

The 21st century is predicted to be the Century of Biology, a shift from the previous century dominated by physics. It seems fitting, then, to begin the century by turning the universe outside-in and unifying the foundations of science with a simple idea discovered by one of the leading life-scientists of our age. Biocentrism awakens in readers a new sense of possibility, and is full of so many shocking new perspectives that the reader will never see reality the same way again.

During the last 20-25 years, classical mechanics has undergone an important revival associated with the progress in non-linear dynamics, applications of Noether’s theorem and the extension of variational principles in various interdisciplinary sciences (for instance, magnetofluid dynamics). Thus, there ought to exist a book concerned with the applied analytical formalism, first developed in the frame of theoretical mechanics, which has proved to be one of the most efficient tools of investigation in the entire arena of science.

The present book is an outcome of the authors’ teaching experience over many years in different countries and for different students studying diverse fields of physics. The book is intended for students at the level of undergraduate and graduate studies in physics, engineering, astronomy, applied mathematics and for researchers working in related subjects.

We hope that the original presentation and the distribution of the topics, the various applications in many branches of physics and the set of more than 100 proposed problems, shall make this book a comprehensive and useful tool for students and researchers.

The present book is an outcome of the authors’ teaching experience over many years in different countries and for different students studying diverse fields of physics. The book is intended for students at the level of undergraduate and graduate studies in physics, engineering, astronomy, applied mathematics and for researchers working in related subjects.

We hope that the original presentation and the distribution of the topics, the various applications in many branches of physics and the set of more than 100 proposed problems, shall make this book a comprehensive and useful tool for students and researchers.

From the Trade Paperback edition.