A Leading Figure in the Development of the New Cosmology Explains What It All Means Among his peers, Alex Vilenkin is regarded as one of the most imaginative and creative cosmologists of our time. His contributions to our current understanding of the universe include a number of novel ideas, two of which—eternal cosmic inflation and the quantum creation of the universe from nothing—have provided a scientific foundation for the possible existence of multiple universes. With this book—his first for the general reader—Vilenkin joins another select group: the handful of first-rank scientists who are equally adept at explaining their work to nonspecialists. With engaging, well-paced storytelling, a droll sense of humor, and a generous sprinkling of helpful cartoons, he conjures up a bizarre and fascinating new worldview that—to paraphrase Niels Bohr—just might be crazy enough to be true.
A Leading Figure in the Development of the New Cosmology Explains What It All Means Among his peers, Alex Vilenkin is regarded as one of the most imaginative and creative cosmologists of our time. His contributions to our current understanding of the universe include a number of novel ideas, two of which—eternal cosmic inflation and the quantum creation of the universe from nothing—have provided a scientific foundation for the possible existence of multiple universes. With this book—his first for the general reader—Vilenkin joins another select group: the handful of first-rank scientists who are equally adept at explaining their work to nonspecialists. With engaging, well-paced storytelling, a droll sense of humor, and a generous sprinkling of helpful cartoons, he conjures up a bizarre and fascinating new worldview that—to paraphrase Niels Bohr—just might be crazy enough to be true.
This book is a gentle introduction for all those wishing to learn about modern views of the cosmos. Our universe originated in a great explosion – the big bang. For nearly a century cosmologists have studied the aftermath of this explosion: how the universe expanded and cooled down, and how galaxies were gradually assembled by gravity. The nature of the bang itself has come into focus only relatively recently. It is the subject of the theory of cosmic inflation, which was developed in the last few decades and has led to a radically new global view of the universe. Students and other interested readers will find here a non-technical but conceptually rigorous account of modern cosmological ideas - describing what we know, and how we know it. One of the book's central themes is the scientific quest to find answers to the ultimate cosmic questions: Is the universe finite or infinite? Has it existed forever? If not, when and how did it come into being? Will it ever end? The book is based on the undergraduate course taught by Alex Vilenkin at Tufts University. It assumes no prior knowledge of physics or mathematics beyond elementary high school math. The necessary physics background is introduced as it is required. Each chapter includes a list of questions and exercises of varying degree of difficulty.
This book is a gentle introduction for all those wishing to learn about modern views of the cosmos. Our universe originated in a great explosion – the big bang. For nearly a century cosmologists have studied the aftermath of this explosion: how the universe expanded and cooled down, and how galaxies were gradually assembled by gravity. The nature of the bang itself has come into focus only relatively recently. It is the subject of the theory of cosmic inflation, which was developed in the last few decades and has led to a radically new global view of the universe. Students and other interested readers will find here a non-technical but conceptually rigorous account of modern cosmological ideas - describing what we know, and how we know it. One of the book's central themes is the scientific quest to find answers to the ultimate cosmic questions: Is the universe finite or infinite? Has it existed forever? If not, when and how did it come into being? Will it ever end? The book is based on the undergraduate course taught by Alex Vilenkin at Tufts University. It assumes no prior knowledge of physics or mathematics beyond elementary high school math. The necessary physics background is introduced as it is required. Each chapter includes a list of questions and exercises of varying degree of difficulty.
The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L^2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
Would a loving God really send people to hell? Can we really trust what the Bible says? Is Jesus really the only way to heaven? Becoming a Christian does not mean that all of the questions about faith are instantly answered. In fact, more questions are likely to follow. However, not having knowledge about certain issues can dampen your faith and rob you of the joy that comes from confidently sharing it with others. 10 Questions Every Christian Must Answer provides responses to the toughest conversations regarding one's inward faith as well as the outward expression of it and is relevant to new believers and longtime Christ followers alike. Led by respected scholars Elmer Towns and Alex McFarland, readers can be sure this content is backed by sharp minds, deep thinking, and the unchanging Word of God.
Over the past decade, the field of image processing has made tremendous advances. One type of image processing that is currently of particular interest is "tomographic imaging," a technique for computing the density function of a body, or discontinuity surfaces of this function. Today, tomography is widely used, and has applications in such fields as medicine, engineering, physics, geophysics, and security. The Radon Transform and Local Tomography clearly explains the theoretical, computational, and practical aspects of applied tomography. It includes sufficient background information to make it essentially self-contained for most readers.
Preface 1. Mathematical Logic 2. Abstract Algebra 3. Number Theory 4. Real Analysis 5. Probability and Statistics 6. Graph Theory 7. Complex Analysis Answers to Questions Answers to Odd Numbered Questions Index of Online Resources Bibliography Index.
The physics of non-equilibrium many-body systems is a rapidly expanding area of theoretical physics. Traditionally employed in laser physics and superconducting kinetics, these techniques have more recently found applications in the dynamics of cold atomic gases, mesoscopic and nano-mechanical systems, and quantum computation. This book provides a detailed presentation of modern non-equilibrium field-theoretical methods, applied to examples ranging from biophysics to the kinetics of superfluids and superconductors. A highly pedagogical and self-contained approach is adopted within the text, making it ideal as a reference for graduate students and researchers in condensed matter physics. In this Second Edition, the text has been substantially updated to include recent developments in the field such as driven-dissipative quantum systems, kinetics of fermions with Berry curvature, and Floquet kinetics of periodically driven systems, among many other important new topics. Problems have been added throughout, structured as compact guided research projects that encourage independent exploration.
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