While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world inwhich we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics andengineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

    Emphasizes the applications of theory, and contains new material on particle physics, electron-positron annihilation in solids and the Mossbauer effect. Includes new appendices on such topics as crystallography, Fourier Integral Description of a Wave Group, and Time-Independent Perturbation Theory.

    Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.

    Inspired by Einstein, Coltrane put physics and geometry at the core of his music. Physicist and jazz musician Stephon Alexander follows suit, using jazz to answer physics' most vexing questions about the past and future of the universe. Following the great minds that first drew the links between music and physics-a list including Pythagoras, Kepler, Newton, Einstein, and Rakim-The Jazz of Physics reveals that the ancient poetic idea of the Music of the Spheres," taken seriously, clarifies confounding issues in physics. The Jazz of Physics will fascinate and inspire anyone interested in the mysteries of our universe, music, and life itself.

    That collaboration would mark the dawn of modern science . . . and end in murder.Johannes Kepler changed forever our understanding of the universe with his three laws of planetary motion. He demolished the ancient model of planets moving in circular orbits and laid the foundation for the universal law of gravitation, setting physics on the course of revelation it follows to this day. Kepler was one of the greatest astronomers of all time. Yet if it hadn't been for the now lesser-known Tycho Brahe, the man for whom Kepler apprenticed, Kepler would be a mere footnote in today's science books. Brahe was the Imperial Mathematician at the court of the Holy Roman Emperor in Prague and the most famous astronomer of his era. He was one of the first great systematic empirical scientists and one of the earliest founders of the modern scientific method. His forty years of planetary observations—an unparalleled treasure of empirical data—contained the key to Kepler's historic breakthrough. But those observations would become available to Kepler only after Brahe's death. This groundbreaking history portrays the turbulent collaboration between these two astronomers at the turn of the seventeenth century and their shattering discoveries that would mark the transition from medieval to modern science. But that is only half the story. Based on recent forensic evidence (analyzed here for the first time) and original research into medieval and Renaissance alchemy—all buttressed by in-depth interviews with leading historians, scientists, and medical specialists—the authors have put together shocking and compelling evidence that Tycho Brahe did not die of natural causes, as has been believed for four hundred years. He was systematically poisoned—most likely by his assistant, Johannes Kepler. An epic tale of murder and scientific discovery, Heavenly Intrigue reveals the dark side of one of history’s most brilliant minds and tells the story of court politics, personal intrigue, and superstition that surrounded the protean invention of two great astronomers and their quest to find truth and beauty in the heavens above.

    

    By tracking a pendulum's path as it swung repeatedly across the interior of the large ceremonial hall, Foucault offered the first definitive proof -- before an audience that comprised the cream of Parisian society, including the future emperor, Napoleon III -- that the earth revolves on its axis.Through careful, primary research, world-renowned author Amir Aczel has revealed the life of a gifted physicist who had almost no formal education in science, and yet managed to succeed despite the adversity he suffered at the hands of his peers. The range and breadth of Foucault's discoveries is astonishing: He gave us the modern electric compass, devised an electric microscope, invented photographic technology, and made remarkable deductions about color theory, heat waves, and the speed of light. Yet until now so little has been known about his life.Richly detailed and evocative, Pendulum tells of the illustrious period in France during the Second Empire; of Foucault's relationship with Napoleon III, a colorful character in his own right; and -- most notably -- of the crucial triumph of science over religion.Dr. Aczel has crafted a fascinating narrative based on the life of this most astonishing and largely unrecognized scientist, whose findings answered many age-old scientific questions and posed new ones that are still relevant today.

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    It covers all relevant areas, including molecular spectroscopy, electronic structure computations, molecular beam methods and time-resolved measurements of chemical systems.