This top-selling, theorem-proof text presents a careful treatment of the principal topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.

    The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

    You'll find out how to unknot your DNA, how to count like a supercomputer and how to become famous for solving mathematics' most challenging problem.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    There's a lot for astronomers to be smug about. But when it comes to understanding how the Universe began and grew up we are literally in the dark ages. In effect, we are missing the first one billion years from the timeline of the Universe.This brief but far-reaching period in the Universe's history, known to astrophysicists as the 'Epoch of Reionisation', represents the start of the cosmos as we experience it today. The time when the very first stars burst into life, when darkness gave way to light. After hundreds of millions of years of dark, uneventful expansion, one by the one these stars suddenly came into being. This was the point at which the chaos of the Big Bang first began to yield to the order of galaxies, black holes and stars, kick-starting the pathway to planets, to comets, to moons, and to life itself.Incorporating the very latest research into this branch of astrophysics, this book sheds light on this time of darkness, telling the story of these first stars, hundreds of times the size of the Sun and a million times brighter, lonely giants that lived fast and died young in powerful explosions that seeded the Universe with the heavy elements that we are made of. Emma Chapman tells us how these stars formed, why they were so unusual, and what they can teach us about the Universe today. She also offers a first-hand look at the immense telescopes about to come on line to peer into the past, searching for the echoes and footprints of these stars, to take this period in the Universe's history from the realm of theoretical physics towards the wonder of observational astronomy.

    The First seven chapters deal with structure related aspects such as lattice and crystal structures, bonding, packing and diffusion of atoms followed by imperfections and lattice vibrations. Chapter eight deals mainly with experimental methods of determining structures of given materials. While the next nine chapters cover various physical properties of crystalline solids, the last chapter deals with the anisotropic properties of materials. This chapter has been added for benefit of readers to understand the crystal properties (anisotropic) in terms of some simple mathematical formulations such as tensor and matrix. New to the Second Edition: Chapter on: *Anisotropic Properties of Materials

    From the months each of us spent suspended in the womb anticipating birth to the moments when we wait for sleep to transport us to other realities, we are always aware of gravity. In On Gravity, physicist A. Zee combines profound depth with incisive accessibility to take us on an original and compelling tour of Einstein's general theory of relativity.Inspired by Einstein's audacious suggestion that spacetime could ripple, Zee begins with the stunning discovery of gravity waves. He goes on to explain how gravity can be understood in comparison to other classical field theories, presents the idea of curved spacetime and the action principle, and explores cutting-edge topics, including black holes and Hawking radiation. Zee travels as far as the theory reaches, leaving us with tantalizing hints of the utterly unknown, from the intransigence of quantum gravity to the mysteries of dark matter and energy.Concise and precise, and infused with Zee's signature warmth and freshness of style, On Gravity opens a unique pathway to comprehending relativity and gaining deep insight into gravity, spacetime, and the workings of the universe.

    Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    Learn about Dr Karl, the universe and everything, and discover how air-conditioning is sexist, how you can kill a spinning hard drive by shouting at it and how space junk is threatening our future capabilities for space travel.Could there be life on one of Saturn's moons? How much power could you collect from all the lightning on Earth? Why do books have book-smell? Why is 10 per cent of the Earth's land area prone to sinkholes?Why are some people chronically late? What would happen if the Earth stopped spinning? Why do most people hardly remember anything from the first half-a-dozen years of their life?How close are we to the Artificial Uterus? Why do some songs turn into "earworms" and stick inside your brain? Why does your hotel room access card get wiped so easily?And is your home WiFi really spying on you?

    The new edition provides invitations - not requirements - to use technology, as well as new conceptual problems, and new projects that focus on writing and working in teams.

    They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators..

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.

    Today, scientists are attempting to measure the entire universe and to determine its origin. Although the methods have changed, the quest to chart the horizons of space and time continues to be one of the great adventures of science.Measuring the Universe is an eloquent chronicle of the men and women– from Aristarchus to Cassini, Sir Isaac Newton to Henrietta Leavitt and Stephen Hawking–who have gradually unlocked the mysteries of "how far" and in so doing have changed our ideas about the size and nature of the universe and our place in it. Kitty Ferguson reveals their methods to have been as inventive as their results were–and are–eye-opening. Advances such as Copernicus's revolutionary insights about the arrangement of the solar system, William Herschel's meticulous creation of the first three-dimensional map of the universe, and Edwin Hubble's astonishing discovery that the universe is expanding have by turns revolutionized our concept of the universe. Connecting centuries of breakthroughs with the political and cultural events surrounding them, Ferguson makes astronomy part of the sweep of history.To measure the seemingly immeasurable, scientists have always pushed the boundaries of the imagination–today, for example, facing the paradox of an ever-expanding universe that doesn't appear to expand into anything. In Kitty Fergeson's skillfill hands, the unimaginable becomes accessible and the splendid quest something we all can share.

    Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

    Without a doubt, the development of the computer was a massive leap forward in humankind's progress and will stand as one of the twentieth century's greatest achievements. But how many of us know how it really works? "Turing And The Computer" offers a brilliant encapsulation of the groundwork that led to the invention of the computer as we know it, and an absorbing account of the man who helped develop it, only to be largely forgotten after his death. Eccentric and principled, Turing would lay aside a brilliant career in mathematics to serve his country by breaking German codes during the Second World War. Openly homosexual, he would later be put on trial on indecency charges and forced to undergo hormone treatments that wrecked his body and his spirit. But the modern machine he helped create lives on.Concise and thoroughly compelling, "Turing And The Computer" is for all those curious about the philosophy and mechanics behind the now indispensable computer, and for anyone awed by the spark of invention that inspires its birth.