Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    It explores the critical concepts while also examining why they are relevant. The core content is presented within the framework of predicting products, proposing mechanisms, and solving synthesis problems. Readers will fine-tune the key skills involved in solving those types of problems with the help of interactive, step-by-step instructions and problems.

    This edition contains NEW tables on Properties of Ionic Liquids, Solubilities of Hydrocarbons in Sea Water, Solubility of Organic Compounds in Superheated Water, and Nutritive Value of Foods. It also updates many tables including Critical Constants, Heats of Vaporization, Aqueous Solubility of Organic Compounds, Vapor Pressure of Mercury, Scientific Abbreviations and Symbols, and Bond Dissociation Energies. The 88th Edition also presents a new Foreword written by Dr. Harold Kroto, a 1996 Nobel Laureate in Chemistry.

    Starting once again with fossils, he turns his gaze skyward, showing us how the entirety of the universe’s fourteen-billion-year history can be seen in our bodies. As he moves from our very molecular composition (a result of stellar events at the origin of our solar system) through the workings of our eyes, Shubin makes clear how the evolution of the cosmos has profoundly marked our own bodies. Fully illustrated with black and white drawings.

    Why? In John McMurry's words: "I have been asked hundreds of times over the past ten years why I wrote this book. I wrote this book because I love writing. I get great pleasure and satisfaction from taking a complicated subject, turning it around until I see it clearly from a new angle, and then explaining it in simple words. I write to explain chemistry to students the way I wish it had been explained to me years ago." Through his lucid writing and ability to show the beauty and logic of organic chemistry, McMurry makes learning enjoyable for students. The highest compliment that can be given to a chemistry book applies to McMurry: It works! Mainstream in level, McMurry's coverage is concise yet doesn't omit any key topics. McMurry blends the traditional functional-group approach with a mechanistic approach. The primary approach, by functional group, begins with the simple and progresses to the more complex so that readers who are not yet versed in the subtleties of mechanisms are first exposed to the "what" of chemistry before beginning to grapple with the "why." Within this primary organization, the author places a heavy emphasis on explaining the fundamental mechanistic similarities. In this edition, McMurry retains his standard-setting features (including his innovative vertical format for explaining reaction mechanisms) while revising his text line-by-line to include hundreds of small but important improvements. For example, the Sixth Edition includes new examples, additional steps in existing examples, new problems, new phrases to clarify the exposition, and a vibrant new art program. In addition, new icons in the text lead students to a variety of new online resources. McMurry's text is in use at hundreds of colleges and universities around the world, from North America, to the United Kingdom and the Pacific Rim.

    Penned by award-winning science writer John Emsley, Nature's Building Blocks explains the what, why and wherefore of the chemical elements. Arranged alphabetically, from Actinium to Zirconium, it is a complete guide to all 115 of those that are currently known, with more extensive coverage of those elements we encounter in our everyday life. The entry on each element reveals where it came from, what role it may have in the human body, and the foods that contain it. There are also sections on its discovery, its part in human health or illness, the uses and misuses to which it is put, and its environmental role. Readers discover that the Earth consists of around 90 elements, some of which are abundant, such as the silicon and oxygen of rocks and soils, while some are so rare that they make gold seem cheap. Our own bodies contain about 30 elements, some in abundance, some in trace amounts; some vital to our health, and some that are positively harmful. A list of the main scientific data, and outline properties, are given for every element and each section ends with an Element of Surprise, which highlights some unexpected way in which each element influences our everyday life. Both a reliable reference source and a high browsable account of the elements, Nature's Building Blocks offers a pleasurable tour of the very essence of our material world.

    More than a series of fascinating case studies, To Engineer Is Human is a work that looks at our deepest notions of progress and perfection, tracing the fine connection between the quantifiable realm of science and the chaotic realities of everyday life."Alert, inquisitive, unspecialized, wholly human...refreshingly eclectic." --The Spectator"Henry Petroski is an ardent engineer, and if he writes more good books like this, he might find himself nominated to become the meistersinger of the guild. [This is] a refreshing plunge into the dynamics of the engineering ethos...as straightforward as an I-beam."--Science

    They bring a conceptual approach to chemistry and integrate problem-solving skills throughout, helping students transition from theory to practice. A strong emphasis on models, real-world applications, and visual learning prevails throughout the text. The Seventh Edition seamlessly integrates the strengths of the Zumdahl approach through a comprehensive and interwoven print and technology program. Enhanced Sample Exercises, online homework problems, and Classroom Response System content help instructors assess conceptual understanding and problem-solving skills, while new animations and images support visual learning. In addition, Houghton Mifflin offers implementation services through our TeamUP program to help instructors and students get the most out of the text and its supplements.

    For more than two centuries, our understanding of the laws of nature expanded rapidly. But today, despite our best efforts, we know nothing more about these laws than we knew in the 1970s. Why is physics suddenly in trouble? And what can we do about it?One of the major problems, according to Smolin, is string theory: an ambitious attempt to formulate a “theory of everything” that explains all the particles and forces of nature and how the universe came to be. With its exotic new particles and parallel universes, string theory has captured the public’s imagination and seduced many physicists.But as Smolin reveals, there’s a deep flaw in the theory: no part of it has been tested, and no one knows how to test it. In fact, the theory appears to come in an infinite number of versions, meaning that no experiment will ever be able to prove it false. As a scientific theory, it fails. And because it has soaked up the lion’s share of funding, attracted some of the best minds, and effectively penalized young physicists for pursuing other avenues, it is dragging the rest of physics down with it.With clarity, passion, and authority, Smolin charts the rise and fall of string theory and takes a fascinating look at what will replace it. A group of young theorists has begun to develop exciting ideas that, unlike string theory, are testable. Smolin not only tells us who and what to watch for in the coming years, he offers novel solutions for seeking out and nurturing the best new talent—giving us a chance, at long last, of finding the next Einstein.

    The Structure of Scientific Revolutions is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty years later, it still has many lessons to teach. With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age. This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context.  Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.

    The text takes a unified approach to the subject, aiming to help the reader develop a real overview of chemical processes, byavoiding the traditional divisions of physical, inorganic and organic chemistry.To understand how chemical reactions happen we need to know about the bonding in molecules, how molecules interact, what determines whether an interaction is favorable or not, and what the outcome will be. Answering these questions requires an understanding of topics from quantum mechanics, throughthermodynamics, to curly arrows. In this book all of these topics are presented in a coherent and coordinated fashion, showing how each leads to a deeper understanding of chemical reactions.

    A unique combination of authoritative content and stimulating applications. * Numerous improvements in the text, based on feedback from the many users of the sixth edition (both instructors and students) * Several thousand end-of-chapter problems have been rewritten to streamline both the presentations and answers * 'Chapter Puzzlers' open each chapter with an intriguing application or question that is explained or answered in the chapter * Problem-solving tactics are provided to help beginning Physics students solve problems and avoid common error * The first section in every chapter introduces the subject of the chapter by asking and answering, "What is Physics?" as the question pertains to the chapter * Numerous supplements available to aid teachers and students The extended edition provides coverage of developments in Physics in the last 100 years, including: Einstein and Relativity, Bohr and others and Quantum Theory, and the more recent theoretical developments like String Theory.

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.

    Taken literally, it implies that there are many universes “parallel” to the one we see around us. This multiplicity of universes, according to Deutsch, turns out to be the key to achieving a new worldview, one which synthesizes the theories of evolution, computation, and knowledge with quantum physics. Considered jointly, these four strands of explanation reveal a unified fabric of reality that is both objective and comprehensible, the subject of this daring, challenging book. The Fabric of Reality explains and connects many topics at the leading edge of current research and thinking, such as quantum computers (which work by effectively collaborating with their counterparts in other universes), the physics of time travel, the comprehensibility of nature and the physical limits of virtual reality, the significance of human life, and the ultimate fate of the universe. Here, for scientist and layperson alike, for philosopher, science-fiction reader, biologist, and computer expert, is a startlingly complete and rational synthesis of disciplines, and a new, optimistic message about existence.

    The books published on the subject are so technical that only a person trained in pure physics and higher mathematics is able to fully understand them. In order to make a popular explanation of this far-reaching theory available, the present book is published.