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.

    New emphasis has been given to complexity, networks, and patterns of organisation, leading to a novel kind of 'systemic' thinking. This volume integrates the ideas, models, and theories underlying the systems view of life into a single coherent framework. Taking a broad sweep through history and across scientific disciplines, the authors examine the appearance of key concepts such as autopoiesis, dissipative structures, social networks, and a systemic understanding of evolution. The implications of the systems view of life for health care, management, and our global ecological and economic crises are also discussed. Written primarily for undergraduates, it is also essential reading for graduate students and researchers interested in understanding the new systemic conception of life and its implications for a broad range of professions - from economics and politics to medicine, psychology and law.

    "Introductory Readings" provides accurate, readable, and integrated translations that allow the reader to follow Aristotle's use of crucial technical terms and to grasp the details of his argument. Included are adaptations of the glossary and notes that helped make its parent volume a singularly useful aid to the study of Aristotle.

    “A riveting tale of derring-do” (Nature), this book reads like James Gleick’s Chaos combined with an Indiana Jones adventure.When leading Princeton physicist Paul Steinhardt began working in the 1980s, scientists thought they knew all the conceivable forms of matter. The Second Kind of Impossible is the story of Steinhardt’s thirty-five-year-long quest to challenge conventional wisdom. It begins with a curious geometric pattern that inspires two theoretical physicists to propose a radically new type of matter—one that raises the possibility of new materials with never before seen properties, but that violates laws set in stone for centuries. Steinhardt dubs this new form of matter “quasicrystal.” The rest of the scientific community calls it simply impossible. The Second Kind of Impossible captures Steinhardt’s scientific odyssey as it unfolds over decades, first to prove viability, and then to pursue his wildest conjecture—that nature made quasicrystals long before humans discovered them. Along the way, his team encounters clandestine collectors, corrupt scientists, secret diaries, international smugglers, and KGB agents. Their quest culminates in a daring expedition to a distant corner of the Earth, in pursuit of tiny fragments of a meteorite forged at the birth of the solar system. Steinhardt’s discoveries chart a new direction in science. They not only change our ideas about patterns and matter, but also reveal new truths about the processes that shaped our solar system. The underlying science is important, simple, and beautiful—and Steinhardt’s firsthand account is “packed with discovery, disappointment, exhilaration, and persistence...This book is a front-row seat to history as it is made” (Nature).

    The effects of homeopathy don’t go away under rigorous scientific conditions. The laws of nature aren’t what they used to be. Thirty years on, no one has an explanation for a seemingly intelligent signal received from outer space. The US Department of Energy is re-examining cold fusion because the experimental evidence seems too solid to ignore. The placebo effect is put to work in medicine while doctors can’t agree whether it even exists.In an age when science is supposed to be king, scientists are beset by experimental results they simply can’t explain. But, if the past is anything to go by, these anomalies contain the seeds of future revolutions. While taking readers on an entertaining tour d’horizon of the strangest of scientific findings – involving everything from our lack of free will to Martian methane that offers new evidence of life on the planet – Michael Brooks argues that the things we don’t understand are the key to what we are about to discover.This mind-boggling but entirely accessible survey of the outer limits of human knowledge is based on a short article by Michael Brooks for New Scientist magazine. It became the sixth most circulated story on the internet in 2005, and provoked widespread comment and compliments (Google “13 things that do not make sense” to see).Michael Brooks has now dug deeply into those mysteries, with extraordinary results.

    It focuses throughout on phylogenetic trees.

    All of those organisms are rooted in a single origin, with a common code that underwrites our existence. This paradox - that our biology is indistinct from all life, yet we consider ourselves to be special - lies at the heart of who we are.In this original and entertaining tour of life on Earth, Adam Rutherford explores how many of the things once considered to be exclusively human are not: we are not the only species that communicates, makes tools, utilises fire, or has sex for reasons other than to make new versions of ourselves. Evolution has, however, allowed us to develop our culture to a level of complexity that outstrips any other observed in nature.THE BOOK OF HUMANS tells the story of how we became the creatures we are today, bestowed with the unique ability to investigate what makes us who we are. Illuminated by the latest scientific discoveries, it is a thrilling compendium of what unequivocally fixes us as animals, and reveals how we are extraordinary among them.

    Global climate change, shifting global cycles of the weather, widespread pollution, radioactive fallout, plastic accumulation, species invasions, the mass extinction of species - these are just some of the many indicators that we will leave a lasting record in rock, the scientific basis for recognizing new time intervals in Earth's history. The "Anthropocene," as the proposed new epoch has been named, is regularly in the news.Even with such robust evidence, the proposal to formally recognize our current time as the Anthropocene remains controversial both inside and outside the scholarly world, kindling intense debates. The reason is clear. The Anthropocene represents far more than just another interval of geologic time. Instead, the Anthropocene has emerged as a powerful new narrative, a concept through which age-old questions about the meaning of nature and even the nature of humanity are being revisited and radically revised.This Very Short Introduction explains the science behind the Anthropocene and the many proposals about when to mark its beginning: The nuclear tests of the 1950s? The beginnings of agriculture? The origins of humans as a species? Erle Ellis considers the many ways that the Anthropocene's "evolving paradigm" is reshaping the sciences, stimulating the humanities, and foregrounding the politics of life on a planet transformed by humans. The Anthropocene remains a work in progress. Is this the story of an unprecedented planetary disaster? Or of newfound wisdom and redemption? Ellis offers an insightful discussion of our role in shaping the planet, and how this will influence our future on many fronts.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, and enthusiasm to make interesting and challenging topics highly readable.

    But how much do these types of entertainment really tell us about recent scientific discoveries and the latest research into the world of the dinosaur?This is the first book explain how scientists have been able to put together a picture of how dinosaurs looked, what they ate, and how they moved and interacted with each other. Taking a new approach to the subject, David Norman combines different areas of science, such as anatomy, genetics, forensics, and engineering design, to piece together the latest evidence of how animal life evolved on earth. Norman engagingly lays out the history of dinosaur research, from the speculation over ancient myths about dragons, to the latest virtual reality animation sequences and engineering design analysis. He also discusses the role that informed speculation and luck has played in many of the major discoveries.This book is a fantastic introduction for those just beginning to take an interest in dinosaurs and a must-read for true dinosaur-lovers who want to know not just the latest theories and discoveries, but how scientists achieved them.

    This book includes a companion CD-ROM that adds a visual emphasis with animations.

    Boatwright, Daniel J. Gargola, and Richard J.A. Talbert.This shorter version lucidly unfolds Rome's remarkable evolution through monarchy, republic, and then an empire that, at its height, stretched from Scotland to Iraq and the Nile Valley. Concise narrative integrates the political, military, social, and cultural landmarks of over 1,500 years--from the early struggles against Etruscans, Samnites, and Gauls to the sack of Rome by Alaric and his Visigoths. The book gives readers a basic yet engaging introduction to Roman history and society. It is an ideal text for courses on Ancient civilization, Roman civilization, or Roman history.FEATURES* Fourteen boxes featuring excerpts from writings by Romans themselves* Extensive variety of photos and illustrations, all with detailed captions; twenty-four custom-drawn maps of the city of Rome, Italy, the Mediterranean, and the wider Roman world* Narrative enlivened by such fascinating individuals as Hannibal, Mithridates, Pompey, Caesar, Cleopatra, Augustus, Livia, Nero, Trajan, Shapur, and Constantine* Selective, up-to-date recommendations for further reading; timeline of key events; glossary of Latin terms

    For over half a century, the MLA Handbook is the guide millions of writers have relied on.The seventh edition is a comprehensive, up-to-date guide to research and writing in the online environment. It provides an authoritative update of MLA documentation style for use in student writing, including simplified guidelines for citing works published on the Web and new recommendations for citing several kinds of works, such as digital files and graphic narratives.Every copy of the seventh edition of the MLA Handbook comes with a code for accessing the accompanying Web site. New to this edition, the Web site provides- the full text of the print volume of the MLA Handbook- over two hundred additional examples- several research-project narratives--stories, with sample papers, that illustrate the steps successful students take in researching and writing papers- searching of the entire site, including the full text of the MLA Handbook- continuous access throughout the life of the seventh edition of the MLA Handbook

    Their subjects include the components, function, and weight of the atmosphere; capillary attraction; the carbon content in oxygen and living bodies; respiration and its analogy to the burning of a candle; and much more. Numerous illustrations.

    It sparked a national debate on evolution, which continues to intensify across the country. From one end of the spectrum to the other, Darwin's Black Box has established itself as the key intelligent design text -- the one argument that must be addressed in order to determine whether Darwinian evolution is sufficient to explain life as we know it.In a major new Afterword for this edition, Behe explains that the complexity discovered by microbiologists has dramatically increased since the book was first published. That complexity is a continuing challenge to Darwinism, and evolutionists have had no success at explaining it. Darwin's Black Box is more important today than ever.

    This text, organized with a traditional functional-group approach, applies the most modern teaching and pedagogical techniques to the study of organic chemistry. In a highly accessible fashion, this top-selling text bridges the gap between conceptual understanding and actual application - while strongly emphasizing the development of problem-solving skills. Additionally, it provides up-to-date aspects of spectroscopy, relevant photographs, and many applications to polymer chemistry integrated throughout the text.