Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

    How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book--a model of clarity, succinctness, and a humor bordering at times on the sardonic.

    Fields, farms, hills and hedgerows appear altered, the wildlife behaves differently, and over time the terrain itself is transformed.In Rain, Melissa Harrison explores our relationship with the weather as she follows the course of four rain showers, in four seasons, across Wicken Fen, Shropshire, the Darent Valley and Dartmoor.Blending these expeditions with reading, research, memory and imagination, she reveals how rain is not just an essential element of the world around us, but a key part of our own identity too.

    Miller delivers!" - Jeffrey Long, MD Reports of near-death experiences (NDEs) are flooding the media with books, articles and interviews. People describe hovering over their bodies, details of their surgeries, talking with deceased relatives, and reviewing their lives in vivid detail, often while their brains should be incapable of producing rational thought or memories. While the accounts are no doubt interesting, do they provide any solid evidence for the afterlife and the existence of God? Miller argues, in nontechnical and engaging prose, that it does indeed. He began his study doubting that NDEs provided such evidence, but found himself convinced by the weight of the evidence. In this multiple award-winning book, the reader will explore: The common naturalistic explanations for NDEs. Evidence that NDEs point to God and heaven. The results of 35 years of research into NDEs by doctors and other professionals, fully documented for those who want to study further. A comparison of NDEs with Christian teachings. Recommendations of key books, researchers, and publications for further study. "Can we survive death? Is there a God or a heaven? Miller provides the discerning reader with ample reason to think that the answer to these all-important questions is 'yes'." - Dr. Peter Schaefer, Senior Research Psychologist, Department of Defense

    He proposes his solution.

    It moves beyond a mere study of algorithms without sacrificing the rigor that faculty desire. As in every edition, Winston reinforces the book's successful features and coverage with the most recent developments in the field. The Student Suite CD-ROM, which now accompanies every new copy of the text, contains the latest versions of commercial software for optimization, simulation, and decision analysis.

    This authoritative yet accessible study is the ultimate astronomy lesson. Combining fascinating and often alarming scenarios that seem plucked from science fiction with the latest research and opinions, Plait illustrates why outer space is not as remote as most people think. Each chapter explores a different phenomenon, explaining it in easy-to-understand terms, and considering how life on earth and the planet itself would be affected should the event come to pass. Rather than sensationalizing the information, Plait analyzes the probability of these catastrophes occurring in our lifetimes and what we can do to stop them. With its entertaining tone and enlightening explanation of unfathomable concepts, Death from the Skies! will appeal to science buffs and beginners alike.

    In those years the author was teaching philosophy at American universities and exercising a growing influence on America's student population. The essays assembled here are fundamentally concerned with "the art of reckoning" in the fields of mathematics, logic and philosophy. The simplicity of Russell's exposition is astonishing, as is his ability to get to the core of the great philosophical issues and to skillfully probe the depth of philosophical analysis. Bertrand Arthur William Russell, 3rd Earl Russell was a British philosopher, logician, mathematician, historian, social reformer, and pacifist. Although he spent the majority of his life in England, he was born in Wales, where he also died. Russell led the British "revolt against Idealism" in the early 1900s and is considered one of the founders of analytic philosophy along with his prot�g� Wittgenstein and his elder Frege. He co-authored, with A. N. Whitehead, Principia Mathematica, an attempt to ground mathematics on logic. His philosophical essay "On Denoting" has been considered a "paradigm of philosophy." Both works have had a considerable influence on logic, mathematics, set theory, linguistics and analytic philosophy. He was a prominent anti-war activist, championing free trade between nations and anti-imperialism. Russell was imprisoned for his pacifist activism during World War I, campaigned against Adolf Hitler, for nuclear disarmament, criticized Soviet totalitarianism and the United States of America's involvement in the Vietnam War. In 1950, Russell was awarded the Nobel Prize in Literature, "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought."

    Readerswill find information on frequency distributions; mean, median, and mode; range, variance, and standard deviation;probability; and more.-Emphasizes Microsoft Excel for number-crunching and computationsDownload a sample chapter.

    A spellbinding look into the natural world's most fascinating and baffling phenomena, with illustrated explanations of rainbows, meteors, sunsets, hurricanes, the northern lights, and dozens of other curiosities of the sky.

    Randall never gave sleep much thought. That is, until he began sleepwalking. One midnight crash into a hallway wall sent him on an investigation into the strange science of sleep.In Dreamland, Randall explores the research that is investigating those dark hours that make up nearly a third of our lives. Taking readers from military battlefields to children’s bedrooms, Dreamland shows that sleep isn't as simple as it seems. Why did the results of one sleep study change the bookmakers’ odds for certain Monday Night Football games? Do women sleep differently than men? And if you happen to kill someone while you are sleepwalking, does that count as murder?This book is a tour of the often odd, sometimes disturbing, and always fascinating things that go on in the peculiar world of sleep. You’ll never look at your pillow the same way again.

    The lightest birds in the sky, hummingbirds are capable of incredible feats, such as flying backwards, diving at speeds of sixty-one MPH, and beating their wings more than sixty times a second. Miraculous creatures, they are also incredibly vulnerable when they first emerge from their eggs. That’s where Brenda Sherburn comes in.With tenderness and patience, she rescues abandoned hummingbirds and nurses them back to health until they can fly away and live in the wild. In The Hummingbird’s Gift, the care that Brenda provides her peanut-sized patients is revealed and, in the process, shows us just how truly amazing hummingbirds are.

     Desert Notebooks examines how the unprecedented pace of destruction to our environment and an increasingly unstable geopolitical landscape have led us to the brink of a calamity greater than any humankind has confronted before. As inhabitants of the Anthropocene, what might some of our own histories tell us about how to confront apocalypse? And how might the geologies and ecologies of desert spaces inform how we see and act toward time--the pasts we have erased and paved over, this anxious present, the future we have no choice but to build? Ehrenreich draws on the stark grandeur of the desert to ask how we might reckon with the uncertainty that surrounds us and fight off the crises that have already begun.In the canyons and oases of the Mojave and in Las Vegas's neon apocalypse, Ehrenreich finds beauty, and even hope, surging up in the most unlikely places, from the most barren rocks, and the apparent emptiness of the sky. Desert Notebooks is a vital and necessary chronicle of our past and our present--unflinching, urgent--yet timeless and profound.

    Decoding more than 150 cryptic ingredients, the guide explains each component's structural formula, offers synonymous names, and describes its common uses. This informative resource can serve curious readers as a basic primer to commercial chemistry or as an indexed reference for specific compounds found on a product label. Grouped according to type, these chemical descriptions will dissolve common misunderstandings and help make consumers more product savvy.

    From the first lesson to the last, each chapter introduces games of increasing complexity and then teaches the game theoretical tools necessary to solve them. Inside, you will find: All the basics fully explained, including pure strategy Nash equilibrium, mixed strategy Nash equilibrium, the mixed strategy algorithm, how to calculate payoffs, strict dominance, weak dominance, iterated elimination of strictly dominated strategies, iterated elimination of weakly dominated strategies, and more! Dozens of games solved, including the prisoner's dilemma, stag hunt, matching pennies, zero sum games, battle of the sexes/Bach or Stravinsky, chicken/snowdrift, pure coordination, deadlock, and safety in numbers! Crystal clear, line-by-line calculations of every step, with more than 200 images so you don't miss a thing! Tons of applications: war, trade, game shows, and duopolistic competition. Quick, efficient, and to the point, Game Theory 101: The Basics is perfect for introductory game theory, intermediate microeconomics, and political science.