The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    Bringing together the best and most interesting science stories appearing in Quanta Magazine over the past five years, Alice and Bob Meet the Wall of Fire reports on some of the greatest scientific minds as they test the limits of human knowledge. Quanta, under editor-in-chief Thomas Lin, is the only popular publication that offers in-depth coverage of today's challenging, speculative, cutting-edge science. It communicates science by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves.In the title story, Alice and Bob--beloved characters of various thought experiments in physics--grapple with gravitational forces, possible spaghettification, and a massive wall of fire as Alice jumps into a black hole. Another story considers whether the universe is impossible, in light of experimental results at the Large Hadron Collider. We learn about quantum reality and the mystery of quantum entanglement; explore the source of time's arrow; and witness a eureka moment when a quantum physicist exclaims: "Finally, we can understand why a cup of coffee equilibrates in a room." We reflect on humans' enormous skulls and the Brain Boom; consider the evolutionary benefits of loneliness; peel back the layers of the newest artificial-intelligence algorithms; follow the "battle for the heart and soul of physics"; and mourn the disappearance of the "diphoton bump," revealed to be a statistical fluctuation rather than a revolutionary new particle. These stories from Quanta give us a front-row seat to scientific discovery.ContributorsPhilip Ball, K. C. Cole, Robbert Dijkgraaf, Dan Falk, Courtney Humphries, Ferris Jabr, Katia Moskvitch, George Musser, Michael Nielsen, Jennifer Ouellette, John Pavlus, Emily Singer, Andreas von Bubnoff, Frank Wilczek, Natalie Wolchover, Carl Zimmer

     And the Australian government does not pay ransoms.After more than a year of stalled negotiations, Nigel's family takes matters into their own hands.  They go against government advice, scarifying their livelihoods, their houses and personal lives to bring the hostages home.  Meanwhile, the kidnappers are losing patience.  Brutalised, shackled, not knowing when or how the situation will end, Nigel faces the fight of his life.This is a story about what it takes to survive, and how far a family will go for freedom, whatever the price.

    

    Lisa Mills, an experienced general transcriptionist and publisher of work-at-home site Work at Home Mom Revolution, shares everything you need to know to get started in this exciting career. This ebook also includes links to valuable resources, including a list of 60 general transcription companies that hire home-based transcriptionists (with links).

    Once mired in controversy and doubt, ST6 has blossomed into one of the most accomplished fighting units the world has ever known. Having taken down the highest of high-value targets, rescued American hostages in Africa, the Middle East, Asia, and the Indian Ocean, and served as the silent guardian of the Coalition's conventional forces, SEAL Team Six has defined the post-9/11 world as much as it has been defined by it. The follow-up to SHAPING THE WORLD FROM THE SHADOWS -- the definitive open-source guide to Delta Force -- BEYOND NEPTUNE SPEAR is a contextual examination of DEVGRU's post-9/11 existence, from the most high-profile operations to the little-known missions that are still barely more than whispers. "Once again, Chris Martin has proven himself to be one of journalism's sharpest observers of U.S. special operations forces. BEYOND NEPTUNE SPEAR is a remarkable synthesis of the history, operations, and organization of SEAL Team Six. It is the most comprehensive guide to the unit ever published." - D.B. Grady, co-author of THE COMMAND: DEEP INSIDE THE PRESIDENT'S SECRET ARMY. "BEYOND NEPTUNE SPEAR tells much of what you wanted to know about SEAL Team Six post-9/11 but didn’t ask for fear of getting shot. Chris Martin begins with Team Six’s “rogue” beginnings then quickly springs into its operations post-9/11 until present. Although a short book, you’ll get bang for your buck here. For newcomers to the topic, BEYOND NEPTUNE SPEAR provides an exhaustive overview of Team Six’s current happenings. For experts on Team Six, Chris’s work provides an excellent summary of the post-9/11 Team with occasional information you probably missed. The reference page alone is a treasure for studying/reviewing the unit that whacked bin Laden. Also, because Chris used open sources to write this book, you don’t have to fear stealing government secrets and taking a bullet to the head." -Stephen Templin, New York Times bestselling co-author of SEAL TEAM SIX.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    Now in a new Ninth Edition, this reader-friendly book has been completely revised and improved to ensure that the learning experience is enhanced. It's built on the strength of Irwin's problem-solving methodology, providing readers with a strong foundation as they advance in the field.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno's Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs, but through it all, the paradox of motion remains.

    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.

    Since the publication of the First Edition over thirty years ago, Div, Grad, Curl, and All That has been widely renowned for its clear and concise coverage of vector calculus, helping science and engineering students gain a thorough understanding of gradient, curl, and Laplacian operators without required knowledge of advanced mathematics.

    One day, she received a message from a stranger. This woman offered to lead her on a self-healing trip hiking through the Scottish highlands.It seemed like a sign—a big sister sent when she needed one most.In this sometimes hilarious, sometimes terrifying, but always inspiring memoir, an introverted pollyanna is paired up with her polar opposite—a steamrolling, abrasive female with completely unorthodox healing methods. As they barrel through the winding one lane roads in a tiny rental car stopping to hike at breathtaking mountains and glens, an outrageous series of events forces Ninya to reclaim her power and find the strength to heal herself in one of the most beautiful places on earth.Readers of “Eat, Pray, Love” and “Wild” will love this memoir.

    If all we ever hear or speak is negativity, then when life pressures us, we're going to spew out toxic waste-doubt, fear, anxiety, poverty. As believers, we must be so filled with a Godly spirit, that when we are squeezed, nothing comes out but faith and Holy Ghost power. Its time to stop wavering in our faith and start living like we are positively sure of God's faithfulness. This inspirational 31 day positive self-talk declarations will bless you. It is a guide designed to compliment the Negative Self Talk Series. But can definitely stand on its own. It will provide examples of daily declarations that you can change to fit your situation. Each declaration is followed by a short inspirational message. Use this book as a bible study, alone or with a group of your closest friends. Encourage each other to be positive Christians. Lets allow our light to shine before men so that others will see our good works and glorify the Father in heaven (Matthew 5:16). Let's get delivered from negative self talk. Its time to live the blessed life God intended.

    So it's not surprising that we persist in thinking that we're in with a chance, whether we're playing the lottery or working out the likelihood of extra-terrestrial life. In Chance, a (not entirely) random selection of the New Scientist's sharpest minds provide fascinating insights into luck, randomness, risk and probability. From the secrets of coincidence to placing the perfect bet, the science of random number generation to the surprisingly haphazard decisions of criminal juries, it will explore these, and many other, tantalising questions.Following on from the bestselling Nothing and Question Everything, this book will open your eyes to the weird and wonderful world of chance - and help you see when some things, in fact, aren't random at all.