Haskell emerged in the last decade as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvellous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures.This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others.

    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

    In this book, a wealth of exercises are provided throughout each section, designed to reinforce learning and the logical comprehension of topics. The use of real data is incorporated much more extensively than in any other book on the market. Consist of strong coverage of computer-based methods, especially in the coverage of analysis of variance and regression. This text stresses mastery of methods most often used in medical research, with specific reference to actual medical literature and actual medical research. The approach minimizes mathematical formulation, yet gives complete explanations of all important concepts. Every new concept is systematically developed through completely worked-out examples from current medical research problems. Computer output is used to illustrate concepts when appropriate.

    As exciting as any action/adventure novel, this is actually the story of incredible individuals and engrossing tales behind the most profound, enduring mathematical theorems.Archimedes famously ran naked through the streets shouting, “Eureka, eureka!” after finding a method for measuring the volume of an irregular-shaped object. René Descartes was not only a great French mathematician, philosopher, physicist, and natural scientist; he was also an expert swordsman who traveled with European armies from town to town, dressed in green taffeta and accompanied by a valet. Georg Cantor grappled with mental illness as he explored the highly counterintuitive, bizarre properties of infinite sets and numbers. Emmy Noether struggled to find employment as she laid the mathematical groundwork for modern theoretical physics. And Alexander Grothendieck taught himself mathematics while interned in Nazi concentration camps, only to disappear into the Pyrenees at the zenith of his career.These are just a few stories recounted in this absorbing narrative. In probing the lives of the preeminent mathematicians in history, a Strange Wilderness will leave you entertained and enlightened, with a newfound appreciation of the tenacity, complexity, and brilliance of the mathematical genius.

    Designed for the junior- level astrophysics course, each topic is approached in the context of the major unresolved questions in astrophysics. The core chapters have been designed for a course in stellar structure and evolution, while the extended chapters provide additional coverage of the solar system, galactic structure, dynamics, evolution, and cosmology. * Two versions of this text are available: An Introduction to Modern Stellar Astrophysics, (Chapters 1-17), and An Introduction to Modern Astrophysics, (Chapters 1-28). * Computer programs included with the text allow students to explore the physics of stars and galaxies. * In designing a curriculum, instructors can combine core and extended chapters with the optional advanced sections so as to meet their individual goals. * Up-to-date coverage of current astrophysical discoveries are included. * This text emphasizes computational physics, including computer problems and on-line programs. * This text also includes a selection of over 500 problems. For additional information and computer codes to be used

    Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.

    In the early days of AA, sponsors would come to the alcoholic's home and talk him through Steps 1 and 2, and when they were thoroughly convinced he was ready, they would start him on the program. Step 12 is the foundation of sponsorships: "Having had a spiritual awakening as the result of these steps, we tried to carry this message to alcoholics, to practice these principles in all our affairs." Carry This Message addresses McQ's concern that sponsors have lost some skills in working with alcoholics. AA sponsors need to refocus on the Big Book, on the Twelve Steps, and on their message, urges McQ, to recognize the value of the program and to return to its roots and essence. Directed to sponsors, this is a companion book to The Steps We Took, offering tools for helping others find recovery and new life through the Twelve Step program.

    Collected here to keep your wits sharp, The Best Brain Teasers of All Time features the cleverest brain teasers from around the world and throughout history.The Best Brain Teasers of All Time gives you hours of fun-filled entertainment with brain teasers that develop your problem-solving skills in math, logic, and wordplay. Organized as an integrated challenge, these brain teasers build in momentum as they increase in difficulty from classic nursery rhymes to the riddle of the sphinx.The Best Brain Teasers of All Time puts your mind to the test with: 125 Brain Teasers that require no special skills to solve. Plus, each question comes with an optional clue in case you get stumped and a handy answer key in the back to test yourself or play with friends Brain Teasers for Every Level that cater to beginners and advanced masterminds alike, with brain teasers organized by level of difficulty to improve your skills as you move forward Hints of History that provide fun facts and background information for every brain teaser Get ready to sharpen your wit with every “aha” moment. The Best Brain Teasers of All Time is a go-to source for timeless fun and mind-blowing challenges.

    Most books on world history overly emphasize the role of Western nations in the vast saga of mankind - the author of this book rectifies the gaps in books by Western historians by beginning the narration of world history with East Asia, and progresses from there through the rest of Asia to the Middle East.

    Some mammoths were smaller than children. Owls are the dumbest birds in the world. Very few people with Tourette's syndrome swear. You can't get a six-pack from doing sit-ups. King Arthur's sword wasn't called Excalibur. Milk doesn't make your bones strong. There's no bones in your fingers. The Bible states that humans can't become angels. Humans have more than two nostrils. It's impossible to slide down a bannister. At a wedding, the bride doesn't walk down the aisle. Ties were invented for war, not fashion. Most Disney classics made almost no money. Slavery has only been illegal in the UK since 2010. George Washington wasn't the first American President. Velcro doesn’t exist. Nobody knows why we sleep.

    No human being who stood on her decks that fateful night was alive to commemorate the event on its 100th anniversary. Their stories are with us, however, and the lessons remain. From the moment the world learned the Titanic had sunk, we wanted to know, who had survived? Those answers didn’t come until the evening of Thursday, April 18, 1912―when the Cunard liner Carpathia finally reached New York with the 706 survivors who had been recovered from Titanic’s lifeboats. Harold Bride, “Titanic’s surviving wireless operator,” relayed the story of the ship’s band. “The way the band kept playing was a noble thing. I heard it first while still we were working wireless when there was a ragtime tune for us. The last I saw of the band, when I was floating out in the sea with my lifebelt on, it was still on deck playing ‘Autumn.’ How they ever did it I cannot imagine.” There were stories of heroism―such as that of Edith Evans, who was waiting to board collapsible Lifeboat D, the last boat to leave Titanic, when she turned to Caroline Brown and said, “You go first. You have children waiting at home.” The sacrifice cost Evans her life, but as Mrs. Brown said later, “It was a heroic sacrifice, and as long as I live I shall hold her memory dear as my preserver, who preferred to die so that I might live.” There was mystery. There was bravery. There was suspense. There was cowardice. Most men who survived found themselves trying to explain how they survived when women and children had died. But mostly, there was loss. On her return to New York after picking up Titanic’s survivors, Carpathia had become known as a ship of widows. Rene Harris, who lost her husband, Broadway producer Henry Harris, in the disaster, later spoke of her loss when she said, “It was not a night to remember. It was a night to forget.” Drawing on a wealth of previously unpublished letters, memoirs, and diaries as well as interviews with survivors and family members, veteran author and writer Alan Rockwell brings to life the colorful voices and the harrowing experiences of many of those who lived to tell their story. More than 100 years after the RMS Titanic met its fatal end, the story of the tragic wreck continues to fascinate people worldwide. Though many survivors and their family members disappeared into obscurity or were hesitant to talk about what they went through, others were willing to share their experiences during the wreck and in its aftermath. This book recounts many of these first-hand accounts in graphic, compelling detail.

    Why be a product junkie when you can use the most renowned natural ingredients (biodiversity's solution) to make your curls pop! These are tried and tested, proven to have worked with all curl types from 3c- bigger curls, through to 4c-smaller coils/ kinky hair. What I recommend is that you choose your preferred recipe for each of the 5 stages and use these consistently for 6 weeks and give us feedback on how your curls have been transformed. This time period is long enough to build moisture in your hair to its maximum hydration and achieve its ultimate curl factor. Feel free to come back to this page and comment on your results. Our unique book picks on the top recipes and covers all the key stages to achieve the most pronounced and luscious curls regardless of curl type, making this book for ALL curlies! The recipe chapters comprise: Step 1: Clarify Step 2: Condition Step 3: Style Step 4: Spritz Step 5: Detangle Oil Mixes (new addition) Enjoy all the tried and tested recipes, and choose the ones that best suit your hair. This is a very valuable handbook , a must have handbook for every curly girl across all ethnicities!

    How to Read is a new sort of introduction — a personal master class in reading — that brings you face to face with the work of some of the most influential and challenging writers in history. In lucid, accessible language, these books explain essential topics such as Wittgenstein's determination to insist on the integrity and the autonomy of nonscientific forms of understanding.Though Wittgenstein wrote on the same subjects that dominate the work of other analytic philosophers — the nature of logic, the limits of language, the analysis of meaning — he did so in a peculiarly poetic style that separates his work sharply from that of his peers and makes the question of how to read him particularly pertinent.At the root of Wittgenstein's thought, Monk argues, is a determination to resist the scientism characteristic of our age, a determination to insist on the integrity and the autonomy of non-scientific forms of understanding. The kind of understanding we seek in philosophy, Wittgenstein tried to make clear, is similar to the kind we might seek of a person, a piece of music, or, indeed, of a poem.

    Your guide to a higher math score on standardized tests*SATACT(R)ASVABGMAT(R)GRE(R)CBEST(R)PRAXIS I(R)GED(R) And More!Why CliffsNotes?Go with the name you know and trustGet the information you need-fast!About the Contents:IntroductionHow to use this bookOverview of the examsPart I: Basic Skills ReviewArithmetic and Data AnalysisAlgebraPart II: Strategies and PracticeMathematical AbilityQuantitative ComparisonData SufficiencyEach section includes a diagnostic test, explanations of rules, concepts withexamples, practice problems with complete explanations, a review test, and aglossary!Test-Prep Essentials from the Experts at CliffsNotes(R)For more test-prep help, visit CliffsNotes.com(R)*SAT is a registered trademark of the College Board, which was not involved inthe production of, and does not endorse, this product.

     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.