Hardy, in the years before World War I. Through their eyes the reader is taken on a journey through numbers theory. Ramanujan would regularly telescope 12 steps of logic into two - the effect is said to be like Dr Watson in the train of some argument by Sherlock Holmes. The language of symbols and infinitely large (and small) regions of mathematics should be rendered with clarity for the general reader.

    This is a book about how many of the 'big' philosophical and religious questions that have puzzled mankind for centuries can be answered by recent breakthroughs in science.

    But it’s never too late to write your next story, and to go on your next adventure. In partnership with Cayman Jack, Thought Catalog presents a collection of 25 travel stories to inspire you to leave behind the predictable and take to the open road in search of the unforgettable. Your next great memory is waiting for you, whether you realize it or not. And these exceptional stories will help you find it.

    One of the biggest fears of fasting is the fear hunger, the false hunger that most people are afraid of while depleting their glycogen stores (the body sugar storage). Fasting has often been associated with religious customs. It is time to define a line between the two. In Periodic Fasting, I embark on a timeless journey from the very beginning of life on Earth, through early human societies, through the middle Ages and into modern days to explore the concepts and practices of prolonged fasting and intermittent fasting (IF). Periodic Fasting is about: 1. My early life encounters with fasting in the small village of my grandparents (using a high-carb diet). 2. How primitive life-forms on Earth and fasting co-evolved; fasting in the animal kingdom. 3. Early hominid species, food restriction, and meal frequency. The first organized human societies and the switch between irregular feeding to regular dietary patterns. Circadian rhythmicity and meal timing. 4. The personal story of a man from the middle Ages who started consuming less food in his mid-thirties because of poor health and lived to 102 years (narrated by himself). 5. The dozens of prolonged fasting experiments in the beginning of the 20th century; fasting as a cure to many ailments. 6. How people can live without food for 139, 236 and even 382 days (medically supervised experiments). Details of 7-40 days fasts done by lean people for rejuvenation, detoxification and increased life span. 7. The emerging science and the studies of fasting from the mid-20th century (pathological implications - diabetes, obesity, CVD, cancer, and others). 8. How fasting and semi-starvation can be totally opposite: disturbing stories from the Second World War. 9. The molecular mechanisms of fasting: what happens when your body focuses on cell repair and tissue rejuvenation, instead of digesting food. 10. How the secretion of some hormones may be widely misunderstood: especially thyroid hormones and insulin. On muscle-loss phobia, mainstream media, and bro-science. 11. The modern-day science of prolonged fasting and intermittent fasting (AMPk, SIRT, FOXO, etc). 12. My personal prolonged water-only fasting experiment; insights into refeeding and realimentation after long-term fasting. 13. My 1 year and 3 months daily intermittent fasting protocol (still on-going). My ever-adapting exercising protocol (lifting), what I eat everyday, what supplements I use and what other cool strategies help me stay consistent and compliant with the protocol. 14. How I combine intermittent fasting (IF), a well formulated ketogenic diet, and calorie restriction to immensely increase the quality of my life, and paradoxically, never feel hungry; how energy levels and mood can increase if you correctly adopt a fasting protocol. Once armed with this knowledge, you will drastically alter your perspective about your body's limits.

    . .he believes these ideas to be accessible to the audience he wantsto reach, and he writes so that they are. -- NatureIf you want to encourage anyone's interest in math, get them TheMathematical Universe. * New Scientist

    For all ages and all levels of difficulty, these puzzles range from those that can be solved in minutes to those that will beguile for hours.

    The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.

    Unlike the rest of the world's archipelagoes, it still has 95 percent of its prehuman quota of species. Wildlife of the Galapagos is the most superbly illustrated and comprehensive identification guide ever to the natural splendor of these incomparable islands--islands today threatened by alien species and diseases that have diminished but not destroyed what so enchanted Darwin on his arrival there in 1835. Covering over 200 commonly seen birds, mammals, reptiles, invertebrates, and plants, it reveals the archipelago's striking beauty through more than 400 color photographs, maps, and drawings and well-written, informative text. While the Galapagos Giant Tortoise, the Galapagos Sea Lion, and the Flightless Cormorant are recognized the world over, these thirty-three islands--in the Pacific over 600 miles from mainland Ecuador--are home to many more unique but less famous species. Here, reptiles well outnumber mammals, for they were much better at drifting far from a continent the archipelago was never connected with; the largest native land mammals are rice rats. The islands' sixty resident bird species include the only penguin to breed entirely in the tropics and to inhabit the Northern Hemisphere. There is a section offering tips on photography in the Equatorial sunlight, and maps of visitors' sites as well as information on the archipelago's history, climate, geology, and conservation. Wildlife of the Galapagos is the perfect companion for anyone who wants to know what so delighted Darwin. Covers over 200 commonly seen species including birds, mammals, reptiles, invertebrates, plants, and coastal and marine life Illustrated with over 400 color photographs, maps, and drawings; includes maps of visitors' sites Written by wildlife experts with extensive knowledge of the area Includes information on the history, climate, geology, and conservation of the islands The most complete identification guide to the wildlife of the Galapagos

    This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

    This is done in a way that is not only easy to understand, but is actually fun! Professors and engineers, with high school and college students following closely, comprise the largest percentage of our readers. It is a must-have for anyone interested in music, mathematics, physics, engineering, or complex science. Dr. Yoichiro Nambu, 2008 Nobel Prize Winner in Physics, served as a senior adviser to the English version of Who is Fourier? A Mathematical Adventure.

    Written by Amy Eldridge, founder and CEO of Love Without Boundaries, this poignant chronicle of LWB's life-changing work, told through the stories of individual children, offers personal insight into the complex issues surrounding orphan care, abandonment, international aid, and adoption. Both thought-provoking and inspirational, "The Heart of an Orphan" reminds us all that while the needs of vulnerable children around the world may seem overwhelming, the human heart triumphs in believing that every life has value and every child deserves love.

    This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject.Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world.The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.

    Here, from author Jay Williams, is the moving story of the man behind the Renaissance myth.

    The more we interact online, the more we crave intimacy. The more filtered our lives become, the harder it is to be real.It’s time to refresh and rediscover what it means to be “like Jesus” and find true authenticity, a healthy self-image, and compassion for others in an age when we relate to each other so differently than ever before. Groeschel taps into some of the most leading-edge studies on the effects of social media on our emotions and friendships. He offers real-life examples of how we struggle with screens and likes, how these things mask our struggles with who we really are, and how we can reclaim a Christ-centered life.Packed with helpful topics like the “10 Commandments of Using Social Media to Strengthen Your Faith” and “Creating Safeguards for Your Digital Devices,” readers from ages sixteen to sixty will find Liking Jesus to be just the guide to bring balance and real-world engagement to everyday life.

    As a professional C++ developer and former Harvard teaching fellow, I know what you need to know to be a great C++ programmer, and I know how to teach it, one step at a time. I know where people struggle, and why, and how to make it clear. I cover every step of the programming process, including:Getting the tools you need to program and how to use them*Basic language feature like variables, loops and functions*How to go from an idea to code*A clear, understandable explanation of pointers*Strings, file IO, arrays, references*Classes and advanced class design*C++-specific programming patterns*Object oriented programming*Data structures and the standard template library (STL)Key concepts are reinforced with quizzes and over 75 practice problems.