Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    Integrating the ancient teachings of Tibetan Buddhism into the everyday grind, A Spiritual Renegade’s Guide to the Good Life presents a fresh take on our quest for a joyful existence. Each chapter includes an action plan designed to elicit true happiness and forge a clear path toward fulfillment. You’ll learn how to: • transform problems into opportunities; • set yourself free from fear and anxiety; • unburden yourself of past resentment; • create an action plan for true happiness. Further explore the concepts of a spiritual renegade lifestyle through Microsoft Tags within this book, which link to online videos of Lama Marut discussing each of his concepts firsthand. This book is bound to disrupt your suffering, disturb your dissatisfaction, and elicit a deep-seated contentment. Happiness is in your hands.

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    In late 2017, scientists at a Hawaiian observatory glimpsed an object soaring through our inner solar system, moving so quickly that it could only have come from another star. Avi Loeb, Harvard’s top astronomer, showed it was not an asteroid; it was moving too fast along a strange orbit, and left no trail of gas or debris in its wake. There was only one conceivable explanation: the object was a piece of advanced technology created by a distant alien civilization.   In Extraterrestrial, Loeb takes readers inside the thrilling story of the first interstellar visitor to be spotted in our solar system. He outlines his controversial theory and its profound implications: for science, for religion, and for the future of our species and our planet. A mind-bending journey through the furthest reaches of science, space-time, and the human imagination, Extraterrestrial challenges readers to aim for the stars—and to think critically about what’s out there, no matter how strange it seems.

    This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. Students of literature read Shakespeare; students of music listen to Bach, he writes. But this tradition of studying the major works of the masters is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation.Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original category theorem (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, most subtle problems imaginable.Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.

    These amazing masters transcend religion and go beyond time – they are here and willing to help all of those who call on them.   The new Keepers of the Light oracle card deck from Kyle Gray draws together 44 Ascended Masters, spiritual deities, and beings from many world traditions, and embraces spiritual teachings from ancient to modern times. The deck balances male and female energies, and includes traditional masters like Lord Buddha and Mother Mary, Earth-based deities like Gaia and Cernunnos, and modern favorites like Sanat Kumara, Lady Venus, and Saint Germain.   Each card is beautifully hand drawn by visionary artist Lily Moses, who paints what she sees from a deep meditative state. The deck’s aim is to help spiritual seekers to develop their intuition and to really start trusting the messages that spirit shares.

    His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.

    Whether we see ourselves as heroes or victims, good people or bad, everyone lives according to interwoven strands of narrative.   “And yet,” teaches Adyashanti, “the truth is bigger than any concept or story.”   Drawn from intimate, deep-dive talks, The Most Important Thing presents writings devoted to the search for the ultimate reality of a self that exists beyond the bounds of storytelling.   Here you will find vivid anecdotes and teaching stories that illuminate the felt experience of Adyashanti’s teachings—those moments of grace in which every stone, tree, ray of light, and fraught silence reveal that none of us is alone and no one is ever truly isolated from the whole of existence.   These selections consider: Exploration of the true meaning of birth, life, and death Why grace can arrive both through struggle and as an unexpected gift Meditation as the art of “listening with one’s entire being” Why a good question can be far more powerful than a concrete answer How the things you choose to serve shape your life Discovering the wisdom found in surprise, sadness, and uncertainty Embodying your innate and inextricable connection with the total environment The nature of ego and the ways it manifests The moments of grace upon which all great religions pivot What is the story of your life? Is it happy or adventurous? Sad or lonely? In The Most Important Thing, Adyashanti shows you how to look past your personal narratives, delve inward, and connect with the truths that fundamentally animate all of us.

    When he was only nine years old, Satish Kumar renounced the world and joined the wandering brotherhood of Jain monks. Dissuaded from this path by an inner voice at the age of 18, he became a campaigner for land reform, working to turn Gandhi's vision of a renewed India into reality. Fired by the example of Bertrand Russell, he undertook an 8,000-mile peace pilgrimage, walking from India to America without any money, through mountains, deserts, storms, and snow. It was an adventure during which he was thrown into jail in France, faced a loaded gun in America, and delivered packets of “peace tea” to the leaders of the four nuclear powers. In 1973 he settled in England, taking on the editorship of Resurgence magazine, and becoming the guiding light behind a number of ecological spiritual and educational ventures. Following Indian tradition, in his 50th year he undertook another pilgrimage: again without any money, he walked to the holy places of Britain—Glastonbury Lindisfarne and Iona. All of this and more is recounted in this fascinating autobiography.

    In The Sabbats, Edain McCoy reveals the eight major holidays of this faith and the many ways in which they are celebrated.There are two basic types of holidays. The first come at the Solstices and Equinoxes. The others divide the time between those dates in two, resulting in eight major holidays or Sabbats with approximately the same amount of days between them. The balance, here, gives the appearance of spokes in a wheel, so this cycle is commonly called the Wheel of the Year.The holidays represent two things. First, the harvest cycle. Each holiday represents a time in the growth of crops. From planting to growth, from harvesting to letting the lands lie fallow in the cold winter, the festivals follow the agricultural cycles of ancient times. However, they also represent the eternal love of the God and Goddess, following the God's birth from the Goddess and his death before she gives birth to him again. This also follows the pattern of the Sun which moves from warm and high in the sky to cold and low in the sky.The book is filled with ways you can follow the Wheel of the Year, whether you work with a coven, with your family, or by yourself. You will learn the secrets of ritual construction and handicrafts appropriate to each of the festivals. You will also learn recipes for traditional foods for each holiday and even songs appropriate to the Sabbats.This is a wonderful, joyous book filled with color, information, and wisdom. If you are involved with Paganism in any way, this book is a must for your studies and practices. This book functions as both a resource and as a practical manual for the celebration of the holidays. Get your copy today.

    Along the way we’ll learn how selection bias can explain why your boss doesn’t know he sucks (even when everyone else does); how to use Bayes’ Theorem to decide if your partner is cheating on you; and why Mark Zuckerberg should never be used as an example for anything. See the world in a whole new light, and make better decisions and judgements without ever going near a t-test. Think. Think Statistically.

    Then, in a dramatic change, described by scientists as 'the greatest riddle in human history', all the skills & qualities that we value most highly in ourselves appeared already fully formed, as tho bestowed on us by hidden powers. In Supernatural Hancock sets out to investigate this mysterious before-&-after moment & to discover the truth about the influences that gave birth to the modern mind. His quest takes him on a detective journey from the beautiful painted caves of prehistoric France, Spain & Italy to rock shelters in the mountains of S. Africa, where he finds extraordinary Stone Age art. He uncovers clues that lead him to the Amazon rainforest to drink the hallucinogen Ayahuasca with shamans, whose paintings contain images of 'super-natural beings' identical to the animal-human hybrids depicted in prehistoric caves. Hallucinogens such as mescaline also produce visionary encounters with exactly the same beings. Scientists at the cutting edge of consciousness research have begun to consider the possibility that such hallucinations may be real perceptions of other dimensions. Could the supernaturals 1st depicted in the painted caves be the ancient teachers of humankind? Could it be that human evolution isn't just the meaningless process Darwin identified, but something more purposive & intelligent that we've barely begun to understand?AcknowledgementsPart 1: Visions 1: Plant that enables men to see the dead 2: Greatest riddle of archeology 3: Vine of souls Part 2: Caves 4: Therianthropy5: Riddles of the caves6: Shabby academy 7: Searching for a Rosetta Stone8: Code in the mind 9: Serpents of the Drakensberg10: Wounded healer Part 3: Beings 11: Voyage into the supernatural 12: Shamans in the sky 13: Spirit love 14: Secret commonwealth15: Here is a thing that will carry me away16: Dancers between worlds Part 4: Codes 17: Turning in to channel DMT18: Amongst the machine elves19: Ancient teachers in our DNA?20: Hurricane in the junkyard Part 5: Religions 21: Hidden Shamans22: Flesh of the GodsPart 6: Mysteries 23: Doors leading to another world Appendices Critics & criticisms of David Lewis-Williams' Neuropsychological theory of rock & cave artPsilocybe semilanceata-a hallucinogenic mushroom native to Europe / Roy Watlng Interview with Rick StrassmanReferences Index

    Phil Zuckerman, a Pitzer College sociologist, makes this case as fluidly and pleasurably as anybody in his book, Living the Secular Life."A Best Book of 2014, Publishers Weekly Over the last twenty-five years, “no religion” has become the fastest-growing religion in the United States. Around the world, hundreds of millions of people have turned away from the traditional faiths of the past and embraced a moral yet nonreligious—or secular—life, generating societies vastly less religious than at any other time in human history. Revealing the inspiring beliefs that empower secular culture—alongside real stories of nonreligious men and women based on extensive in-depth interviews from across the country—Living the Secular Life will be indispensable for millions of secular Americans. Drawing on innovative sociological research, Living the Secular Life illuminates this demographic shift with the moral convictions that govern secular individuals, offering crucial information for the religious and nonreligious alike. Living the Secular Life reveals that, despite opinions to the contrary, nonreligious Americans possess a unique moral code that allows them to effectively navigate the complexities of modern life. Spiritual self-reliance, clear-eyed pragmatism, and an abiding faith in the Golden Rule to adjudicate moral decisions: these common principlesare shared across secular society. Living the Secular Life demonstrates these principles in action and points to their usage throughout daily life. Phil Zuckerman is a sociology professor at Pitzer College, where he studied the lives of the nonreligious for years before founding a Department of Secular Studies, the first academic program in the nation dedicated to exclusively studying secular culture and the sociological consequences of America’s fastest-growing “faith.” Zuckerman discovered that despite the entrenched negative beliefs about nonreligious people, American secular culture is grounded in deep morality and proactive citizenship—indeed, some of the very best that the country has to offer.Living the Secular Life journeys through some of the most essential components of human existence—child rearing and morality, death and ritual, community and beauty—and offers secular readers inspiration for leading their own lives. Zuckerman shares eye-opening research that reveals the enduring moral strength of children raised without religion, as well as the hardships experienced by secular mothers in the rural South where church attendance defines the public space. Despite the real sorrows of mortality, Zuckerman conveys the deep psychological health of secular individuals in their attitudes toward illness, death, and dying. Tracking the efforts of nonreligious groups to construct their own communities, Zuckerman shows how Americans are building institutions and cultivating relationships without religious influence. Most of all, Living the Secular Life infuses the sociological data and groundbreaking research with the moral convictions that govern secular individuals, and demonstrates how readers can integrate these beliefs into their own lives. A manifesto for a booming social movement—and a revelatory survey of this overlooked community—Living the Secular Life offers essential and long-awaited information for anyone building a life based on his or her own principles. New York Times Book Review (Susan Jacoby) “[A] humane and sensible guide to and for the many kinds of Americans leading secular lives in what remains one of the most religious nations in the developed world."

    Awe prompts indignation at the exploitation and destruction of the earth's people and resources. Awe leads to action.Showing how we can learn from each other, Fox's spirituality weds the healing and liberation found in both North and South America. Creation Spirituality challenges readers of every religious and political persuasion to unite in a new vision through which we learn to honor the earth and the people who inhabit it as the gift of a good and just creator.

    Roger J. Woolger, a graduate of Oxford University and a certified Jungian analyst, reveals an exciting psychotherapeutic technique that produces astoundingly beneficial emotional and physical results--whether you believe in reincarnation as a literal or symbolic phenomenon.Drawing on both Western science and Eastern spirituality, Dr. Woolger shows how patients have unlocked the secrets of their innermost memories--the often self-destructive cycles that are repeated life after life--to overcome the insecurity, depression, guilt, inhibition, family dysfunction, and physical illness that they have inherited from their past lives. A lucid, compelling account of a revolutionary therapeutic technique, Other Lives, Other Selves offers an alternative path to self-improvement and self-enlightenment that addresses the whole person: mind, body, and spirit."An important and powerful book . . . fascinating."--Journal of Regression Therapy