Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

    Thoroughly updated, this edition offers new, faster techniques for solving differential equations generated by the emergence of high-speed computers.

    The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.], a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status.Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher.

    The work of Yagyῡ Munenori from 1632 concerns martial arts and military science. It is translated by Thomas Cleary and can be found tucked behind Miyamoto Musashi‘s “the Book of five rings” from 1643. Both these texts analyse conflict between two men armed with swords and scale this up bigger battles. These important treaties on swordsmanship, and have been taken as giving lessons on life in general.

    This book tells the story of Swamiji through the eyes of Pandit Rajmani Tigunait, PhD, his devoted student and successor as the spiritual head of the Himalayan Institute. As you read Pandit Tigunait's account of life with his master, you will gain insight into the guru-disciple relationships Swami Rama had both with his master and with his own students.This book serves as a guide to some of the more esoteric practices of tantra not commonly known or understood in the West. It brings you to holy places in India, to the source of the Himalayan Tradition, revealing why these sacred sites are important and how to go about visiting them. The wisdom in these stories penetrates beyond the power of words. Discover the legacy of a true Himalayan master and the nature of the yogic wisdom he shared. Purchase your copy of At the Eleventh Hour today!

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.

    But are there limits to what we can discover about our physical universe?In this very personal journey to the edges of knowledge, Marcus du Sautoy investigates how leading experts in fields from quantum physics and cosmology, to sensory perception and neuroscience, have articulated the current lie of the land. In doing so, he travels to the very boundaries of understanding, questioning contradictory stories and consulting cutting edge data.Is it possible that we will one day know everything? Or are there fields of research that will always lie beyond the bounds of human comprehension? And if so, how do we cope with living in a universe where there are things that will forever transcend our understanding?In What We Cannot Know, Marcus du Sautoy leads us on a thought-provoking expedition to the furthest reaches of modern science. Prepare to be taken to the edge of knowledge to find out if there’s anything we truly cannot know.

    In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired by the complexity of snowflakes, Anne Boleyn's eleven fingers, or his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. Thinking In Numbers will change the way you think about math and fire your imagination to see the world with fresh eyes.

    Being Mortal by Atul Gawande - A 20-minute Summary Inside this Instaread Summary: • Overview of the entire book• Introduction to the important people in the book• Summary and analysis of all the chapters in the book• Key Takeaways of the book• A Reader's Perspective Preview of this summary: Chapter 1 Gawande grew up in Ohio. His parents were immigrants from India and both were doctors. His grandparents stayed in India, and there were few older people in his neighborhood, so he had little experience with aging or death until he met his wife’s grandmother, Alice Hobson. Hobson was seventy-seven and living on her own in Virginia. She was a spirited widow who fixed her own plumbing and volunteered with Meals On Wheels. However, Hobson was losing strength and height steadily each year as her arthritis worsened.Gawande’s father enthusiastically adopted the customs of his new country, but he could not understand the way in which seniors were treated in the US. In India, the elderly were treated with great respect and lived out their lives with family.In the United States, Sitaram Gawande, Gawande’s grandfather, likely would have been sent to a nursing home like most of the elderly who cannot handle the basics of daily living by themselves. However, in India, Sitaram Gawande was able to live in his own home and manage his own affairs, with family constantly around him. He died at the age of one hundred and ten when he fell off a bus during a business trip.Until recently, most elderly people stayed with their families. Even as the nuclear family unit became predominant, replacing the multi-generational family unit, people cared for their elderly relatives. Families were large and one child, usually a daughter, would not marry in order to take care of the parents.This has changed in much of the world, where elderly people end up struggling to live alone, like Hobson, rather than living with dignity amid family, like Sitaram Gawande.One cause of this change can be found in the nature of knowledge. When few people lived to be very old, elders were honored. Their store of knowledge was greatly useful. People often portrayed themselves as older to command respect. Modern society’s emphasis on youth is a complete reversal of this attitude. Technological advances are perceived as the territory of the young, and everyone wants to be younger. High-tech job opportunities are all over the world, and young people do not hesitate to leave their parents behind to pursue them.In developed countries, parents embrace the concept of a retirement filled with leisure activities. Parents are happy to begin living for themselves once children are grown. However, this system only works for young, healthy retirees, but not for those who cannot continue to be independent. Hobson, for example, was falling frequently and suffering memory lapses. Her doctor did tests and wrote prescriptions, but did not know what to do about her deteriorating condition. Neither did her family… About the Author With Instaread Summaries, you can get the summary of a book in 30 minutes or less. We read every chapter, summarize and analyze it for your convenience.

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.

    Dozens of examples in innumeracy show us how it affects not only personal economics and travel plans, but explains mis-chosen mates, inappropriate drug-testing, and the allure of pseudo-science.

    Today, according to Professor Phillip Cary, Augustine is recognizable even to non-Christians as the most important Christian writer outside of the Bible. Yet Augustine was also a man-a rhetorician trained in the Roman way whose life and discovery of his calling make for one of the most fascinating stories in the history of religious philosophy. Explore Augustine's Life, Teachings, and Doctrine This course paints a rich and detailed portrait of the life, works, and ideas of this remarkable figure, whose own search for God has profoundly shaped all of Western Christianity. You learn what Augustine taught and why he taught it-and how those teachings and doctrines helped shape the Roman Catholic Church. These lectures are rewarding even if you have no background at all in classical philosophy or Christian theology. This is because Professor Cary, who has taught Villanova's nationally recognized seminars on ancient, medieval, Renaissance, and modern thought, has organized an entirely self-contained course. Professor Cary (Ph.D. in Philosophy and Religious Studies, Yale University) is a scholar-in-residence at the Templeton Honors College at Eastern University, where he is director of the Philosophy program and teaches a year-long Great Books seminar. He is author of Augustine's Invention of the Modern Self (Oxford University Press). Professor Cary explains any special religious or philosophical concepts you need to know in order to appreciate Augustine's impact, with real-life examples and analogies that make even the most subtle concepts clear and easy to understand. You'll gain a sense of what Augustine was saying, how his own experiences led him to say it, and how his thoughts fit into the theological, philosophical, and political worlds that swirled around him. Who Was Augustine? A Brief Biography Augustine was born in 354. Early in his life he was inspired by the works of Cicero to devote his life to the pursuit of truth. He started this pursuit as a Rhetorician, then he became a Manichaean, and later a Skeptic. Ambrose, bishop of Milan, and Augustine's mother, Monica, were among those instrumental in his conversion to Catholic Christianity in 386. In North Africa he founded a small monastic community and in 391 was elected Bishop of Hippo at a time when people still had some say in who would lead their religious community. From 395 to 430, he served as bishop. He wrote many treatises among which we find the celebrated Confessions, published in 400 as an open letter to his congregation and a prayer to God. His works also include The City of God and On the Trinity. Many of his writings were directed against heresies, particularly Manichaeism, Donatism, and Pelagianism. He is noted for founding the Western theological tradition and establishing doctrines of the Trinity and Christology. The Life, Works, and Significance of Augustine The course begins with two extremely helpful lectures that help place Augustine in context as both a Church Father (interpreter of the Bible and teacher of Christian doctrine) and philosopher (one who has given us new conceptions of the human heart and its depths). In Lecture 1 you meet Augustine the Roman Christian, one of the Church Fathers responsible for the transition from Bible stories to actual Christian doctrine, a man writing with the end of the Roman Empire at hand. In Lecture 2 you also meet Augustine the Christian Platonist and learn the Platonic concepts-including the idea of a non-bodily, eternal mode of being and the way that concept applies to God-which so deeply influenced him and other religious thinkers of the time. With Augustine's role in-and debt to-these two worlds established, Professor Cary then looks at Augustine's life and legacy in three parts. Part 1: Augustine's Life Lectures 3 through 6 are devoted to a study of Augustine's life. You look at the Confessions, his great spiritual autobiography, written when he was a 45-year-old bishop reflecting on the spiritual path of a questing young man of whom the grown Augustine might not always approve. You examine the Confessions from three angles: The intellectual angle spotlights his passionate search for truth. The emotional angle focuses on the love that drives this search, and the aching sense of loss, grief, and yearning which the Confessions evokes in order to show how love can go wrong.The religious angle explores Augustine's search for truth that leads him to Christ and the Christian life, conceived as a journey toward heaven.The section on Augustine's life ends with a focus on his career as a Christian writer following the period of his life covered by the Confessions, which culminated in his almost 15-year effort to write the 22 books of The City of God. Part II: Augustine's Thought The next series of three lectures explains key concepts of Augustine's thought, all related to his epochal doctrine of grace. You examine how Augustine relates the human qualities of faith and love to the divine gift of grace (Lecture 7); how his doctrine of grace addresses troublesome issues like the origin of evil, original sin, and predestination (Lecture 8); and how he relates the inward gift of grace to the external side of human life in his teachings about signs, words, sacraments, and the Church (Lecture 9). Part III: Augustine's Concept of Persons The final three lectures address Augustine's concept of persons, both human and divine. You look at Augustine's distinctive conception of the human soul as a private inner world (Lecture 10); then his distinctive way of relating his concept of the soul to the doctrine of the Trinity, which is the orthodox Christian conception of God (Lecture 11); and finally his understanding of God's relationship to specific human communities in history, specifically focusing on The City of God (Lecture 12).Great Courses, #611

    She draws on conversations with hundreds of the world's top scientists and on her own work as a Pulitzer Prize-winning writer for the New York Times to create a thoroughly entertaining guide to scientific literacy. Angier's gifts are on full display in The Canon, an ebullient celebration of science that stands to become a classic. The Canon is vital reading for anyone who wants to understand the great issues of our time -- from stem cells and bird flu to evolution and global warming. And it's for every parent who has ever panicked when a child asked how the earth was formed or what electricity is. Angier's sparkling prose and memorable metaphors bring the science to life, reigniting our own childhood delight in discovering how the world works. "Of course you should know about science," writes Angier, "for the same reason Dr. Seuss counsels his readers to sing with a Ying or play Ring the Gack: These things are fun and fun is good." The Canon is a joyride through the major scientific disciplines: physics, chemistry, biology, geology, and astronomy. Along the way, we learn what is actually happening when our ice cream melts or our coffee gets cold, what our liver cells do when we eat a caramel, why the horse is an example of evolution at work, and how we're all really made of stardust. It's Lewis Carroll meets Lewis Thomas -- a book that will enrapture, inspire, and enlighten.

    A modern classic by an accomplished mathematician and best-selling author has been updated to encompass and explain the recent headline-making advances in the field in non-technical terms.

    Taking us on a journey through every fundamental field of science, as well as the history of civilization, art, moral values, and the theory of political institutions, Deutsch tracks how we form new explanations and drop bad ones, explaining the conditions under which progress—which he argues is potentially boundless—can and cannot happen. Hugely ambitious and highly original, The Beginning of Infinity explores and establishes deep connections between the laws of nature, the human condition, knowledge, and the possibility for progress.