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The official book behind the Academy Award-winning film The Imitation Game, starring Benedict Cumberbatch and Keira Knightley

It is only a slight exaggeration to say that the British mathematician Alan Turing (1912-1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades--all before his suicide at age forty-one. This New York Times–bestselling biography of the founder of computer science, with a new preface by the author that addresses Turing's royal pardon in 2013, is the definitive account of an extraordinary mind and life.

Capturing both the inner and outer drama of Turing’s life, Andrew Hodges tells how Turing’s revolutionary idea of 1936--the concept of a universal machine--laid the foundation for the modern computer and how Turing brought the idea to practical realization in 1945 with his electronic design. The book also tells how this work was directly related to Turing’s leading role in breaking the German Enigma ciphers during World War II, a scientific triumph that was critical to Allied victory in the Atlantic. At the same time, this is the tragic account of a man who, despite his wartime service, was eventually arrested, stripped of his security clearance, and forced to undergo a humiliating treatment program--all for trying to live honestly in a society that defined homosexuality as a crime.

The inspiration for a major motion picture starring Benedict Cumberbatch and Keira Knightley, Alan Turing: The Enigma is a gripping story of mathematics, computers, cryptography, and homosexual persecution.

The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

In Illusions, the unforgettable follow-up to his phenomenal bestseller Jonathan Livingston Seagull, Richard Bach takes to the air to discover the ageless truths that give our souls wings: that people don't need airplanes to soar...that even the darkest clouds have meaning once we lift ourselves above them... and that messiahs can be found in the unlikeliest places--like hay fields, one-traffic-light midwestern towns, and most of all, deep within ourselves.

A New York Times Notable Book.

The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything.

In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.

LOVE KNOWS NO BOUNDARIES—NOT EVEN DEATH

Dr. Elisa Medhus never believed in life after death. As an accomplished physician, she placed her faith in science. All of that changed after her son Erik took his own life and then reached out from the other side.

Intimate, heartbreaking, and illuminating, go on an incredible journey from grief and skepticism to healing and belief. Based on Medhus’s wildly popular blog, Channeling Erik, My Son and the Afterlife provides answers to the most universal questions of being human.

At once tragic and uplifting, Erik speaks from the other side with candor, wisdom, and depth as he describes his own experiences and provides new answers about the nature of souls, death, and the afterlife—answers that have the potential to change our lives forever.

you are just beginning to walk a spiritual path or have already been

walking it for a while, you need to have a solid foundation for your

continued spiritual and psychic development. Wendy Kay has studied and

researched the path of psychic development and communicating with Spirit

for over 25 years. Make sure that you have the basics so you can get

the most from your work with Spirit.

This story is at the same time a historical novel and an accessible explication of some of the biggest ideas of mathematics and modern philosophy. With rich characterizations and expressive, atmospheric artwork, the book spins the pursuit of these ideas into a highly satisfying tale.

Probing and ingeniously layered, the book throws light on Russell's inner struggles while setting them in the context of the timeless questions he spent his life trying to answer. At its heart, Logicomix is a story about the conflict between an ideal rationality and the unchanging, flawed fabric of reality.

We each live in our own personal dream, and all of our dreams come together to make the Dream of the Planet. Problems arise when we forget that the dream is just a dream and fall victim to believing that we have no control over it.

The Mastery of Self takes the Toltec philosophy of the Dream of the Planet and the personal dream and explains how a person can:

Wake upLiberate themselves from illusory beliefs and storiesLive with authenticityOnce released, we can live as our true, authentic, loving self, not only in solitude and meditation, but in any place—at the grocery store, stuck in traffic, etc.—and in any situation or scenario that confronts us.

The Ruiz family has an enormous following, and this new book from don Miguel, Jr. will be greeted with enthusiasm by fans around the world. This new book from don Miguel, Jr. will be greeted with enthusiasm by fans around the world.

Men of Mathematics provides a rich account of major mathematical milestones, from the geometry of the Greeks through Newton’s calculus, and on to the laws of probability, symbolic logic, and the fourth dimension. Bell breaks down this majestic history of ideas into a series of engrossing biographies of the great mathematicians who made progress possible—and who also led intriguing, complicated, and often surprisingly entertaining lives.

Never pedantic or dense, Bell writes with clarity and simplicity to distill great mathematical concepts into their most understandable forms for the curious everyday reader. Anyone with an interest in math may learn from these rich lessons, an advanced degree or extensive research is never necessary.

The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples—from ice cream scoops and poker hands to measuring mountains and making magic squares—this book empowers you to see the beauty, simplicity, and truly magical properties behind those formulas and equations that once left your head spinning. You'll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry, and calculus, but you'll also have fun fooling around with Fibonacci numbers, investigating infinity, and marveling over mathematical magic tricks that will make you look like a math genius!

A mathematician who is known throughout the world as the “mathemagician,” Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand. In The Magic of Math, Benjamin does more than just teach skills: with a tip of his magic hat, he takes you on as his apprentice to teach you how to appreciate math the way he does. He motivates you to learn something new about how to solve for x, because there is real pleasure to be found in the solution to a challenging problem or in using numbers to do something useful. But what he really wants you to do is be able to figure out why, for that's where you'll find the real beauty, power, and magic of math.

If you are already someone who likes math, this book will dazzle and amuse you. If you never particularly liked or understood math, Benjamin will enlighten you and—with a wave of his magic wand—turn you into a math lover.

Do you want to read tarot, but don't want to wade through piles of long tedious explanations that bore you to tears? Then Tarot Made Simple is for you.

Tarot Made Simple is a tarot guide for the 21st century. Forget about having to try and memorise page after dull page of metaphysical nonsense, Tarot Made Simple explains how the cards really work, and how anyone can start reading them in a day.

What's Inside

✩ How and why the tarot works, with no mumbo-jumbo involved.

✩ How to read the four corners of a tarot card.

✩ The only three shuffles you'll ever need.

✩ A full complement of spreads you can use to answer any question you can think of.

✩ How to customise spreads, and even make your own from scratch.

✩ The one thing you must do before you start each reading to get the maximum benefit.

✩ Three ways to deal with reversed cards.

Tarot Made Simple covers every card, showing you what you need to know to perform accurate effective readings with ease, but without boring you to death with unnecessary details that you'll never use in real life readings. It tells you how to interpret the hidden aspects of each card, giving you real depth and insight into your readings.

This no-fluff guide is written in easy to understand plain English and makes learning the tarot, well, simple! You could be doing your first reading today.

Taking Tarot Further

If you decide you want to take things further, Tarot Made Simple also includes a detailed section on how to make money with tarot by charging for readings. You'll discover:

✩ A proven roadmap to take you from novice to professional reader.

✩ Three unusual places to find customers to read for.

✩ How to get people coming to you ready to hand over cash for your tarot readings.

✩ How to know precisely how much you can charge, and how much you should.

Tarot Made Simple is fully illustrated throughout. Learning tarot has never been easier.

Beginning with the ancient Near East, the author traces the ideas and techniques developed in Egypt, Babylonia, China, and Arabia, looking into such manuscripts as the Egyptian Papyrus Rhind, the Ten Classics of China, and the Siddhantas of India. He considers Greek and Roman developments from their beginnings in Ionian rationalism to the fall of Constantinople; covers medieval European ideas and Renaissance trends; analyzes 17th- and 18th-century contributions; and offers an illuminating exposition of 19th century concepts. Every important figure in mathematical history is dealt with — Euclid, Archimedes, Diophantus, Omar Khayyam, Boethius, Fermat, Pascal, Newton, Leibniz, Fourier, Gauss, Riemann, Cantor, and many others. For this latest edition, Dr. Struik has both revised and updated the existing text, and also added a new chapter on the mathematics of the first half of the 20th century. Concise coverage is given to set theory, the influence of relativity and quantum theory, tensor calculus, the Lebesgue integral, the calculus of variations, and other important ideas and concepts. The book concludes with the beginnings of the computer era and the seminal work of von Neumann, Turing, Wiener, and others.

"The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature Magazine.

Benoit Mandelbrot, the creator of fractal geometry, has significantly improved our understanding of, among other things, financial variability and erratic physical phenomena. In The Fractalist, Mandelbrot recounts the high points of his life with exuberance and an eloquent fluency, deepening our understanding of the evolution of his extraordinary mind. We begin with his early years: born in Warsaw in 1924 to a Lithuanian Jewish family, Mandelbrot moved with his family to Paris in the 1930s, where he was mentored by an eminent mathematician uncle. During World War II, as he stayed barely one step ahead of the Nazis until France was liberated, he studied geometry on his own and dreamed of using it to solve fresh, real-world problems. We observe his unusually broad education in Europe, and later at Caltech, Princeton, and MIT. We learn about his thirty-five-year affiliation with IBM’s Thomas J. Watson Research Center and his association with Harvard and Yale. An outsider to mainstream scientific research, he managed to do what others had thought impossible: develop a new geometry that combines revelatory beauty with a radical way of unfolding formerly hidden laws governing utter roughness, turbulence, and chaos.

Here is a remarkable story of both the man’s life and his unparalleled contributions to science, mathematics, and the arts.

The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.

But that was just the beginning.

In Beyond Biocentrism, acclaimed biologist Robert Lanza, one of TIME Magazine’s "100 Most Influential People in 2014," and leading astronomer Bob Berman, take the reader on an intellectual thrill-ride as they re-examine everything we thought we knew about life, death, the universe, and the nature of reality itself.

The first step is acknowledging that our existing model of reality is looking increasingly creaky in the face of recent scientific discoveries. Science tells us with some precision that the universe is 26.8 percent dark matter, 68.3 percent dark energy, and only 4.9 percent ordinary matter, but must confess that it doesn’t really know what dark matter is and knows even less about dark energy. Science is increasingly pointing toward an infinite universe but has no ability to explain what that really means. Concepts such as time, space, and even causality are increasingly being demonstrated as meaningless.

All of science is based on information passing through our consciousness but science hasn’t the foggiest idea what consciousness is, and it can’t explain the linkage between subatomic states and observation by conscious observers. Science describes life as an random occurrence in a dead universe but has no real understanding of how life began or why the universe appears to be exquisitely designed for the emergence of life.

The biocentrism theory isn’t a rejection of science. Quite the opposite. Biocentrism challenges us to fully accept the implications of the latest scientific findings in fields ranging from plant biology and cosmology to quantum entanglement and consciousness.

By listening to what the science is telling us, it becomes increasingly clear that life and consciousness are fundamental to any true understanding of the universe. This forces a fundamental rethinking of everything we thought we knew about life, death, and our place in the universe.

Most people are familiar with history's great equations: Newton's Law of Gravity, for instance, or Einstein's theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the Unknown, celebrated mathematician Ian Stewart untangles the roots of our most important mathematical statements to show that equations have long been a driving force behind nearly every aspect of our lives.

Using seventeen of our most crucial equations--including the Wave Equation that allowed engineers to measure a building's response to earthquakes, saving countless lives, and the Black-Scholes model, used by bankers to track the price of financial derivatives over time--Stewart illustrates that many of the advances we now take for granted were made possible by mathematical discoveries.

An approachable, lively, and informative guide to the mathematical building blocks of modern life, In Pursuit of the Unknown is a penetrating exploration of how we have also used equations to make sense of, and in turn influence, our world.

Dr. Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations.

As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics.

Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself.

Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery.

At two-thirty in the morning of June 6, 1998, Whitley Streiber was awakened by somebody knocking on his hotel room door. A man came in, and everything he said was life-altering.

This is the unsettling and ultimately enlightening narrative of what happened that night. Strieber was never really sure who this strange and knowing visitor was--a "Master of Wisdom"? A figure from a different realm of consciousness? A preternaturally intelligent being? He called him the Master of the Key. The one thing of which Strieber was certain is that both the man and the encounter were real.

The main concern of the Master of the Key is to save each of us from self-imprisonment. "Mankind is trapped," the stranger tells Strieber. "I want to help you spring the trap." In a sweeping exchange between Strieber and the stranger--which takes the form of a classical student- teacher dialogue in pursuit of inner understanding--the unknown man presents a lesson in human potential, esoteric psychology, and man's fate. He illuminates why man has been caught in a cycle of repeat violence and self-destruction--and the slender, but very real, possibility for release.

In its breadth and intimacy, The Key is on par with contemporary metaphysical traditions, such as A Course in Miracles, or even with the dialogues of modern wisdom teachers, such as D.T. Suzuki and Carl Jung.

For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs.

Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments.Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

But while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek "method of exhaustion" and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.

Join J. Warner Wallace, former atheist, seasoned cold-case detective, and popular national speaker as he tackles his most important case ... with you on the jury!

With the expertise of a cold-case detective, J. Warner examines eight critical pieces of evidence in the “crime scene” of the universe to determine if they point to a Divine Intruder. If you have ever wondered if something (or someone) outside the natural realm created the universe and everything in it, this is the case for you.

On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.

In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.

The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.

From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

Arguing that we must take seriously the possibility that the Nazis were in some measure correct, Gimbel examines Einstein and his work to explore how beliefs, background, and environment may—or may not—have influenced the work of the scientist. You cannot understand Einstein’s science, Gimbel declares, without knowing the history, religion, and philosophy that influenced it.

No one, especially Einstein himself, denies Einstein's Jewish heritage, but many are uncomfortable saying that he was being a Jew while he was at his desk working. To understand what "Jewish" means for Einstein’s work, Gimbel first explores the many definitions of "Jewish" and asks whether there are elements of Talmudic thinking apparent in Einstein’s theory of relativity. He applies this line of inquiry to other scientists, including Isaac Newton, René Descartes, Sigmund Freud, and Émile Durkheim, to consider whether their specific religious beliefs or backgrounds manifested in their scientific endeavors.

Einstein's Jewish Science intertwines science, history, philosophy, theology, and politics in fresh and fascinating ways to solve the multifaceted riddle of what religion means—and what it means to science. There are some senses, Gimbel claims, in which Jews can find a special connection to E = mc2, and this claim leads to the engaging, spirited debate at the heart of this book.

"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."

With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

Declaration of the Four Sacred Things

The earth is a living, conscious being. In company with cultures of many different times and places, we name these things as sacred: air, fire, water, and earth.

Whether we see them as the breath, energy, blood, and body of the Mother, or as the blessed gifts of a Creator, or as symbols of the interconnected systems that sustain life, we know that nothing can live without them.

To call these things sacred is to say that they have a value beyond their usefulness for human ends, that they themselves became the standards by which our acts, our economics, our laws, and our purposes must be judged. no one has the right to appropriate them or profit from them at the expense of others. Any government that fails to protect them forfeits its legitimacy.

All people, all living things, are part of the earth life, and so are sacred. No one of us stands higher or lower than any other. Only justice can assure balance: only ecological balance can sustain freedom. Only in freedom can that fifth sacred thing we call spirit flourish in its full diversity.

To honor the sacred is to create conditions in which nourishment, sustenance, habitat, knowledge, freedom, and beauty can thrive. To honor the sacred is to make love possible.

To this we dedicate our curiosity, our will, our courage, our silences, and our voices. To this we dedicate our lives.

Praise for The Fifth Sacred Thing

“This is wisdom wrapped in drama.”—Tom Hayden, California state senator

“Starhawk makes the jump to fiction quite smoothly with this memorable first novel.”—Locus

“Totally captivating . . . a vision of the paradigm shift that is essential for our very survival as a species on this planet.”—Elinor Gadon, author of The Once and Future Goddess

“This strong debut fits well against feminist futuristic, utopic, and dystopic works by the likes of Charlotte Perkins Gilman, Ursula LeGuin, and Margaret Atwood.”—Library Journal

As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex.

Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.

After he finished school, René Descartes was left with more doubts than certainties. His Jesuit education included some of the best teaching available in mathematics, physics, and letters, and yet Descartes found the foundations of his schooling hollow. Determined to discover for himself what was real, he spent the next nine years traveling through Europe, interacting with locals of all walks of life, including nobles, soldiers, and laborers, in search of the breadth of experience that would later inspire his greatest work: Discourse on Method. When it was first published, the book offered a remarkable new approach to gaining knowledge based on reason and skepticism, the steps for which Descartes lays out sequentially, from the deconstruction of all previously held beliefs to the slow and methodical rebuilding of fact anchored in the first and most innate truth: I think, therefore I am.

This ebook has been professionally proofread to ensure accuracy and readability on all devices.

From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.

Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

Do long division as the ancient Egyptians did! Solve quadratic equations like the Babylonians! Study geometry just as students did in Euclid's day! This unique text offers students of mathematics an exciting and enjoyable approach to geometry and number systems. Written in a fresh and thoroughly diverting style, the text — while designed chiefly for classroom use — will appeal to anyone curious about mathematical inscriptions on Egyptian papyri, Babylonian cuneiform tablets, and other ancient records.

The authors have produced an illuminated volume that traces the history of mathematics — beginning with the Egyptians and ending with abstract foundations laid at the end of the nineteenth century. By focusing on the actual operations and processes outlined in the text, students become involved in the same problems and situations that once confronted the ancient pioneers of mathematics. The text encourages readers to carry out fundamental algebraic and geometric operations used by the Egyptians and Babylonians, to examine the roots of Greek mathematics and philosophy, and to tackle still-famous problems such as squaring the circle and various trisectorizations.

Unique in its detailed discussion of these topics, this book is sure to be welcomed by a broad range of interested readers. The subject matter is suitable for prospective elementary and secondary school teachers, as enrichment material for high school students, and for enlightening the general reader. No specialized or advanced background beyond high school mathematics is required.

With coverage spanning the foundations of origami construction and advanced methods using both paper and pencil and custom-built free software, Origami Design Secrets helps readers cultivate the intuition and skills necessary to develop their own designs. It takes them beyond merely following a recipe to crafting a work of art.

For every problem mathematicians solve, another awaits to perplex and galvanize them. Such challenges offer a tantalizing glimpse of the field's unlimited potential and keep mathematicians looking toward the horizons of intellectual possibility.

In Visions of Infinity, Ian Stewart explains why these problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole. Stewart describes solved problems as well as those like the P/NP problem, which could easily remain unproved for another hundred years.

An approachable and illuminating history of mathematics as told through fourteen of its greatest problems, Visions of Infinity reveals how mathematics the world over have risen to meet the challenges set by their predecessors-and how the enigmas of the past inevitably surrender to the powerful techniques of the present.

Julian Havil explores Napier’s original development of logarithms, the motivations for his approach, and the reasons behind certain adjustments to them. Napier’s inventive mathematical ideas also include formulas for solving spherical triangles, "Napier’s Bones" (a more basic but extremely popular alternative device for calculation), and the use of decimal notation for fractions and binary arithmetic. Havil also considers Napier’s study of the Book of Revelation, which led to his prediction of the Apocalypse in his first book, A Plaine Discovery of the Whole Revelation of St. John—the work for which Napier believed he would be most remembered.

John Napier assesses one man’s life and the lasting influence of his advancements on the mathematical sciences and beyond.

Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.

In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

Contemporary research has shown that optimistic people experience longer and healthier lives, better relationships, and higher incomes. Generations before such findings, however, inspirational writer Christian D. Larson showed an amazing grasp of the life-changing power of gratitude and optimism. Today, Larson is known worldwide for his powerful meditation, “The Optimist Creed,” and other classics of spiritual living.

But no single volume has collected his greatest writings. Here, at last, is a long-overdue anthology that makes Larson’s foundational writings available to the countless readers who already know his name and work.

Like no one else of his day, Larson understood the metaphysical and psychological dimensions of grateful living – or, as he famously put it, “an attitude of gratitude.” Affirmative thought, Larson reasoned, sets in motion unseen forces, both spiritual and psychical, and aids in manifesting our desires.

The Optimist Creed features complete editions of Larson’s most deeply affecting works, each redesigned and reset. It contains: The Pathway of Roses; Your Forces and How to Use Them (the work that features his original “Optimist Creed”); Mastery of Self; The Ideal Made Real; and Just Be Glad.

Here is a signature volume of one of the most quietly impactful and radical works ever written on the creative potentialities of human thought, The Power of Awareness. In this book, author Neville presents a concise, unforgettable statement of his core philosophy: that the world around you is a picture in your mind’s eye, created by your thinking, and susceptible to change by altering your thoughts and feelings.

Originally published in 1952, The Power of Awareness not only prefigured the revolution in mind-power metaphysics, but surpassed it. Before the public had heard about quantum physics experiments (popularized in our own time through movies such as The Secret and What the Bleep Do We Know!?), Neville was conveying the unheard-of message that reality is directly impacted by the perspective and consciousness of the observer himself. Moreover, he wrote, each of us is ultimately responsible for, and capable of reshaping, the outer circumstances we perceive.

Neville’s authorial genius is his ability to deliver these ideas in an immensely readable and enjoyable way. Like few other metaphysical figures of his era, Neville captured complexities in simple stories, memorable examples, and practical advice. His books are unfailingly brief and easy to read, because his command of his material is so masterly and complete.

The Power of Awareness also includes a special bonus work, Awakened Imagination, originally published in 1954. This two-in-one volume forms a brilliant introduction and user’s guide to the practical philosophy of a great spiritual thinker.

Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism.

Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.

Using his extensive study of biomedical chemistry and brain science at the Massachusetts Institute of Technology, Pete A. Sanders, Jr., has developed a method to show how we can tap into our psychic abilities at will to expand our knowledge and gain control of our destiny. By sharing the techniques that he and his instructors have taught to more than half a million people, You Are Psychic! offers a program of simple exercises to teach you how to: Experience nine senses, instead of only five. Locate the body's four Psychic Reception Areas and find out whether you are strongest in psychic vision, hearing, intuition, or feeling. Tap your extrasensory awareness whenever you wish. Use your psychic abilities to improve your professional success, your relationships, and your creativity, and to heal your body. Apply your sharpened perceptual powers to solve complex problems and handle difficult people.

"In this brilliant work, Pete Sanders clearly and skillfully charts a safe course for adventurous souls to explore new frontiers of human potential in their inner quest for personal and spiritual growth."

— Edward E. Winchester, President, Pentagon Meditation Club