For real.If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry," from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

    Language is informal, examples are vivid and lively, and the perspectivie is fresh. Based on lectures delivered to engineering students, this work will also be valued by scientists, engineers, technicians, businessmen, anyone facing energy challenges of the future.

    But there remains a critical gap in our knowledge: we still know very little about what happened in the first seconds after the Big Bang. At the Edge of Time focuses on what we have recently learned and are still striving to understand about this most essential and mysterious period of time at the beginning of cosmic history.Delving into the remarkable science of cosmology, Dan Hooper describes many of the extraordinary and perplexing questions that scientists are asking about the origin and nature of our world. Hooper examines how we are using the Large Hadron Collider and other experiments to re-create the conditions of the Big Bang and test promising theories for how and why our universe came to contain so much matter and so little antimatter. We may be poised to finally discover how dark matter was formed during our universe's first moments, and, with new telescopes, we are also lifting the veil on the era of cosmic inflation, which led to the creation of our world as we know it.Wrestling with the mysteries surrounding the initial moments that followed the Big Bang, At the Edge of Time presents an accessible investigation of our universe and its origin.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    

    This book gives a lucid, exciting, and accessible account of the surprising and counterintuitive ideas that shape our understanding of the sub-atomic world. It does not disguise the problems of interpretation that still remain unsettled 75 years after the initial discoveries. The main text makes no use of equations, but there is a Mathematical Appendix for those desiring stronger fare. Uncertainty, probabilistic physics, complementarity, the problematic character of measurement, and decoherence are among the many topics discussed. This volume offers the reader access to one of the greatest discoveries in the history of physics and one of the outstanding intellectual achievements of the twentieth century.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    Stengers and Prigogine show how the two great themes of classic science, order and chaos, which coexisted uneasily for centuries, are being reconciled in a new and unexpected synthesis.

    These sections together make an appropriate one-term advanced/graduate level course (mathematical prerequisites: vector analysis and simple partial-differential equations). The book is printed to make it easy for readers to identify these sections.• The remaining Track 2 material provides a wealth of advanced topics instructors can draw from to flesh out a two-term course, with Track 1 sections serving as prerequisites.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    Crease tells the stories behind ten of the greatest equations in human history. Was Nobel laureate Richard Feynman really joking when he called Maxwell's electromagnetic equations the most significant event of the nineteenth century? How did Newton's law of gravitation influence young revolutionaries? Why has Euler's formula been called "God's equation," and why did a mysterious ecoterrorist make it his calling card? What role do betrayal, insanity, and suicide play in the second law of thermodynamics?The Great Equations tells the stories of how these equations were discovered, revealing the personal struggles of their ingenious originators. From "1 + 1 = 2" to Heisenberg's uncertainty principle, Crease locates these equations in the panoramic sweep of Western history, showing how they are as integral to their time and place of creation as are great works of art.

     In MATH WITH BAD DRAWINGS, Ben Orlin answers math's three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone.Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark "bad drawings," which convey both his humor and his message with perfect pitch and clarity. Organized by unconventional but compelling topics such as "Statistics: The Fine Art of Honest Lying," "Design: The Geometry of Stuff That Works," and "Probability: The Mathematics of Maybe," MATH WITH BAD DRAWINGS is a perfect read for fans of illustrated popular science.

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

     Nate Arturi isn't a knight in shining armor. He sure as hell isn't a king. And the last time someone called him heroic, it was because he fetched his neighbor's corgi off the roof. But when an ancient alien beacon awakens on Earth, sounding the call to enemies near and far, the Merlin is left with little choice. Any Knight in a Doomsday, or so the saying goes. Ambushed by a hulking alien brute and tricked into accepting a foul-mouthed sword from a homeless wizard, Nate suddenly finds his senior year at Penn State more than a little out of hand. But when an armada of butt-ugly troglodans and exotic gorgon killers starts raining from the sky, one thing becomes inescapably clear: Unless he mans up and gets that damned beacon off of his planet, everything he knows is about to be burned to a crisp. Can Nate master the Excalibur in time to stop the trogs? Buy The Eighth Excalibur to find your freakin’ destiny today!

    It was the first force to be recognized and described yet it is the least understood. It is a "force" that keeps your feet on the ground yet no such force actually exists.Gravity, to steal the words of Winston Churchill, is "a riddle, wrapped in a mystery, inside an enigma." And penetrating that enigma promises to answer the biggest questions in science: what is space? What is time? What is the universe? And where did it all come from?Award-winning writer Marcus Chown takes us on an unforgettable journey from the recognition of the "force" of gravity in 1666 to the discovery of gravitational waves in 2015. And, as we stand on the brink of a seismic revolution in our worldview, he brings us up to speed on the greatest challenge ever to confront physics.