And yet amid the flood of information today, it's often difficult to recognize the truly revolutionary ideas that will have lasting impact. In the spirit of identifying the most significant new theories and discoveries, John Brockman, publisher of Edge.org ("The world's smartest website" -- The Guardian), asked 198 of the finest minds What do you consider the most interesting recent scientific news? What makes it important?Pulitzer Prize-winning author of Guns, Germs, and Steel Jared Diamond on the best way to understand complex problems * author of Seven Brief Lessons on Physics Carlo Rovelli on the mystery of black holes * Harvard psychologist Steven Pinker on the quantification of human progress * TED Talks curator Chris J. Anderson on the growth of the global brain * Harvard cosmologist Lisa Randall on the true measure of breakthrough discoveries * Nobel Prize-winning physicist Frank Wilczek on why the twenty-first century will be shaped by our mastery of the laws of matter * philosopher Rebecca Newberger Goldstein on the underestimation of female genius * music legend Peter Gabriel on tearing down the barriers between imagination and reality * Princeton physicist Freeman Dyson on the surprising ability of small (and cheap) upstarts to compete with billion-dollar projects. Plus Nobel laureate John C. Mather, Sun Microsystems cofounder Bill Joy, Wired founding editor Kevin Kelly, psychologist Alison Gopnik, Genome author Matt Ridley, Harvard geneticist George Church, Why Does the World Exist? author Jim Holt, anthropologist Helen Fisher, and more.

    From manhole covers to bubbles to subway maps, each page gives you a glimpse of the world through renowned mathematicians' eyes and reveals how their theorems and equations can be applied to nearly everything you encounter. Covering dozens of your favorite math topics, you'll find fascinating answers to questions like:How are the waiting times for buses determined?Why is Romanesco Broccoli so mesmerizing?How do you divide a cake evenly?Should you run or walk to avoid rain showers?Filled with compelling mathematical explanations, Math Geek sheds light on the incredible world of numbers hidden deep within your day-to-day life.

    From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

     This graphic novel recounts the spiritual odyssey of philosopher Bertrand Russell. In his agonized search for absolute truth, he crosses paths with thinkers like Gottlob Frege, David Hilbert & Kurt Gödel, & finds a passionate student in Ludwig Wittgenstein. But his most ambitious goal—to establish unshakable logical foundations of mathematics—continues to loom before him. Thru love & hate, peace & war, he persists in the mission threatening to claim both his career & happiness, finally driving him to the brink of insanity. This story is at the same time a historical novel & an accessible explication of some of the biggest ideas of mathematics & modern philosophy. With rich characterizations & atmospheric artwork, it spins the pursuit of such ideas into a satisfying tale. Probing, layered, the book throws light on Russell’s inner struggles while setting them in the context of the timeless questions he tried to answer. At its heart, Logicomix is a story about the conflict between ideal rationality & the flawed fabric of reality.

    He never expected to be dragged into a terrifying series of events that culminates in a single moment of horror, one that would forever change his life in a way no teenager should have to endure. Now Eric must face an uncertain future while combating the ghosts of the past that threaten to rip away any happiness in his life.

    While all learning requires effort, better learning does not require more effort, but rather effectively aligning how the brain naturally learns with the demands of your studies. This book shows you what is involved in learning new material, how the human brain processes new information, and what it takes for that information to stick with you even after the test.Taking a small amount of time to read and act upon the material in this book will prove to be one of the best decisions you can make as a learner. What you discover will change the way you learn in college and be helpful in your personal and professional life. You live in a world where you will have to be a lifelong learner, constantly updating your skills and changing jobs to compete in the global marketplace. Most college students today will have as many as 10-14 different jobs by age 38. Learning how to learn in harmony with your brain is crucial to your long-term success.This succinct book explains straightforward strategies for changing how you prepare to learn, engage with your course material, and set about improving recall of newly learned material whenever you need it. This is not another book about study skills and time management strategies, but instead an easy to read description of the research about how the human brain learns in a way that you can put into practice right away. Did you know neuroscientists have shown that memories are made while you sleep, and by studying right before sleeping you can make stronger memories for your information? In this book the authors explain the role that sleep, exercise and your senses play in learning; how memory works and what makes the brain pay attention; the importance of your mindset towards learning and pattern recognition; as well as new breakthroughs in brain science that can enhance your ability to learn new information and make later recall (for tests or everyday life) easier.This book will put you on the path to reaching your full learning potential.

    H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    Each concept is presented in a full two- or four-page spread, making the text practical and easy for students to refer to while they work. The modular format also gives instructors the utmost flexibility in organizing their course. Visual examples from many periods, peoples, and cultures are provided for all elements and principles of design, and the diversity of illustrations also includes examples from nature and non-art sources, encouraging students to see these principles in the world.

    How exactly does the animal world deal with the flip side of the life cycle? And what are the lessons, ecological to spiritual, raised by a close look at how the animal world renews itself? Heinrich focuses his wholly original gaze on the fascinating doings of creatures most of us would otherwise turn away from—field mouse burials conducted by carrion beetles; the communication strategies of ravens, “the premier northern undertakers”; and the “inadvertent teamwork” among wolves and large cats, foxes and weasels, bald eagles and nuthatches in cold-weather dispersal of prey. Heinrich reveals, too, how and where humans still play our ancient and important role as scavengers, thereby turning—not dust to dust—but life to life.

    It covers such areas as biotechnology and biomedical engineering.

    

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    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."

    This groundbreaking book reveals how today's global businesses can be both environmentally responsible and highly profitable.