Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    Written By Two Of Today'S Most Respected Computer Science Educators, Nell Dale And John Lewis, The Text Provides A Broad Overview Of The Many Aspects Of The Discipline From A Generic View Point. Separate Program Language Chapters Are Available As Bundle Items For Those Instructors Who Would Like To Explore A Particular Programming Language With Their Students. The Many Layers Of Computing Are Thoroughly Explained Beginning With The Information Layer, Working Through The Hardware, Programming, Operating Systems, Application, And Communication Layers, And Ending With A Discussion On The Limitations Of Computing. Perfect For Introductory Computing And Computer Science Courses, Computer Science Illuminated, Third Edition's Thorough Presentation Of Computing Systems Provides Computer Science Majors With A Solid Foundation For Further Study, And Offers Non-Majors A Comprehensive And Complete Introduction To Computing.

    Result: The world's first vaccine. Experiment: A slave woman is forced to undergo more than thirty operations without anesthesia. Result: The beginnings of modern gynecology. Experiment: From 1946 to 1953, seventy-four boys are fed oatmeal laced with radioactive iron and calcium. Result: A better understanding of the effects of radioactivity on the human body. Experimental incidents such as these paved the way for crucial medical discoveries and lifesaving cures and procedures. But they also violated the rights of their subjects, many of whom did not give their consent to the experiments. The subjects suffered excruciating pain and humiliation. Some even died as a result of the procedures. Even in the twenty-first century—despite laws, regulations, and ethical conventions—the tension between medical experimentation and patient rights continues. How do doctors balance the need to test new medicines and procedures with their ethical and moral duty to protect the rights of human subjects? What price has been paid for medical knowledge? Can we learn from the broken oaths of the past? Take a harrowing journey through some of history's greatest medical advances—and its most horrifying medical atrocities. You'll read about orphans injected with lethal tuberculosis and concentration camp inmates tortured by Nazi doctors. You’ll also learn about radiation experimentation and present-day clinical trials that prove fatal. Through these stories, explore the human suffering that has gone hand in hand with medical advancement.

    One island, two unique societies (Norse and Inuit). Only one of these societies would succeed--the other would fail. But how? With his trademark accessibility and comprehensiveness, Diamond documents how environmental damage, climate change, loss of friendly contacts and the rise of hostile ones, and the unique political, economic, and social settings of prehistoric Greenland combine to demonstrate exactly why and how societies choose to fail or succeed. Jared Diamond's latest book, "The World Until Yesterday: What Can We Learn from Traditional Societies?," is available from Viking.

    In order to join this unit they have to commit to being in the army for ten years, rather than the three years a normal soldier serves.Talpiots are taught advanced level physics, math and computer science as they train with soldiers from every other branch of the IDF. The result: young men and women become research and development machines. Talpiots have developed battle ready weapons that only Israel's top military officers and political leaders know about. They have also dramatically improved much of the weapons already in Israel's arsenal.Talpiot has been tasked with keeping Israel a generation ahead of a rapidly strengthening and technologically capable Iran. Talpiots contribute to all of the areas that will be most important to the IDF as Iran becomes even more powerful including missile technology, anti-missile defense, cyber-warfare, intelligence, satellite technology and high powered imaging. Talpiot soldiers have also been a major factor in the never ending fight against Israel's other enemies and many have left the R&D lab to fly fighter planes, serve in the field as commanders of elite army ground units and at sea commanding Israel's fleet of naval ships.After leaving the army, Talpiots have become a major force in the Israeli economy, developing some of Israel's most famous and powerful companies.Israel's Edge contains dozens of interviews with Talpiot graduates and some of the early founders of the program. It explains Talpiot's highly successful recruiting methods and discloses many of the secrets of the program's success. The book also profiles some of the most successful businesses founded by Talpiot graduates including CheckPoint, Compugen, Anobit, recently bought by Apple, and XIV, recently bought by IBM. No other military unit has had more of an impact on the State of Israel and no other unit will have more of an impact in the years ahead. The soldiers of Talpiot are truly unsung heroes.

    As body armor and advanced trauma care helped save the lives—if not the limbs—of American soldiers fighting in Afghanistan and Iraq, Walter Reed quickly became the world leader in amputee rehabilitation. But no matter the injury, physical therapy began the moment the soldiers emerged from surgery. Days at Walter Reed were intense, chaotic, consuming, and heartbreaking, but they were also filled with camaraderie and humor. Working in a glassed-in fishbowl gymnasium, Levine, her colleagues, and their combat-injured patients were on display at every moment to tour groups, politicians, and celebrities. Some would shudder openly at the sight—but inside the glass and out of earshot, the PTs and the patients cracked jokes, played pranks, and compared stumps. With dazzling storytelling, Run, Don’t Walk introduces a motley array of oddball characters including:  Jim, a retired lieutenant-colonel who stays up late at night baking cake after cake, and the militant dietitian who is always after him; a surgeon who only speaks in farm analogies; a therapy dog gone rogue; —and Levine’s toughest patient, the wild, defiant Cosmo, who comes in with one leg amputated and his other leg shattered. Entertaining, engrossing, and ultimately inspiring, Run, Don’t Walk is a fascinating look into a hidden world.

    With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction--and whether the universe truly has a future.

    Beginning near the speed of light and proceeding to explorations of space-time and curved spaces, "Introducing Relativity" plots a visually accessible course through the thought experiments that have given shape to contemporary physics. Scientists from Newton to Hawking add their unique contributions to this story, as we encounter Einstein's astounding vision of gravity as the curvature of space-time and arrive at the breathtakingly beautiful field equations. Einstein's legacy is reviewed in the most advanced frontiers of physics today - black holes, gravitational waves, the accelerating universe and string theory. This is a superlative, fascinating graphic account of Einstein's strange world and how his legacy has been built upon since.

    A timeless introduction to the field and a landmark in symbolic logic, showing that classical logic can be treated algebraically.

    Many of the contributors bring their own special touch, presenting a refreshingly eclectic variety of personal icons, from pub signs to seaside piers, from cattle grids to canal boats, and from village cricket to nimbies.First published as a lavish colour coffee-table book, this new expanded paperback edition has double the original number of contributions from many celebrities including Bill Bryson, Michael Palin, Eric Clapton, Bryan Ferry, Sebastian Faulks, Kate Adie, Kevin Spacey, Gavin Pretor-Pinney, Richard Mabey, Simon Jenkins, John Sergeant, Benjamin Zephaniah, Joan Bakewell, Antony Beevor, Libby Purves, Jonathan Dimbleby, and many more: and a new preface by HRH Prince Charles.

    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.

    The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

    FWUMP! A secret door suddenly closed behind them . . .Matt and Bibi use math to escape from a pharaoh's tomb!When the Zills family is summoned to Egypt to help find the hidden burial site of an ancient pharaoh, Matt and Bibi are locked into an adventure they did not expect. Stuck inside a pyramid with only each other, their dog Riley, and geometric hieroglyphics to help them find their way, the twins must use their math knowledge to solve the riddles on the walls and locate the burial chamber. Luckily, the two know their stuff when it comes to geometric solids.

    It is the complex dynamics of flow that structures our atmosphere, land, and oceans.Part of a trilogy of books exploring the science of patterns in nature by acclaimed science writer Philip Ball, this volume explores the elusive rules that govern flow - the science of chaotic behavior.

    And for most of modern history, swimming has caused a ripple that touches us all--the heroes and the ordinary folk; the real and the mythic.Splash! dives into Egypt, winds through ancient Greece and Rome, flows mostly underground through the Dark and Middle Ages (at least in Europe), and then reemerges in the wake of the Renaissance before taking its final lap at today's Olympic games. Along the way, it kicks away the idea that swimming is just about moving through water, about speed or great feats of aquatic endurance, and shows you how much more it can be. Its history offers a multi-tiered tour through religion, fashion, architecture, sanitation and public health, colonialism, segregation and integration, sexism, sexiness, guts, glory, and much, much more.Unique and compelling, Splash! sweeps across the whole of humankind's swimming history--and just like jumping into a pool on a hot summer's day, it has fun along the way.