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.

    From the Difference Engine to magic squares and from the Fibonacci rabbits to Fermat's Last Theorem, this book features the weird world of numbers, imaginary, real or infinite.

    Hardy, in the years before World War I. Through their eyes the reader is taken on a journey through numbers theory. Ramanujan would regularly telescope 12 steps of logic into two - the effect is said to be like Dr Watson in the train of some argument by Sherlock Holmes. The language of symbols and infinitely large (and small) regions of mathematics should be rendered with clarity for the general reader.

    Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of Princeton’s Institute for Advanced Study, where Gödel and Einstein both worked.Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.

    But while this medieval medicine now seems archaic, it also made a critical contribution to modern science.Medieval Bodies guides us on a head-to-heel journey through this era’s revolutionary advancements and disturbing convictions. We learn about the surgeons who dissected a living man’s stomach, then sewed him up again; about the geographers who delineated racial groups by skin color; and about the practice of fasting to gain spiritual renown. Encompassing medicine and mysticism, politics and art—and complete with vivid, full-color illustrations—Medieval Bodies shows us how it felt to live and die a thousand years ago.

    The calculus is not a hard subject and I prove this through an easy to read and obvious approach spanning only 100 pages. I have written this book with the following type of student in mind; the non-traditional student returning to college after a long break, a notoriously weak student in math who just needs to get past calculus to obtain a degree, and the garage tinkerer who wishes to understand a little more about the technical subjects. This book is meant to address the many fundamental thought-blocks that keep the average 'mathaphobe' (or just an interested person who doesn't have the time to enroll in a course) from excelling in mathematics in a clear and concise manner. It is my sincerest hope that this book helps you with your needs.Show more Show less

    Book by Waring, Chris

    The author assures us it is not!Three years before they came together, four young American men left their fraternities and college campuses for an adventure exceeding their imaginations. Wanting something more than the draft and unknown to each other, they chose Naval Aviation as the next step in their lives. Generally, they were better than their navy peers, all qualifying for high performance aircraft to be flown from steel decks over foreign seas. They would become the pointy end of the stick in aerial battles over North Vietnam, the most heavily defended patch of real estate in the history of aerial warfare. They were to do this in 1967, the year in which Naval Aviation experienced its greatest losses.These four young men, now Lieutenants Junior Grade, United States Navy, were ordered to Attack Squadron 34 to fly A4 Skyhawks into combat. They were assigned Junior Officer's stateroom 0111 aboard USS Intrepid, a venerable aircraft carrier with a distinguished history. This "bunkroom" better known to them as Triple Sticks was the repository for a log (in navy terms) or journal written by these four young aviators. Forty years later this log was the genesis of this memoir.In the lethal environment over the northern reaches of North Vietnam or ashore in the Officer's clubs and bars of Asia, the writing brings to life wonderful humor, bizarre behavior, vivid aerial battles, uncommon loyalty, anger, frustration and respect. One survived or did not according to his skill and luck.

    She entered Ah-gwah-ching State Sanatorium at Walker, Minnesota, for what she thought would be a short stay. In January, her tuberculosis spread, and she nearly died. Her recovery required many months of bed rest and medical care.Marilyn loved to write, and the story of her three-year residency at the sanatorium is preserved in hundreds of letters that she mailed back home to her parents, who could visit her only occasionally and whom she missed terribly. The letters functioned as a diary in which Marilyn articulately and candidly recorded her reactions to roommates, medical treatments, Native American nurses, and boredom. She also offers readers the singular perspective of a bed-bound teenager, gossiping about boys, requesting pretty new pajamas, and enjoying Friday evening popcorn parties with other patients.Selections from this cache of letters are woven into an informative narrative that explores the practices and culture of a midcentury tuberculosis sanatorium and fills in long-forgotten details gleaned from recent conversations with Marilyn, who "graduated" from the sanatorium and went on to lead a full, productive life.

    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.

    Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives—from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century.Many of the greatest names in intellectual history—Pythagoras, Plato, Archimedes, Euclid— were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions—his famed Coxeter groups and Coxeter diagrams—have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational.Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.

    Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

    Tutored by her father, the mathematician Theon, Hypatia quickly became an authority in the subjects of mathematics, astronomy, and philosophy. Word spread of her brilliance, and scholars from all over the world journeyed to Alexandria to seek her teachings.

    You can use these ideas and methods as-is, or better yet, tweak them and create your own enticing educational meals. The message the authors share is that, with imagination and preparation, every teacher can be a Classroom Chef.

    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.