Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    Numerous tables and figures.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    He proposes his solution.

    All chapters are supplemented by thought-provoking problems. A useful work for graduate-level students with backgrounds in computer science, operations research, and electrical engineering. "Mathematicians wishing a self-contained introduction need look no further." — American Mathematical Monthly.

     Hope turns to ashes when, on final approach to the new world, a mysterious malfunction damages the ship, triggering a crisis that results in the death of the captain and a rash of infighting over the ship's undamaged colony pods. The "Unity" breaks apart in space and seven colonial factions are scattered across the surface of the planet. As the "Unity" surviviors struggle to rebuild human civilization on this strange and mysterious alien world, old tensions resurface and one man sets in motion forces that may destroy any dream of a lasting peace.

    Evidence Dismissed

    Mathematics, Applied & Natural Sciences

    Genetic manipulation and artificial intelligence shape an astounding destiny for our species. With these wondrous changes come unexpected new truths of heart and mind that challenge the very definition of human—and that threaten not only our existence but the universe itself as our surprising powers—both miraculous and monstrous—evolve through the centuries.

    This book discusses Von Neumann's work in areas such as game theory, mathematics, physics, and meteorology which formed the building blocks for the most important discoveries of the century: the modern computer, game theory, and the atom bomb.

    You proceed at your own rate and any difficulties you may encounter are resolved before you move on to the next topic. With a step-by-step programmed approach that is complemented by hundreds of worked examples and exercises, Advanced Engineering Mathematics is ideal as an on-the-job reference for professionals or as a self-study guide for students.Uses a unique technique-oriented approach that takes the reader through each topic step-by-step.Features a wealth of worked examples and progressively more challenging exercises.Contains Test Exercises, Learning Outcomes, Further Problems, and Can You? Checklists to guide and enhance learning and comprehension.Expanded coverage includes new chapters on Z Transforms, Fourier Transforms, Numerical Solutions of Partial Differential Equations, and more Complex Numbers.Includes a new chapter, Introduction to Invariant Linear Systems, and new material on difference equations integrated into the Z transforms chapter.

    This all-purpose CCNA study guide methodically covers all the objectives of the ICND1 (100-101) and ICND2 (200-101) exams as well as providing additional insight for those taking CCNA Composite (200-120) exam. It thoroughly examines operation of IP data networks, LAN switching technologies, IP addressing (IPv4/IPv6), IP routing technologies, IP services, network device security, troubleshooting, and WAN technologies.Valuable study tools such as a companion test engine that includes hundreds of sample questions, a pre-assessment test, and multiple practice exams. Plus, you'll also get access to hundreds of electronic flashcards, author files, and a network simulator.CCNA candidates may choose to take either the ICND1(100-101) and ICND2 (200-101) exams or the CCNA Composite exam (200-120); this study guide covers the full objectives of all three Written by bestselling Sybex study guide author Todd Lammle, an acknowledged authority on all things Cisco Covers essential Cisco networking topics such as operating an IP data network, IP addressing, switching and routing technologies, troubleshooting, network device security, and much more Includes a comprehensive set of study tools including practice exams, electronic flashcards, comprehensive glossary of key terms, videos, and a network simulator that can be used with the book's hands-on labs Bonus Content: Access to over 40 MicroNugget videos from CBT Nuggets CCNA Routing and Switching Study Guide prepares you for CCNA certification success.

    Turing’s openness about his homosexuality at a time when it was an imprisonable offense ultimately led to his untimely lo death at the age of only forty-one. In Alan Turing: Unlocking the Enigma, David Boyle reveals the mysteries behind the man and his remarkable career. Aged just 22, Turing was elected a fellow at King's College, Cambridge on the strength of a dissertation in which he proved the central limit theorem. By the age of 33, he had been awarded the OBE by King George VI for his wartime services: Turing was instrumental in cracking the Nazi Enigma machines at the top secret code breaking establishment at Bletchley Park during the Second World War.But his achievements were to be tragically overshadowed by the paranoia of the post-War years. Hounded for his supposedly subversive views and for his sexuality, Turing was prosecuted in 1952, and forced to accept the humiliation of hormone treatment to avoid a prison sentence. Just two years later, at the age of 41 he was dead. The verdict: cyanide poisoning.Was Turing’s death accidental as his mother always claimed? Or did persistent persecution drive him to take him own life?Alan Turing: Unlocking the Enigma seeks to find the man behind the science, illuminating the life of a person who is still a shadowy presence behind his brilliant achievements.

    Connecting games to math, science, and psychology, GameTek has grown to be one of the most popular parts of the show.This volume commemorates the anniversary with a collection of over seventy of the best segments, many with annotations and illustrations.With chapters on everything from Rock, Paper, Scissors to the Prisoner’s Dilemma to Player Engagement to Quasicrystals to Buddha’s Forbidden Games, GameTek is sure to delight not just game designers and players, but anyone who wants to learn about the world from a new perspective.Sections:• Game Theory• Math• Psychology• Science• Game Mechanics• Psychology Games• HistoryFrom the first time I heard it, the GameTek segment in The Dice Tower podcast became my favorite part of the show. Listening to Geoff is like going to your favorite lesson with your favorite teacher. He teaches about games (yay!) and does it in a very interesting way with lots of examples. He does amazing stuff. He knows about the construction of games, he knows the theory, he knows all that stuff behind the scenes that we gamers do not see when just playing a game and having fun.Ignacy Trzewiczek, Portal GamesThere are many hobby game 'experts' out there, dying to give you their opinion on how the industry works, how games work, what types of games are best, and so on. Geoff Engelstein is the expert that requires your attention. He is a scholar of games, and his research on games and other principles that apply to gaming is matched by none.Stephen Buonocore, Stronghold GamesOver the years, I’ve listened to a lot of people talk about board games, yet the short snippets that Geoff puts out are the ones that I find myself thinking about in the quiet of the night. His are the segments that you laugh at and say, “I have NO idea what you are talking about” — but later on use to show people just how intellectual you are.Tom Vasel, The Dice Tower

    The latter half of our century has seen its own Renaissance - informations technology has changed irrevocable the way we live, work, and think about the world. We are fortunate, therefore, that the authors of Out of Their Minds have been able to talk so candidly with the founders of computer science. In Out of their Minds, readers will hear the Newtons and Euclids of the computer age as they talk about their discoveries in information technology that have changed forever the way we live, work, and think about the world. Based on interviews by freelance writer Cathy Lazere and the expertise of computer scientist Dennis Shasha, Out of their Minds introduces readers to fifteen of the planet's foremost computer scientists, including eight winners of the Turing Award, computing's Nobel Prize. The scientists reveal themselves in fascinating anecdotes about their early inspirations and influences, their contributions to computer science, and their thoughts on its explosive future. These are the programmers whose work