Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant results.

    Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

    He was especially careful to present new and unfamiliar puzzles that had not been included in such classic collections as those by Sam Loyd and Henry Dudeney. Later, these puzzles were published in book collections, incorporating reader feedback on alternate solutions or interesting generalizations.The present volume contains a rich selection of 70 of the best of these brain teasers, in some cases including references to new developments related to the puzzle. Now enthusiasts can challenge their solving skills and rattle their egos with such stimulating mind-benders as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, The Fork in the Road, Bronx vs. Brooklyn, Touching Cigarettes, and 64 other problems involving logic and basic math. Solutions are included.

    This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

    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.

    He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.

    In her previous book, The Well-Trained Mind, the author provided a road map of classical education for parents wishing to home-school their children, and that book is now the premier resource for home-schoolers. In this new book, Bauer takes the same elements and techniques and adapts them to the use of adult readers who want both enjoyment and self-improvement from the time they spend reading.The Well-Educated Mind offers brief, entertaining histories of five literary genres—fiction, autobiography, history, drama, and poetry—accompanied by detailed instructions on how to read each type. The annotated lists at the end of each chapter—ranging from Cervantes to A. S. Byatt, Herodotus to Laurel Thatcher Ulrich—preview recommended reading and encourage readers to make vital connections between ancient traditions and contemporary writing.The Well-Educated Mind reassures those readers who worry that they read too slowly or with below-average comprehension. If you can understand a daily newspaper, there's no reason you can't read and enjoy Shakespeare's Sonnets or Jane Eyre. But no one should attempt to read the "Great Books" without a guide and a plan. Susan Wise Bauer will show you how to allocate time to your reading on a regular basis; how to master a difficult argument; how to make personal and literary judgments about what you read; how to appreciate the resonant links among texts within a genre—what does Anna Karenina owe to Madame Bovary?—and also between genres. Followed carefully, the advice in The Well-Educated Mind will restore and expand the pleasure of the written word.

    It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the universe investigates them; they foreshadow the physical sciences.Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series-Sacred Geometry, Sacred Number, Harmonograph, The Elements of Music, Platonic & Archimedean Solids, and A Little Book of Coincidence-it makes ancient wisdom and its astonishing interconnectedness accessible to us today.Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.

    

    Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

    Who invented zero? Why are there 60 seconds in a minute? Can a butterfly's wings really cause a storm on the far side of the world? In 50 concise essays, Professor Tony Crilly explains the mathematical concepts that allow use to understand and shape the world around us.

    Xenophon continues the account to 362 B.C. These years saw Athens humbled by Sparta; Sparta humbled by Athens and her former ally, Thebes; Athens ground down again by the military genius of the Theban Epaminondas, taking on both Athens and Sparta; and behind the scenes the might of Persia, intervening now on one side, now on another.Xenophon himself knew many of the protagonists and his writing is personal history as well as a chronicle of events; he vividly portrays individuals, heroic and treacherous, influencing politics and battles and leading Greece inevitably towards impotence.

    Suppose, instead of thinking about organisms using genes to reproduce themselves, as we had since Mendel's work was rediscovered, we turn it around and imagine that "our" genes build and maintain us in order to make more genes. That simple reversal seems to answer many puzzlers which had stumped scientists for years, and we haven't thought of evolution in the same way since. Drawing fascinating examples from every field of biology, he paved the way for a serious re-evaluation of evolution. He also introduced the concept of self-reproducing ideas, or memes, which (seemingly) use humans exclusively for their propagation. If we are puppets, he says, at least we can try to understand our strings.

    It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    Now the Augmented Third Edition adds to the established reputation of this premier academic resource. A wealth of new maps, charts, and diagrams further clarify information found in the scripture pages. In addition, section introductions have been expanded and the book introductions have been made more uniform in order to enhance their utility. Of course, the Augmented Third Edition retains the features prized by students, including single column annotations at the foot of the pages, in-text background essays, charts, and maps, a page number-keyed index of all the study materials in the volume, and Oxford's renowned Bible maps. This timely edition maintains and extends the excellence the Annotated's users have come to expect, bringing still more insights, information, and approaches to bear upon the understanding of the biblical text.