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

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    ASIN: 0312295170

    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.

    Agency is the ability to act as an effective agent for yourself—reflecting, making creative choices, and constructing a meaningful life. Grounded in extensive psychological research, The Power of Agency gives you the tools to help alleviate anxiety, manage competing demands and help you live your version of success.Renowned psychology experts Paul Napper and Anthony Rao will help you break through your state of overwhelm by showing you how to access your personal agency with seven empowering principles: control stimuli, associate selectively, move, position yourself as a learner, manage your emotions and beliefs, check your intuition, deliberate and then act.Featuring stories of people who have successfully applied these principles to improve their lives, The Power of Agency will give you the insights and skills to build your confidence, conquer challenges, and live more authentically.

    The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    From the text that revealed the famous “Theory of Relativity”-renowned as the most important scientific discovery of the 20th Century-to his significant works on quantum theory, statistical mechanics, and the photoelectric effect, here are the writings that changed physics, and subsequently, the way we view the world. Einstein also thought deeply on both political issues and religious thought, so many of Einstein’s philosophical essays are included. Hawking provides introductions to each work, which provides both historical and scientific perspective. From the papers that shaped modern scientific thought to Einstein’s later musings on his landmark findings, A Stubbornly Persistent Illusion is a collection of Einstein’s most important work, with commentary from our greatest living physicist.

    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.

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    O'Conner and Stewart Kellerman explode the misconceptions that have led generations of language lovers astray. They reveal why some of grammar's best-known "rules" aren't--and never were--rules at all. They explain how Brits and Yanks wound up speaking the same language so differently, and why British English isn't necessarily purer. This playfully witty yet rigorously researched book sets the record straight about bogus word origins, politically correct fictions, phony français, fake acronyms, and more. English is an endlessly entertaining, ever-changing language, and yesterday's blooper could be tomorrow's bon mot--or vice versa!

    Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

    Yet, no records exist explaining how, why, or who built Egypt’s megalithic monuments and statues. The ancient Egyptians did, however, record that their civilization resided in the shadow of a kingdom of “gods” whose reign ended many thousands of years before their first dynasty. What was this Civilization X that antiquity’s most accomplished people revered as gods?The recent discovery of a large stone at one of Egypt’s oldest ruins presents physical evidence that clearly and distinctly shows the markings of a machining process far beyond the capabilities of the Ancient Egyptians. Likewise, experimental modeling of the Great Pyramid’s subterranean chambers and passageways gives scientific evidence to further support the theory that the civilization responsible for such magnificent monuments is much older than presently believed. Ancient Egypt 39,000 BCE examines this evidence from historical and technical points of view, explaining who these prehistoric people were, what happened to them, why they built their civilization out of granite, and why they built a series of pyramids along the west bank of the Nile River.

    Emphasis on developing algebraic skills is extended to the exercises--including both drill problems and applications. The authors work through examples and explanations with a blend of rigor and accessibility. In addition, they have refined the flow, transitions, organization, and portioning of the content over many editions to optimize learning for readers. The table of contents covers a wide range of topics efficiently, enabling readers to gain a diverse understanding.

    Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, alwayschoosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum ofmathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issuesand has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

    Topics include the development of counting and numbers systems, the emergence of zero, cultures that don’t have numbers, algebra, solid geometry, symmetry and beauty, perspective, riddles and problems, calculus, mathematical logic, friction force and displacement, subatomic particles, and the expansion of the universe. Great mathematical thinkers covered include Napier, Liu Hui, Aryabhata, Galileo, Newton, Russell, Einstein, Riemann, Euclid, Carl Friedrich Gauss, Charles Babbage, Montmort, Wittgenstein, and many more. The book is beautifully illustrated throughout in full color.