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.

    The work is powerful and has established a passionate following as well as harsh critics.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    Cosmic Universe and Human History, microcosm and macrocosm, inorganic and living matter coexist and form a unique unity manifested in multiple forms. The Physical and the Mental constitute the form and the content of the World. The world does not consist of subjects and objects, the “subject” and the “object” are metaphysical abstractions of the single and indivisible Wholeness. Man’s finite knowledge separates the Whole into parts and studies fragmentarily the beings. The Wholeness is manifested in multiple forms and each form encapsulates the Wholeness. The rational explanation of the excerpts and the intuitive apprehension of the Wholeness are required to combine and create the open thought and the holistic knowledge. This means that the measurement should be defined by the ''measure'', but the responsibility for determining the ''measure'' depends on the man. This requires that man overcomes the anthropocentric arrogance and the narcissistic selfishness and he joins the Cosmic World in a friendly and creative manner.

    Unique in basing relativity on the Principle of Equivalence of Gravitation and Inertia over Riemannian geometry, this book explores relativity experiments and observational cosmology to provide a sound foundation upon which analyses can be made. Covering special and general relativity, tensor analysis, gravitation, curvature, and more, this book provides an engaging, insightful introduction to the forces that shape the universe.

    

    This ideal guide shows us how mathematics can illuminate the human condition.

    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.

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

    In Peter Woit's view, superstring theory is just such an idea. In Not Even Wrong , he shows that what many physicists call superstring "theory" is not a theory at all. It makes no predictions, even wrong ones, and this very lack of falsifiability is what has allowed the subject to survive and flourish. Not Even Wrong explains why the mathematical conditions for progress in physics are entirely absent from superstring theory today and shows that judgments about scientific statements, which should be based on the logical consistency of argument and experimental evidence, are instead based on the eminence of those claiming to know the truth. In the face of many books from enthusiasts for string theory, this book presents the other side of the story.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    Readers will progress from building a basic physics engine to creating intelligent moving objects and complex systems, setting the foundation for further experiments in generative design. Subjects covered include forces, trigonometry, fractals, cellular automata, self-organization, and genetic algorithms. The book's examples are written in Processing, an open-source language and development environment built on top of the Java programming language. On the book's website (http://www.natureofcode.com), the examples run in the browser via Processing's JavaScript mode.

    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.

    Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.