Having just completed his masterpiece, The General Theory of Relativity—which provided a brand-new theory of gravity and promised a new perspective on the cosmos as a whole—he set out at once to share his excitement with as wide a public as possible in this popular and accessible book.Here published for the first time as a Penguin Classic, this edition of Relativity features a new introduction by bestselling science author Nigel Calder.

    There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular “Good Math” blog, you’ll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird.Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing.If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark’s book will both entertain and enlighten you.

    It has been widely praised by a generation of users for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

    While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world inwhich we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics andengineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

    But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them.Hidden symmetries were first discovered nearly two hundred years ago by French mathematician �variste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination.The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.

    Coggan's account of the rise of the world economy is accessible and mercifully free of jargon'Sunday TimesMore tracks the development of the world economy, starting with the first obsidian blades that made their way from what is now Turkey to the Iran-Iraq border 7000 years before Christ, and ending with the Sino-American trade war that we are in right now.Taking history in great strides, More illustrates broad changes by examining details from the design of the standard medieval cottage to the stranglehold that Paris's three belt-buckle-making guilds exercised over innovation in the field of holding up trousers. Along the way Coggan reveals that historical economies were far more sophisticated than we might imagine - tied together by webs of credit and financial instruments much like the modern economy.Coggan shows how, at every step of our long journey, it was connections between people - allowing more trade, more specialisation, more ideas and more freedom - that always created the conditions of prosperity.

    From Plato to Christianity, from the Enlightenment to Nietzsche, the Western tradition has been based on arrogant and erroneous beliefs about human beings and their place in the world. Philosophies such as liberalism and Marxism think of humankind as a species whose destiny is to transcend natural limits and conquer the Earth. Even in the present day, despite Darwin's discoveries, nearly all schools of thought take as their starting point the belief that humans are radically different from other animals. John Gray argues that this humanist belief is an illusion. The aim of Straw Dogs is to explore how the world and human life look once humanism has been finally abandoned.Straw Dogs explores philosophical issues such as the nature of the self, free will, morality, progress and the value of truth. Drawing his inspiration from art, poetry, and the frontiers of science as well as philosophy itself, John Gray presents a post-humanist view of the world and of human life. Straw Dogs is an exhilarating, sometimes disturbing book that leads the reader to question their deepest beliefs.

    If reason is so useful, why didn't it also evolve in other animals? If reason is that reliable, why do we produce so much thoroughly reasoned nonsense? In their groundbreaking account of the evolution and workings of reason, Hugo Mercier and Dan Sperber set out to solve this double enigma. Reason, they argue with a compelling mix of real-life and experimental evidence, is not geared to solitary use, to arriving at better beliefs and decisions on our own. What reason does, rather, is help us justify our beliefs and actions to others, convince them through argumentation, and evaluate the justifications and arguments that others address to us.In other words, reason helps humans better exploit their uniquely rich social environment. This interactionist interpretation explains why reason may have evolved and how it fits with other cognitive mechanisms. It makes sense of strengths and weaknesses that have long puzzled philosophers and psychologists--why reason is biased in favor of what we already believe, why it may lead to terrible ideas and yet is indispensable to spreading good ones.Ambitious, provocative, and entertaining, The Enigma of Reason will spark debate among psychologists and philosophers, and make many reasonable people rethink their own thinking.

    We need a brand new way to take it all in. 'Information is Beautiful' transforms the ideas surrounding and swamping us into graphs and maps that anyone can follow at a single glance.

    While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.

    Beginning with: "It was Sappho who first called eros 'bittersweet.' No one who has been in love disputes her. What does the word mean?", Carson examines her subject from numerous points of view and styles, transcending the constraints of the scholarly exercise for an evocative and lyrical meditation in the tradition of William Carlos William's Spring and All and William H. Gass's On Being Blue.

    It is the secret of what makes humans special, hiding in plain sight. Agustin Fuentes argues that your child's finger painting comes essentially from the same place as creativity in hunting and gathering millions of years ago, and throughout history in making war and peace, in intimate relationships, in shaping the planet, in our communities, and in all of art, religion, and even science.It requires imagination and collaboration. Every poet has her muse; every engineer, an architect; every politician, a constituency. The manner of the collaborations varies widely, but successful collaboration is inseparable from imagination, and it brought us everything from knives and hot meals to iPhones and interstellar spacecraft.Weaving fascinating stories of our ancient ancestors' creativity, Fuentes finds the patterns that match modern behavior in humans and animals. This key quality has propelled the evolutionary development of our bodies, minds, and cultures, both for good and for bad. It's not the drive to reproduce; nor competition for mates, or resources, or power; nor our propensity for caring for one another that have separated us out from all other creatures.As Fuentes concludes, to make something lasting and useful today you need to understand the nature of your collaboration with others, what imagination can and can't accomplish, and, finally, just how completely our creativity is responsible for the world we live in. Agustin Fuentes's resounding multimillion-year perspective will inspire readers and spark all kinds of creativity.

    Its greatest detriment to the world has been its unfettered desire to play with and alter them: science for science's sake, as if it offered the only path to knowledge.According to Lehrer, when it comes to the human brain, the world of art unraveled such mysteries long before the neuroscientists: "This book is about artists who anticipated the discoveries of science who discovered truths about the human mind that science is only now discovering." 'Proust Was a Neuroscientist' is a dazzling inquiry into the nature of the mind and of the truths harvested by its first explorers: artists like Walt Whitman, George Eliot, Auguste Escoffier, Marcel Proust, Paul Cozanne, Igor Stravinsky, Gertrude Stein, and Virginia Woolf. What they understood intuitively and expressed through their respective art forms -- the fallibility of memory, the malleability of the brain, the subtleties of vision, and the deep structure of language -- science has only now begun to measure and confirm. Blending biography, criticism, and science writing, Lehrer offers a lucid examination of eight artistic thinkers who lit the path toward a greater understanding of the human mind and a deeper appreciation of the ineffable mystery of life.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    Bayesian statistics is taught in most first-year statistics classes across the nation, but there is one major problem that many students (and others who are interested in the theorem) face. The theorem is not intuitive for most people, and understanding how it works can be a challenge, especially because it is often taught without visual aids. In this guide, we unpack the various components of the theorem and provide a basic overview of how it works - and with illustrations to help. Three scenarios - the flu, breathalyzer tests, and peacekeeping - are used throughout the booklet to teach how problems involving Bayes Theorem can be approached and solved. Over 60 hand-drawn visuals are included throughout to help you work through each problem as you learn by example. The illustrations are simple, hand-drawn, and in black and white. For those interested, we have also included sections typically not found in other beginner guides to Bayes Rule. These include: A short tutorial on how to understand problem scenarios and find P(B), P(A), and P(B|A). For many people, knowing how to approach scenarios and break them apart can be daunting. In this booklet, we provide a quick step-by-step reference on how to confidently understand scenarios.A few examples of how to think like a Bayesian in everyday life. Bayes Rule might seem somewhat abstract, but it can be applied to many areas of life and help you make better decisions. It is a great tool that can help you with critical thinking, problem-solving, and dealing with the gray areas of life. A concise history of Bayes Rule. Bayes Theorem has a fascinating 200+ year history, and we have summed it up for you in this booklet. From its discovery in the 1700’s to its being used to break the German’s Enigma Code during World War 2, its tale is quite phenomenal.Fascinating real-life stories on how Bayes formula is used in everyday life.From search and rescue to spam filtering and driverless cars, Bayes is used in many areas of modern day life. We have summed up 3 examples for you and provided an example of how Bayes could be used.An expanded definitions, notations, and proof section.We have included an expanded definitions and notations sections at the end of the booklet. In this section we define core terms more concretely, and also cover additional terms you might be confused about. A recommended readings section.From The Theory That Would Not Die to a few other books, there are a number of recommendations we have for further reading. Take a look! If you are a visual learner and like to learn by example, this intuitive booklet might be a good fit for you. Bayesian statistics is an incredibly fascinating topic and likely touches your life every single day. It is a very important tool that is used in data analysis throughout a wide-range of industries - so take an easy dive into the theorem for yourself with a visual approach!If you are looking for a short beginners guide packed with visual examples, this booklet is for you.