C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives. At a deeper level, the book is a detailed and subtle exposition of concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself. In response to confusion over the book's theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms.

    This is done in a way that is not only easy to understand, but is actually fun! Professors and engineers, with high school and college students following closely, comprise the largest percentage of our readers. It is a must-have for anyone interested in music, mathematics, physics, engineering, or complex science. Dr. Yoichiro Nambu, 2008 Nobel Prize Winner in Physics, served as a senior adviser to the English version of Who is Fourier? A Mathematical Adventure.

    As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel's proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from this plus this equals this to this plus what equals this? gave birth to a whole new way of perceiving the world. With a historian's narrative authority and a beloved teacher's clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging historical and mathematical journey.

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    Language is informal, examples are vivid and lively, and the perspectivie is fresh. Based on lectures delivered to engineering students, this work will also be valued by scientists, engineers, technicians, businessmen, anyone facing energy challenges of the future.

    In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets.In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    This updated edition included the complete 1968 text plus a new introduction by Maxine Margolis, which discusses the impact of the book and highlights some of the major trends in anthropological theory since its original publication. RAT, as it is affectionately known to three decades of graduate students, comprehensively traces the history of anthropology and anthropological theory, culminating in a strong argument for the use of a scientific, behaviorally-based, etic approach to the understanding of human culture known as cultural materialism. Despite its popularity and influence on anthropological thinking, RAT has never been available in paperback_until now. It is an essential volume for the library of all anthropologists, their graduate students, and other theorists in the social sciences.

    In The Logical Structure of the World, Carnap adopts the position of “methodological solipsism” and shows that it is possible to describe the world from the immediate data of experience. In his Pseudoproblems in Philosophy, he asserts that many philosophical problems are meaningless.

     This graphic novel recounts the spiritual odyssey of philosopher Bertrand Russell. In his agonized search for absolute truth, he crosses paths with thinkers like Gottlob Frege, David Hilbert & Kurt Gödel, & finds a passionate student in Ludwig Wittgenstein. But his most ambitious goal—to establish unshakable logical foundations of mathematics—continues to loom before him. Thru love & hate, peace & war, he persists in the mission threatening to claim both his career & happiness, finally driving him to the brink of insanity. This story is at the same time a historical novel & an accessible explication of some of the biggest ideas of mathematics & modern philosophy. With rich characterizations & atmospheric artwork, it spins the pursuit of such ideas into a satisfying tale. Probing, layered, the book throws light on Russell’s inner struggles while setting them in the context of the timeless questions he tried to answer. At its heart, Logicomix is a story about the conflict between ideal rationality & the flawed fabric of reality.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    As well as looking at logic in theoretical terms the book considers its everyday uses and demonstrates how it has genuine practical applications. It will take you step by step through the most difficult concepts and is packed with exercises to help you consolidate your learning at every stage. Covering everything from syllogistic logic to logical paradoxes and even looking at logic in Alice in Wonderland, this is the only guide you will ever need.

    An extremely clever account.--The New Yorker.

    That’s a mistake, Tim Harford says in The Data Detective. We shouldn’t be suspicious of statistics—we need to understand what they mean and how they can improve our lives: they are, at heart, human behavior seen through the prism of numbers and are often “the only way of grasping much of what is going on around us.” If we can toss aside our fears and learn to approach them clearly—understanding how our own preconceptions lead us astray—statistics can point to ways we can live better and work smarter.As “perhaps the best popular economics writer in the world” (New Statesman), Tim Harford is an expert at taking complicated ideas and untangling them for millions of readers. In The Data Detective, he uses new research in science and psychology to set out ten strategies for using statistics to erase our biases and replace them with new ideas that use virtues like patience, curiosity, and good sense to better understand ourselves and the world. As a result, The Data Detective is a big-idea book about statistics and human behavior that is fresh, unexpected, and insightful.

    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.