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.

    Beginning with the study of DNA in Egyptian mummies in the early 1980s and culminating in the sequencing of the Neanderthal genome in 2010, Neanderthal Man describes the events, intrigues, failures, and triumphs of these scientifically rich years through the lens of the pioneer and inventor of the field of ancient DNA.We learn that Neanderthal genes offer a unique window into the lives of our hominin relatives and may hold the key to unlocking the mystery of why humans survived while Neanderthals went extinct. Drawing on genetic and fossil clues, Pääbo explores what is known about the origin of modern humans and their relationship to the Neanderthals and describes the fierce debate surrounding the nature of the two species’ interactions. His findings have not only redrawn our family tree, but recast the fundamentals of human history—the biological beginnings of fully modern Homo sapiens, the direct ancestors of all people alive today.A riveting story about a visionary researcher and the nature of scientific inquiry, Neanderthal Man offers rich insight into the fundamental question of who we are.

    In addition to surveying the nature and development of Judaism, this Very Short Introduction outlines the basics of practical Judaism -- its festivals, prayers, customs, and various sects. Modern concerns and debates of the Jewish people are also addressed, such as the impact of the Holocaust, the establishment of the State of Israel, the status of women, and medical and commercial ethics. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy.In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

    To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

    Following a brief account of the historical relationship between structuralism and poststructuralism, this Very Short Introduction traces the key arguments that have ledpoststructuralists to challenge traditional theories of language and culture. While the author discusses such well-known figures as Barthes, Foucault, Derrida, and Lacan, she also draws pertinent examples from literature, art, film, and popular culture, unfolding the poststructuralist account ofwhat it means to be a human being.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam

    Based on her work at the Santa Fe Institute and drawing on its interdisciplinary strategies, Mitchell brings clarity to the workings of complexity across a broad range of biological, technological, and social phenomena, seeking out the general principles or laws that apply to all of them. Richly illustrated, Complexity: A Guided Tour--winner of the 2010 Phi Beta Kappa Book Award in Science--offers a wide-ranging overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for its contribution to solving some of the most important scientific questions of our time.

    But how can it be defined? In this highly readable introduction the mysteries of this most elusive of concepts are unraveled, casting a critical light upon the way we live now, from the politicizing of museumculture to the cult of the politically correct. The key postmodernist ideas are explored and challenged, as they figure in the theory, philosophy, politics, ethics and artwork of the period, and it is shown how they have interacted within a postmodernist culture.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    Now, in The Web of Life, he takes yet another giant step forward, offering a brilliant synthesis of such recent scientific breakthroughs as the theory of complexity, Gaia theory, and chaos theory. 25 line drawings.

    Along the way she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how this little symbol holds the biggest idea of all. "Beyond Infinity is a spirited and friendly guide--appealingly down to earth about math that's extremely far out." --Jordan Ellenberg, author of How Not to Be Wrong "Dr. Cheng . . . has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board." --Natalie Angier, New York Times

    Barrow's Pi in the Sky is a profound -- and profoundly different -- exploration of the world of mathematics: where it comes from, what it is, and where it's going to take us if we follow it to the limit in our search for the ultimate meaning of the universe. Barrow begins by investigating whether math is a purely human invention inspired by our practical needs. Or is it something inherent in nature waiting to be discovered?In answering these questions, Barrow provides a bridge between the usually irreconcilable worlds of mathematics and theology. Along the way, he treats us to a history of counting all over the world, from Egyptian hieroglyphics to logical friction, from number mysticism to Marxist mathematics. And he introduces us to a host of peculiar individuals who have thought some of the deepest and strangest thoughts that human minds have ever thought, from Lao-Tse to Robert Pirsig, Charles Darwin, and Umberto Eco. Barrow thus provides the historical framework and the intellectual tools necessary to an understanding of some of today's weightiest mathematical concepts.

    The result is a completely accessible introduction to the main themes of the philosophy of science. Intended for undergraduates and general readers with no prior background in philosophy, Theory and Reality covers logical positivism; the problems of induction and confirmation; Karl Popper's theory of science; Thomas Kuhn and "scientific revolutions"; the views of Imre Lakatos, Larry Laudan, and Paul Feyerabend; and challenges to the field from sociology of science, feminism, and science studies. The book then looks in more detail at some specific problems and theories, including scientific realism, the theory-ladeness of observation, scientific explanation, and Bayesianism. Finally, Godfrey-Smith defends a form of philosophical naturalism as the best way to solve the main problems in the field. Throughout the text he points out connections between philosophical debates and wider discussions about science in recent decades, such as the infamous "science wars." Examples and asides engage the beginning student; a glossary of terms explains key concepts; and suggestions for further reading are included at the end of each chapter. However, this is a textbook that doesn't feel like a textbook because it captures the historical drama of changes in how science has been conceived over the last one hundred years.Like no other text in this field, Theory and Reality combines a survey of recent history of the philosophy of science with current key debates in language that any beginning scholar or critical reader can follow.

    Christopher Hitchens continues to make the case for a splendidly godless universe in this first-ever gathering of the influential voices--past and present--that have shaped his side of the current (and raging) God/no-god debate. With Hitchens as your erudite and witty guide, you'll be led through a wealth of philosophy, literature, and scientific inquiry, including generous portions of the words of Lucretius, Benedict de Spinoza, Charles Darwin, Karl Marx, Mark Twain, George Eliot, Bertrand Russell, Emma Goldman, H. L. Mencken, Albert Einstein, Daniel Dennett, Sam Harris, Richard Dawkins, and many others well-known and lesser known. And they're all set in context and commented upon as only Christopher Hitchens political and literary journalist extraordinaire can.” (Los Angeles Times) Atheist? Believer? Uncertain? No matter: The Portable Atheist will speak to you and engage you every step of the way.

    Yet, the science underpinning this technology is less visible and little understood outside the professional computer science community. As a scientific discipline, computer science stands alongside the likes of molecular biology and cognitive science as one of the most significant new sciences of the post Second World War era.In this Very Short Introduction, Subrata Dasgupta sheds light on these lesser known areas and considers the conceptual basis of computer science. Discussing algorithms, programming, and sequential and parallel processing, he considers emerging modern ideas such as biological computing and cognitive modelling, challenging the idea of computer science as a science of the artificial.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, and enthusiasm to make interesting and challenging topics highly readable.