Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    Organized around the central concept of a vector space, the book includes numerous physical applications in the body of the text as well as many problems of a physical nature. It is also one of the purposes of this book to introduce the physicist to the language and style of mathematics as well as the content of those particular subjects with contemporary relevance in physics.Chapters 1 and 2 are devoted to the mathematics of classical physics. Chapters 3, 4 and 5 — the backbone of the book — cover the theory of vector spaces. Chapter 6 covers analytic function theory. In chapters 7, 8, and 9 the authors take up several important techniques of theoretical physics — the Green's function method of solving differential and partial differential equations, and the theory of integral equations. Chapter 10 introduces the theory of groups. The authors have included a large selection of problems at the end of each chapter, some illustrating or extending mathematical points, others stressing physical application of techniques developed in the text.Essentially self-contained, the book assumes only the standard undergraduate preparation in physics and mathematics, i.e. intermediate mechanics, electricity and magnetism, introductory quantum mechanics, advanced calculus and differential equations. The text may be easily adapted for a one-semester course at the graduate or advanced undergraduate level.

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    It also explores more advanced topics, such as normal modes, the Lagrangian method, gyroscopic motion, fictitious forces, 4-vectors, and general relativity. It contains more than 250 problems with detailed solutions so students can easily check their understanding of the topic. There are also over 350 unworked exercises which are ideal for homework assignments. Password protected solutions are available to instructors at www.cambridge.org/9780521876223. The vast number of problems alone makes it an ideal supplementary text for all levels of undergraduate physics courses in classical mechanics. Remarks are scattered throughout the text, discussing issues that are often glossed over in other textbooks, and it is thoroughly illustrated with more than 600 figures to help demonstrate key concepts.

    Contributors include Steven Weinberg, Peter Galison, John Maynard Smith, and Frank Wilczek.

    Like artists and poets, they are free spirits who resist the restrictions their cultures impose on them. In their pursuit of Nature’s truths, they are guided as much by imagination as by reason, and their greatest theories have the uniqueness and beauty of great works of art.Dyson argues that the best way to understand science is by understanding those who practice it. He tells stories of scientists at work, ranging from Isaac Newton’s absorption in physics, alchemy, theology, and politics, to Ernest Rutherford’s discovery of the structure of the atom, to Albert Einstein’s stubborn hostility to the idea of black holes. His descriptions of brilliant physicists like Edward Teller and Richard Feynman are enlivened by his own reminiscences of them. He looks with a skeptical eye at fashionable scientific fads and fantasies, and speculates on the future of climate prediction, genetic engineering, the colonization of space, and the possibility that paranormal phenomena may exist yet not be scientifically verifiable.Dyson also looks beyond particular scientific questions to reflect on broader philosophical issues, such as the limits of reductionism, the morality of strategic bombing and nuclear weapons, the preservation of the environment, and the relationship between science and religion. These essays, by a distinguished physicist who is also a lovely writer, offer informed insights into the history of science and fresh perspectives on contentious current debates about science, ethics, and faith.

    But a dispute over its discovery sowed the seeds of discontent between two of the greatest scientific giants of all time - Sir Isaac Newton and Gottfried Wilhelm Leibniz." "Today Newton and Leibniz are generally considered the twin independent inventors of calculus. They are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret." This long and bitter dispute has been swept under the carpet by historians - perhaps because it reveals Newton and Leibniz in their worst light - but The Calculus Wars tells the full story in narrative form for the first time. This history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

    Bolles has scoured the literature of science to build a treasury that is accessible and riveting, and therefore appealing to readers unfamiliar with science, yet erudite enough for the scientifically initiated to enjoy.

    This work includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.

    Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics -- the universal language of science -- keep the masterpieces of the subject hidden behind a veil?"The Universe in Zero Words" tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society -- from the elementary (1+1 = 2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E = mc^2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called a "popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.(From the jacket copy.)Note: The Princeton University Press version (black cover) is for sale in the English-speaking world outside Australia. The Newsouth Press version (blue cover) is for sale in Australia. The two versions are identical except for the covers.

    Sweeping through the centuries from ancient Babylon right up to the latest hi-tech experiments in genetics and particle physics, Fara's book also ranges internationally, challenging notions of European superiority by emphasizing the importance of scientific projects based around the world, including revealing discussions of China and the Islamic Empire alongside the more familiar stories about Copernicus's sun-centered astronomy, Newton's gravity, and Darwin's theory of evolution.We see for instance how Muslim leaders encouraged science by building massive libraries, hospitals, and astronomical observatories and we rediscover the significance of medieval Europe--long overlooked--where, surprisingly, religious institutions ensured science's survival, as the learning preserved in monasteries was subsequently developed in new and unique institutions: universities. Instead of focussing on esoteric experiments and abstract theories, she explains how science belongs to the practical world of war, politics, and business. And rather than glorifying scientists as idealized heroes, she tells true stories about real people--men (and some women) who needed to earn their living, who made mistakes, and who trampled down their rivals.

     Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before He made the world, he wastold: Preparing hell for people who ask questions like that. A Brief History of the Paradox takes a close look at questions like that and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with suchthinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken towardthese puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor.

    But such is Stephen Jay Gould's command of paleontology and evolutionary theory, and his gift for brilliant explication, that he has brought dust and dead bones to life, and developed an immense following for the seeming arcana of this field.In Time's Arrow, Time's Cycle his subject is nothing less than geology's signal contribution to human thought--the discovery of "deep time," the vastness of earth's history, a history so ancient that we can comprehend it only as metaphor. He follows a single thread through three documents that mark the transition in our thinking from thousands to billions of years: Thomas Burnet's four-volume Sacred Theory of the Earth (1680-1690), James Hutton's Theory of the Earth (1795), and Charles Lyell's three-volume Principles of Geology (1830-1833).Gould's major theme is the role of metaphor in the formulation and testing of scientific theories--in this case the insight provided by the oldest traditional dichotomy of Judeo-Christian thought: the directionality of time's arrow or the immanence of time's cycle. Gould follows these metaphors through these three great documents and shows how their influence, more than the empirical observation of rocks in the field, provoked the supposed discovery of deep time by Hutton and Lyell. Gould breaks through the traditional "cardboard" history of geological textbooks (the progressive march to truth inspired by more and better observations) by showing that Burnet, the villain of conventional accounts, was a rationalist (not a theologically driven miracle-monger) whose rich reconstruction of earth history emphasized the need for both time's arrow (narrative history) and time's cycle (immanent laws), while Hutton and Lyell, our traditional heroes, denied the richness of history by their exclusive focus upon time's Arrow.

    The fundamental questions are answered, leaving only the details to be filled in. In this book, Dr Rupert Sheldrake, one of the world's most innovative scientists, shows that science is being constricted by assumptions that have hardened into dogmas. The 'scientific worldview' has become a belief system. All reality is material or physical. The world is a machine, made up of dead matter. Nature is purposeless. Consciousness is nothing but the physical activity of the brain. Free will is an illusion. God exists only as an idea in human minds, imprisoned within our skulls. Sheldrake examines these dogmas scientifically, and shows persuasively that science would be better off without them: freer, more interesting, and more fun.In The God Delusion Richard Dawkins used science to bash God, but here Rupert Sheldrake shows that Dawkins' understanding of what science can do is old-fashioned and itself a delusion.

    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.