With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

    He is beloved around the world for his pioneering detective fiction, tales of horror, and haunting, atmospheric verse. But what if there was another side to the man who wrote "The Raven" and "The Fall of the House of Usher"?In The Reason for the Darkness of the Night, John Tresch offers a bold new biography of a writer whose short, tortured life continues to fascinate. Shining a spotlight on an era when the lines separating entertainment, speculation, and scientific inquiry were blurred, Tresch reveals Poe's obsession with science and lifelong ambition to advance and question human knowledge. Even as he composed dazzling works of fiction, he remained an avid and often combative commentator on new discoveries, publishing and hustling in literary scenes that also hosted the era's most prominent scientists, semi-scientists, and pseudo-intellectual rogues. As one newspaper put it, "Mr. Poe is not merely a man of science--not merely a poet--not merely a man of letters. He is all combined; and perhaps he is something more."Taking us through his early training in mathematics and engineering at West Point and the tumultuous years that followed, Tresch shows that Poe lived, thought, and suffered surrounded by science--and that many of his most renowned and imaginative works can best be understood in its company. He cast doubt on perceived certainties even as he hungered for knowledge, and at the end of his life delivered a mind-bending lecture on the origins of the universe that would win the admiration of twentieth-century physicists. Pursuing extraordinary conjectures and a unique aesthetic vision, he remained a figure of explosive contradiction: he gleefully exposed the hoaxes of the era's scientific fraudsters even as he perpetrated hoaxes himself.Tracing Poe's hard and brilliant journey, The Reason for the Darkness of the Night is an essential new portrait of a writer whose life is synonymous with mystery and imagination--and an entertaining, erudite tour of the world of American science just as it was beginning to come into its own.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    He manned the barricades against superstition and pseudoscience, and pressed for a scientifically literate populace years before science had been deemed worthy of common study. A friend of Charles Dickens and an inspiration to Thomas Edison, the deeply religious Faraday sought no financial gain from his discoveries, content to reveal God's presence through the design of nature. Faraday speaks to us today through the prose of his letters and journals. In The Electric Life of Michael Faraday, Alan Hirshfeld presents an intimate and memorable portrait of an icon of science, making Faraday's most significant discoveries about electricity and magnetism readily understandable, and immortalizing his momentous contributions to the modern world.

    Though most people know of him only for the famous Pythagorean Theorem (a2 +b2=c2), in fact the pillars of our scientific tradition—belief that the universe is rational, that there is unity to all things, and that numbers and mathematics are a powerful guide to truth about nature and the cosmos—hark back to the convictions of this legendary sixth-century B.C. scholar.Born around 570 B.C. on the cultured Aegean island of Samos, Pythagoras (according to ancient tales) studied with the sage Thales nearby at Miletus, and with priests and scribes in Egypt and Babylon. Eventually he founded his own school at Croton in southern Italy, where he and his followers began to unravel the surprising deep truths concealed behind such ordinary tasks as tuning a lyre. While considering why some string lengths produced beautiful sounds and others discordant ones, they uncovered the ratios of musical harmony, and recognized that hidden behind the confusion and complexity of nature are patterns and orderly relationships. They had surprised the Creator at his drafting board and had glimpsed the mind of God! Some of them later would also find something darker in numbers and nature: irrationality, a revelation so unsettling and subversive that it may have contributed to the destruction of their brotherhood.Praised for her ability to illuminate complex subjects, Kitty Ferguson brilliantly evokes the archaic world of Pythagoras, showing how ideas spread in antiquity, chronicling the influence he and his followers have had on so many extraordinary people in the history of Western thought and science, and bringing a poignant human saga to readers who are daily reminded that harmony and chaos can and do coexist.

    Written By Two Of Today'S Most Respected Computer Science Educators, Nell Dale And John Lewis, The Text Provides A Broad Overview Of The Many Aspects Of The Discipline From A Generic View Point. Separate Program Language Chapters Are Available As Bundle Items For Those Instructors Who Would Like To Explore A Particular Programming Language With Their Students. The Many Layers Of Computing Are Thoroughly Explained Beginning With The Information Layer, Working Through The Hardware, Programming, Operating Systems, Application, And Communication Layers, And Ending With A Discussion On The Limitations Of Computing. Perfect For Introductory Computing And Computer Science Courses, Computer Science Illuminated, Third Edition's Thorough Presentation Of Computing Systems Provides Computer Science Majors With A Solid Foundation For Further Study, And Offers Non-Majors A Comprehensive And Complete Introduction To Computing.

    40 illustrations throughout.

    The salient features of the book are as follows: It exactly covers the prescribed syllabus. Nothing undesirable has been included and nothing essential has been left. Its approach is explanatory and language is lucid and communicable. The exposition of the subject matter is systematic and the students are better prepared to solve the problems. All fundamentals of the included topics are explained with a micro-analysis. Sufficient number of solved examples have been given to let the students understand the various skills necessary to solve the problems. These examples are well-graded. Unsolved exercises of multi-varieties have been given in a well-graded style. Attempting those on his own, will enable a student to create confidence and independence in him/her regarding the understanding of the subject. Daily life problems and practical applications have been incorporated in the body of the text. A large number of attractive and accurate figures have been drawn which enable a student to grasp the subject in an easier way. All the answers have been checked and verified. About The Author: N.P. Bali is a prolific author of over 100 books for degree and engineering students. He has been writing books for more than forty years. His books on the following topics are well known for their easy comprehension and lucid presentation: Algebra, Trigonometry, Differential Calculus, Integral Calculus, Real Analysis, Co-ordinate Geometry, Statics, Dynamics etc. Dr. Manish Goyal has been associated with

    The remaining lectures build on that idea, examining the possibility of building a relativistic quantum theory on curved surfaces or flat surfaces.

    Outlining the fascinating history of how superconductivity was discovered, and the race to understand its many mysterious and counter-intuitive phenomena, Stephen Blundell explains in accessible terms the theories that have been developed to explain it, and how they have influenced other areas of science, including the Higgs boson of particle physics and ideas about the early Universe. This Very Short Introduction examines the many strange phenomena observed in superconducting materials, the latest developments in high-temperature superconductivity, the potential of superconductivity to revolutionize the physics and technology of the future, and much more. It is a fascinating detective story, offering invaluable insights into some of the deepest and most beautiful ideas in physics today.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.

    Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science.Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.

    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.

    Historical records are first found in Babylon and Egypt, and after two millennia the arithmetical astronomy of the Babylonians merged with the Greek geometrical approach to culminate in the Almagest of Ptolemy. This legacy was transmitted to the Latin West via Islam, and led to Copernicus's claim that the Earth is in motion. In justifying this Kepler converted astronomy into a branch of dynamics, leading to Newton's universal law of gravity. The book concludes with eighteenth- and nineteenth-century applications of Newton's law, and the first explorations of the universe of stars.

    Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?Table of ContentsPreface 1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins Part One: Zooming Out 2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space? 3 Our Place in TimeWhere Did Our Solar System Come From? • Where Did theGalaxies Come From? • Where Did the Mysterious MicrowavesCome From? • Where Did the Atoms Come From? 4 Our Universe by NumbersWanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From? 5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation 6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup Part Two: Zooming In 7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion 8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words? Part Three: Stepping Back 9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality 10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure? 11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You? 12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse 13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant? Acknowledgments Suggestions for Further Reading Index

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.